This article provides an overview of laser-based absorption spectroscopy applications and discusses the parameter space and requirements of laser systems for each of these applications, with a special emphasis on frequency comb systems. We walk the reader through the basics of laser absorption spectroscopy, review common line-broadening mechanisms as fundamental challenges to precision spectroscopy, look into established solutions, introduce frequency-comb-based absorption spectroscopy, and suggest a novel approach to broadband precision spectroscopy in the mid-infrared spectral region based on a combination of broadband high-power ultra-stable optical frequency combs, crystalline supermirror technology, and an instrumental line-shape-free measurement technique. We conclude after an introduction of noise sources and their implications for precision measurements with an in-depth discussion and overview of the current state-of-the-art laser and optical parametric frequency conversion technologies.

Gas sensing, remote detection, and stand-off molecular spectroscopy are indispensable tools for multiple applications. They can be used to target objects with distant or unknown locations, objects inaccessible for direct probing, or objects that are dangerous, toxic, or contaminate the measurement equipment. Possible applications can be loosely categorized into five branches: (i) fundamental research, including studying molecular structures and challenging commonly accepted physical models; (ii) space studies, dedicated to the mapping of the universe, the evolution of stellar and planetary systems, the search for potentially inhabited planets, and the chemistry of interstellar space; (iii) environmental sensing, spanning from greenhouse gases (GHGs), pollution, and particulate matter monitoring to the optimization of agricultural processes; (iv) fabrication and industrial monitoring, including not only control over combustion processes and exhaustion products but also the design of new materials and the quality control of various chemicals; (v) medical applications, such as non-invasive diagnostics, fundamental protein research, and the detection of health hazard molecules.

Of course, multiple applications fall into several categories simultaneously. For instance, particulate matter or aerosols are essential climate variables that have also been observed in space in the form of cosmic dust and are known to have a significant effect on human health. Spectroscopic studies have revealed the chemical composition and origins of aerosols and have also provided an understanding of their formation processes via the detection of short-lived intermediates. Other molecules, substances, and chemical reactions could also be of interest for different applications.

In this article, our goal is to provide an overview of possible applications of molecular spectroscopy (Fig. 1). We introduce various application criteria (resolution, wavelength, bandwidth, power, and other possible experimental conditions), discuss line broadening and saturation effects, and give an overview of appropriate spectroscopic instruments and light sources suitable for the aforementioned applications. We acknowledge that there are additional specialized applications and advancements that are not covered in this work. We apologize for any omissions and encourage readers to explore further literature and research in order to gain a complete understanding of the diverse and expanding field of molecular spectroscopy.

FIG. 1.

(a) An overview of various spectroscopic experiments. The central wavelength of each experiment is given on the x-axis, and the relative resolution (used here as the inverse of the resolving power) is given on the y-axis. We selected the spectroscopic experiments to showcase measurements in laboratories, outside of a laboratory environment, and in space at various center wavelengths. The plot excludes many similar works with comparable resolution and detection bandwidth, as this paper aims to showcase diverse spectroscopic applications rather than provide a comprehensive review. The black solid lines show the approximate resolution and spectral range of space-borne spectroscopic apparatus and ground-based telescopes. Black rings represent space- and balloon-borne missions using active light sources for atmospheric analysis. Purple symbols represent measurements of broadband absorption features (e), intrinsic to large molecules,1,2 aerosols,3,4 and powders.5 Green represents experiments in which individual lines within absorption bands were resolved (d),6–11 blue represents experiments in which the line shapes of individual absorption features were resolved (c),12–16 and orange represents experiments in which high-precision saturation spectroscopy allowed sub-Doppler resolution and the measurement of Lamb-dip features (b).17–24 Diamond symbols represent dual-comb spectroscopy, and horizontal lines show the spectral bandwidths in which the experiments were performed. Panel (f) shows the atmospheric absorption due to water vapor, carbon dioxide, ozone, and atmospheric transparency windows. The color blocks correspond to fundamental mid-IR and long-wave infrared (LWIR) stretching and bending molecular absorption bands and their near-IR overtones. The yellow shaded area shows solar emission, and the pink shaded area represents black body emission at different temperatures (T = 310 K and T = 210 K). ARIEL (Atmospheric Remote-sensing Infrared Exoplanet Large-survey), CRIRES (CRyogenic high-resolution InfraRed Echelle Spectrograph), ESPRESSO (Echelle SPectrograph for Rocky Exoplanet and Stable Spectroscopic Observations), FINESSE (Fast Infrared Exoplanet Spectroscopy Survey Explorer), FORUM (Far-infrared-Outgoing-Radiation Understanding and Monitoring), GAIA (Global Astrometric Interferometer for Astrophysics), HARPS (High Accuracy Radial velocity Planet Searcher), IASI (Infrared Atmospheric Sounding Interferometer), JWST (James Webb Space Telescope), MERLIN (Methane Remote Sensing LIDAR Mission), SAM (Sample Analyst at Mars), SPIRALE (SPectromètre Infra Rouge d’Absorption à 6 diodes Lasers Embarquées).

FIG. 1.

(a) An overview of various spectroscopic experiments. The central wavelength of each experiment is given on the x-axis, and the relative resolution (used here as the inverse of the resolving power) is given on the y-axis. We selected the spectroscopic experiments to showcase measurements in laboratories, outside of a laboratory environment, and in space at various center wavelengths. The plot excludes many similar works with comparable resolution and detection bandwidth, as this paper aims to showcase diverse spectroscopic applications rather than provide a comprehensive review. The black solid lines show the approximate resolution and spectral range of space-borne spectroscopic apparatus and ground-based telescopes. Black rings represent space- and balloon-borne missions using active light sources for atmospheric analysis. Purple symbols represent measurements of broadband absorption features (e), intrinsic to large molecules,1,2 aerosols,3,4 and powders.5 Green represents experiments in which individual lines within absorption bands were resolved (d),6–11 blue represents experiments in which the line shapes of individual absorption features were resolved (c),12–16 and orange represents experiments in which high-precision saturation spectroscopy allowed sub-Doppler resolution and the measurement of Lamb-dip features (b).17–24 Diamond symbols represent dual-comb spectroscopy, and horizontal lines show the spectral bandwidths in which the experiments were performed. Panel (f) shows the atmospheric absorption due to water vapor, carbon dioxide, ozone, and atmospheric transparency windows. The color blocks correspond to fundamental mid-IR and long-wave infrared (LWIR) stretching and bending molecular absorption bands and their near-IR overtones. The yellow shaded area shows solar emission, and the pink shaded area represents black body emission at different temperatures (T = 310 K and T = 210 K). ARIEL (Atmospheric Remote-sensing Infrared Exoplanet Large-survey), CRIRES (CRyogenic high-resolution InfraRed Echelle Spectrograph), ESPRESSO (Echelle SPectrograph for Rocky Exoplanet and Stable Spectroscopic Observations), FINESSE (Fast Infrared Exoplanet Spectroscopy Survey Explorer), FORUM (Far-infrared-Outgoing-Radiation Understanding and Monitoring), GAIA (Global Astrometric Interferometer for Astrophysics), HARPS (High Accuracy Radial velocity Planet Searcher), IASI (Infrared Atmospheric Sounding Interferometer), JWST (James Webb Space Telescope), MERLIN (Methane Remote Sensing LIDAR Mission), SAM (Sample Analyst at Mars), SPIRALE (SPectromètre Infra Rouge d’Absorption à 6 diodes Lasers Embarquées).

Close modal

Experimentally measured spectra of unknown samples are typically fitted using calculated spectra from suitable reference data with the positions, shapes, and intensities of the individual absorption lines taken into account. The difference between the fit and experimental data is then minimized to determine the sample composition, temperature, and concentrations. Experimental errors and sources of measurement uncertainty have a great impact on the determined experimental values. Likewise, uncertainties in the model parameters, overlapping, and crosstalk of the absorption features of different species, as well as the temporal and spatial integration over the line of sight, often additionally complicate accurate retrieval.

The experimental data on molecular absorption required to build up a spectral model are often scattered in the literature and lack consistency and a unified format. Therefore, there is a need for the systematization and unification of measured values into parameterized databases. There are a number of spectroscopic databases (see Fig. 2), containing line-parameter lists, cross-sections, aerosol properties, ionization potential data, and collisional data, that are available online and can be freely accessed.

FIG. 2.

A map of spectroscopic databases organized by their application space and species of interest. The vertical axis represents the size of the species, from atoms and ions through few-atom molecules and large molecules to aerosols, liquids, and solids. The horizontal axis represents different categories of applications. Green boxes correspond to computational databases, and yellow boxes are species-specific. AIRSpec (Aerosol InfraRed Spectroscopy analysis),54 ASD NIST (NIST Atomic Spectra Database),36 BASECOL (Ro-Vibrational Collisional Excitation Database and Utilities),55 CDMS (Cologne Database for Molecular Spectroscopy),35 CDSD (Carbon Dioxide Spectroscopic Database),30,31 CHIANTI (An Atomic Database for Spectroscopic Diagnostics of Astrophysical Plasmas),56 D. aerosol S. for Cosmic Dust (Database of Aerosol Spectra for Cosmic Dust),57 Deep4Chem,58 Diatom. MSD (NIST Diatomic Molecular Spectral Database),59 ECOSTRESS,60 EM2C (Énergetique Moleculaire et Macroscopique, Combustion),33 ExoMol, (cross sections and k-tables for molecules of interest in high-temperature exoplanet atmospheres)61,62 FPbase (Fluorescent Protein Database),63 GEISA (Gestion et Etude des Informations Spectroscopiques Atmosphériques),27 HITRAN (HIgh-resolution TRANsmission molecular absorption),25 LAMDA, (Leiden Atomic and Molecular Database,64 MARVEL (Measured Active Rotational–Vibrational Energy Levels),42 Mineral Spectroscopy Server,65 MSD NIST (NIST Mass Spectrometry Data Center),66 PNNL IARPA (Pacific Northwest National Laboratory and Intelligence Advanced Research Projects Activity),67 PNNL SERDP (PNNL Strategic Environmental Research and Development Program),68 SDBC (Spectral Database for Organic Compounds),69 SESAM (SpEctroScopy of Atoms and Molecules),70 S&MPO (Spectroscopy and Molecular Properties of Ozone),71 Spectra (Spectroscopy of Atmospheric Gases),72 Spectr-W3,73 SSHADE (Solid Spectroscopy Hosting Architecture of Databases and Expertise),74 TheoReTS (Theoretical Reims-Tomsk Spectra Database),75 TIPbase (ine-structure atomic data computed for ions of astrophysical interest),52 VALD3 (Vienna Atomic Line Database),76 VAMDC (Vienna Atom and Molecular Data Center),28,29 VPL MSD (VPL Molecular Spectroscopy Database).77 

FIG. 2.

A map of spectroscopic databases organized by their application space and species of interest. The vertical axis represents the size of the species, from atoms and ions through few-atom molecules and large molecules to aerosols, liquids, and solids. The horizontal axis represents different categories of applications. Green boxes correspond to computational databases, and yellow boxes are species-specific. AIRSpec (Aerosol InfraRed Spectroscopy analysis),54 ASD NIST (NIST Atomic Spectra Database),36 BASECOL (Ro-Vibrational Collisional Excitation Database and Utilities),55 CDMS (Cologne Database for Molecular Spectroscopy),35 CDSD (Carbon Dioxide Spectroscopic Database),30,31 CHIANTI (An Atomic Database for Spectroscopic Diagnostics of Astrophysical Plasmas),56 D. aerosol S. for Cosmic Dust (Database of Aerosol Spectra for Cosmic Dust),57 Deep4Chem,58 Diatom. MSD (NIST Diatomic Molecular Spectral Database),59 ECOSTRESS,60 EM2C (Énergetique Moleculaire et Macroscopique, Combustion),33 ExoMol, (cross sections and k-tables for molecules of interest in high-temperature exoplanet atmospheres)61,62 FPbase (Fluorescent Protein Database),63 GEISA (Gestion et Etude des Informations Spectroscopiques Atmosphériques),27 HITRAN (HIgh-resolution TRANsmission molecular absorption),25 LAMDA, (Leiden Atomic and Molecular Database,64 MARVEL (Measured Active Rotational–Vibrational Energy Levels),42 Mineral Spectroscopy Server,65 MSD NIST (NIST Mass Spectrometry Data Center),66 PNNL IARPA (Pacific Northwest National Laboratory and Intelligence Advanced Research Projects Activity),67 PNNL SERDP (PNNL Strategic Environmental Research and Development Program),68 SDBC (Spectral Database for Organic Compounds),69 SESAM (SpEctroScopy of Atoms and Molecules),70 S&MPO (Spectroscopy and Molecular Properties of Ozone),71 Spectra (Spectroscopy of Atmospheric Gases),72 Spectr-W3,73 SSHADE (Solid Spectroscopy Hosting Architecture of Databases and Expertise),74 TheoReTS (Theoretical Reims-Tomsk Spectra Database),75 TIPbase (ine-structure atomic data computed for ions of astrophysical interest),52 VALD3 (Vienna Atomic Line Database),76 VAMDC (Vienna Atom and Molecular Data Center),28,29 VPL MSD (VPL Molecular Spectroscopy Database).77 

Close modal

Some such databases, such as HITRAN (HIgh-resolution TRANsmission molecular absorption)25 and GEISA (Gestion et Etude des Informations Spectroscopiques Atmosphériques),26,27 are generic and provide not only parameterized line lists of small molecules (2–6 atoms) but also the absorption cross-sections of larger molecules and even aerosols formed with different condensation nuclei and solvents. The Vienna Atom and Molecular Data Center (VAMDC Consortium)28,29 provides a purely theory-based complete list of transitions complementary to HITRAN (including CF4, SF6, C2H4, and CH4).

Other databases are molecule-specific, such as the Carbon Dioxide Spectroscopic Database (CDSD)30,31 and S&MPO, which specialize in ozone,32 while others are application-specific, such as EM2C,33 which contains information on the hot bands of combustion-relevant molecules. Others focus on a particular spectral region, like the SPEX-tool for the analysis of x-ray spectra,34 the Cologne Database for Molecular Spectroscopy (CDMS),35 which contains radio-frequency, microwave, and far-IR rotational molecular spectra (λ > 16.5 μm), and molecular spectroscopy data provided by the National Institute of Standards and Technology (NIST), which consists of microwave spectra for 1-, 2-, and 3-atom species.36 

When comparing experiments and databases, the term spectral resolving power or resolution comes up. The spectral resolving power of a spectrometer is defined by37 
R = | λ / Δ λ | = | ν / Δ ν | ,
(1)
where λ is the wavelength, Δλ is the minimum distinguishable wavelength difference, and ν and Δν label optical frequencies and the minimum distinguishable frequency difference, respectively. The term “resolution” is frequently used by astronomers to refer to its resolving power.

In Secs. I A–I C, we aim to give a brief overview of the relevant topics and results, followed by a short paragraph listing some of the relevant databases in each area of research.

The development of modern physics, be it the Standard Model (SM), quantum mechanics (QM), or quantum electrodynamics (QED), was made possible by continuous improvement in the precision of metrology, particularly in the field of spectroscopy. This progress revealed the structures of atoms and molecules and their interactions with external fields.

Precision spectroscopy provides an opportunity to experimentally test the symmetrization postulate of quantum mechanics, which predicts that certain rotational quantum states in small molecules, such as O2 and CO2, are prohibited.38 Furthermore, a comparison of the experimentally measured electronic and rovibrational spectra of H2, HD, HD+, and D2 with ab initio calculations based on QED could indicate the presence of a fifth force or extra dimensions as possible explanations for the deviation of measured inter-nuclear distances from predicted values.38,39

Ultracold weakly bound molecules (Yb2, Sr2, and Hg2) with narrow optical transitions and without hyperfine structure can be used as a testing ground for the search for deviations from Newtonian gravity.40 These effects are expected to occur at micrometer-length scales and below and are expected to lead to perturbations of several tens of kHz in energy potentials.40 

The measurement of small frequency perturbations and absorption cross-sections of selection-rule forbidden transitions benefits from high-power ultra-stable laser sources, high-resolution detection schemes, and the possibility of overcoming absorption-line shifts and line-broadening caused by the movement and collisions of particles. Cooling molecules down to temperatures of several mK allows for a reduction in the effects of Doppler-broadening and molecular collisions but requires a complex setup. An alternative approach for precise frequency measurements is saturation spectroscopy, described in detail in Secs. II B 6 and III. A depletion of the ground level of the transition of interest permits Doppler-free spectroscopy but requires high laser power. The necessary average power for saturation (Psat) of rovibrational transitions scales approximately as λ−3 and depends on the strength of the absorption. Naturally, Psat is higher for overtones than for fundamental transitions. However, some technological limitations (which will be discussed in Sec. V) make overtone detection more convenient and accessible.

Saturation spectroscopy studies conducted in the mid-IR21,41 and long-wave infrared (LWIR)22 spectral ranges rely on continuous wave (CW)-laser sources along with moderate-finesse enhancement cavities and report MHz precision (R ≈ 108). In the near-IR, saturation spectroscopy in ortho- and para-acetylene was demonstrated at 1380 nm using an optical frequency comb (OFC) in combination with cavity ring-down spectroscopy, recording a resolution R of 2 × 109 with an accuracy of 3–13 kHz. This experiment was used to test a high-precision database of molecular transitions, MARVEL (Measured Active Rotational–Vibrational Energy Levels),42 based on ab initio calculations.19 Frequency-based Lamb-dip spectroscopy based on an OFC-controlled CW-laser and a high finesse cavity at 1.57 µm was used to measure transitions in the second overtone of CO with a standard uncertainty below 500 Hz, corresponding to a relative uncertainty below 3 × 10−12. This work revealed a collision shift of the Lamb-dip, which is subject to further studies.24 

Physical models, including the SM and QED, include sets of coupling coefficients describing interaction strengths, which are known as fundamental constants. Fundamental constants need to be measured experimentally and cannot be predicted by the theory itself. Observing a temporal variation or a space-time dependence of the fundamental constants would require the introduction of another force in addition to the known forces of interaction (the electromagnetic, gravitational, strong, and weak nuclear forces) included in the SM. Research is currently particularly focused on the fine-structure constant α, which determines the strength of light–matter interactions, and the dimensionless ratio of proton to electron masses, μ = mp/me, as these are sensitive to time variations and can potentially be probed by precision spectroscopy.43 

The search for temporal variations of these two constants is conducted on time scales similar to the age of the universe by registering redshifts of molecular absorption lines with high-precision ground-based space telescopes and spectrographs. The spectrographs are calibrated to absolute frequency standards to allow for comparison with laboratory experiments. Several transitions in various molecules can be chosen for such tests, taking into account their prevalence in the universe, the presence of dipole-allowed transitions coinciding with the Earth’s windows of atmospheric transparency, and the convenience of detection. In fact, an analysis of 293 absorption systems from metal atoms, measured with lamp-calibrated Fourier-transform infrared (FTIR) spectrometers, led to the intriguing conclusion that there is a spatial variation in α across the sky.44 

This result was challenged with the new multi-purpose spectroscopic tool ESPRESSO (Echelle SPectrograph for Rocky Exoplanet and Stable Spectroscopic Observations) installed at the Very Large Telescope (VLT) in Chile. In ESPRESSO, the light collected by a 16-m equivalent telescope is guided by optical fibers into a volume-phase grating-based spectrometer with a resolution of 70 000–190 000 in the spectral range of 379.2–788.7 nm, depending on the operating mode.45 Each fiber can be attached to a hole in a spatial mask, allowing resolution of the spectra of individual stellar objects. The spectrometer is placed in a sealed vacuum chamber, temperature stabilized, and wavelength-calibrated with an OFC based on a femtosecond laser, which has a repetition rate of 250 MHz and is frequency-stabilized to an atomic clock. The OFC spectrum spans 57% of ESPRESSO’s spectral range.46 Since ESPRESSO is not able to resolve individual comb lines at a 250-MHz repetition rate, a Fabry–Pérot interferometer is used to increase the spectral spacing between individual comb lines to 18 GHz. The analysis of the data from ESPRESSO revealed no spatial variation in α, and the previous results were explained by a systematic error in the wavelength calibration of the Fourier transformation spectrometer (FTS) apparatus [HIRES (High Resolution Echelle Spectrometer) at Keck Observatory and UVES (Ultraviolet and Visual Echelle Spectrograph) at VLT].44 

High-precision spectroscopic laboratories can test for variations in fundamental constants using atomic clocks. If fundamental constants were to change, the ticking rates of atomic clocks would be expected to vary accordingly, with the specific magnitude depending on the type of transition employed in the clock.43 Therefore, in Ref. 47, the frequencies of clocks based on the electric-quadrupole (E2) and electric-octupole (E3) transitions of Yb were compared with each other and a Cs-based microwave clock over an observation time of four years. The goal was to trace variations in α over time as the two clock transitions depend differently on the fundamental constants, leading to a non-identical response in their respective variations.

An experimental realization of the above-mentioned comparison can be implemented via the independent stabilization of two lasers to E2 and E3 transitions and subsequent mixing of the laser signals with the second harmonic of a near-infrared (near-IR) OFC, which allows precise measurements of the desired frequency ratio.47 

One of the classical tests of general relativity—a comparison between Earth-borne and Earth-orbiting identical objects—is expected to be implemented in the FOCOS (Fundamental physics with an Optical Clock Orbiting in Space) mission.48 One optical clock will be installed on a spacecraft moving in an elliptical orbit with a large variation in the gravitational potential. The space clock will experience a constant frequency shift relative to a ground clock. This shift can be measured via an accurate free-space optical telecommunication laser link.48 The proposed experiment is aiming to increase the sensitivity of gravitational redshift detection by a factor of 3 × 105.

Many precision experiments would benefit from more accurate optical clocks, which can be achieved by choosing a narrower optical transition. One of the most promising candidates for this endeavor is a nuclear transition in 229mTh at around 150 nm. However, to date, this transition has been investigated with a limited precision of ±3 nm. One of the main challenges to experimental measurements of the exact transition frequency is the absence of suitable OFCs or tunable CW light sources. OFCs around 150 nm can be produced via high harmonic generation (HHG) in gas-jet targets from IR lasers. This process requires high peak and average power levels due to the low efficiency of the process. Moreover, the near-IR driver lasers have to possess extremely high stability, narrow line widths, and a sufficiently large tuning range to cover the whole uncertainty spectral region.49,50

Besides functioning as relative references in comparative studies, atomic clocks and precision spectroscopy have the potential to replace historical artifacts used as metrological standards, such as the prototype meter or kilogram. For example, at present, one of the most widespread methods for analyzing small variations of isotope ratios is mass spectrometry, which has superior precision and accuracy but requires calibration of each apparatus to a reference sample. In the case of the 13C/14C ratio in carbon dioxide, used for age designation in paleontology, small fractions of the same fossil squid were employed to calibrate mass spectrometers until the material was exhausted, leading to a need to replace it with new references calibrated to the original squid-based sample. This poses challenges since one needs to ensure that the isotope content is stable and does not change over the years. Recently, an alternative approach based on cavity-enhanced absorption spectroscopy in the near-IR spectral region51 has demonstrated a level of accuracy and precision comparable with mass spectrometry without the need for calibration.

Fundamental spectroscopic studies have mainly focused on small molecules, ions, and atoms isolated or kept at low pressures and temperatures. High precision and accuracy are required to determine the absorption features. Moreover, an agreement between measured and calculated spectra is usually desired.

Lists of atomic line positions, energy levels, and ionization energies in the spectral range from 20 to 60 pm are summarized in the NIST Atomic Spectra Database (ASD).36 TIPbase52 contains fine-structure atomic data compiled for ions of astrophysical interest. A list of spectroscopic constants of polar diatomic molecules for the ground and the first excited states, as well as Frank–Condon factors, which can be used for the calculation of energy potentials (Morse) and vibrational spectra and for searching suitable candidates for laser cooling, can be found in the Diatomic Molecular Spectroscopy Database.53 Complete line lists for small molecules of astrophysical interest beyond the experimentally observed transitions obtained from ab initio calculations are summarized in the MARVEL spectroscopic database.42 

The number of space missions carrying spectrographic equipment has grown rapidly during the last few decades. Some such missions aim to explore the universe and nearby solar system objects, but the majority are dedicated to monitoring the Earth’s parameters influencing climate and weather. Even though some of the satellites are not equipped with spectrometers themselves, their mission is to identify potential targets for further spectroscopic analysis.

Therefore, for instance, PLAnetary Transits and Oscillation (PLATO),78 scheduled to be launched in 2026, will carry 26 cameras operating in the visible optical spectral range. PLATO’s goal is to detect terrestrial exoplanets orbiting in the habitable area around solar-type stars. Data from this mission will be used to determine the radii, masses, and ages of planets and to identify the most interesting candidates for further atmospheric analysis.

Another all-sky survey project, TESS (Transiting Exoplanet Survey Satellite),79 is equipped with four wide-angle cameras with a bandpass filter, selecting light between 600 and 1000 nm, which helps to reduce photon-counting noise and increase the sensitivity of the instrument to small planets orbiting around cool stars. TESS aims to measure small changes in brightness and is thus able to detect exoplanets with less than 4 Earth radii. The information gathered by TESS is complementary to the data collected by the Kepler space telescope (2009–2018), which operated in the 400–850 nm spectral range and discovered several thousand confirmed exoplanets.80 

The follow-up investigation of targets identified by TESS and PLATO will be performed, for instance, with the James Webb Space Telescope (JWST) or the Atmospheric Remote-sensing Infrared Exoplanet Large-survey (ARIEL). JWST has been orbiting Earth since Christmas 2021, and ARIEL is expected to launch in 2029. JWST operates in an extremely broad spectral range, from the visible red (600 nm) to the LWIR (28.8 μm), and is capable of examining exoplanetary atmospheres and detecting distant, very early, or very cold objects such as debris disks. The JWST instrumental part consists of a near-IR camera and several spectrographs with low resolution R ≈ 5 in the LWIR (4.9–28.8 μm) and a varying resolution (100, 1000, and 2700) in the visible to mid-IR spectral range (0.6–5.3 μm).

Operating in the mid-IR and LWIR spectral ranges is necessary to meet the scientific goals of JWST. First, cold objects have their maximum emission spectra in the infrared. Second, older and more distant objects experience stronger Doppler redshifts as their movement away from us is proportionally faster. Third, the space between stellar objects is filled with dust, which is opaque for visible light but often transparent in IR. Finally, covering the entire molecular fingerprint region allows the simultaneous detection of multiple chemical species, which already led to the discovery of the first photochemical reaction (the production of SO2 via the oxidation of sulfur radicals) in the atmosphere of the hot (∼750 K) giant exoplanet WASP-39b.81 

ARIEL will be equipped with several spectro- and photometers, operating in the visible (500–550 nm), near-IR (0.8–1 μm, and 1–1.2 μm), mid-IR, and LWIR spectral ranges, including the moderate-resolution (30–200) ARIEL InfraRed Spectrometer (AIRS) apparatus covering 1.95–7.8 μm. ARIEL’s goal is to investigate the early stages of exoplanetary evolution. Therefore, it targets very specific objects—planets with hot (>600 K) well-mixed atmospheres containing small GHG molecules (H2O, CO2, CH4, NH3, HCN, and H2S) and metallic oxides (TO and VO).

Another mission planned for 2027, the Nancy Grace Roman Space Telescope,82 will not only investigate the atmospheres of potentially habitable planets during transition events but also contribute to the large-scale mapping of visible and dark matter by combining imaging and spectroscopic information in the visible and near-IR spectral ranges. Typically, 3D-mapping of galaxies and galaxy clusters is performed by measuring frequency shifts of absorption and emission lines, defined as
z = λ obs λ emit λ emit ,
(2)
where λobs is the wavelength of the light emitted by a remote object and λemit is the unshifted central line position as measured in the laboratory. Depending on the nature of the frequency shift (Doppler effect, gravitational lensing, cosmic expansion), z might have positive or negative values, corresponding to a spectral redshift or blueshift.

The primary targets of the Roman Space Telescope are the Hα-line at 656 nm and the O-III line at 6500.7 nm with redshift values of 0.53 < z < 1.88 and z < 2.77, corresponding to detected wavelengths of 1–1.9 μm and <1.9 μm and equivalent lookback times of 8–11 × 109 years, respectively. The near-IR spectrometers of the Roman Space Telescope have a resolution of 80–600 at 0.75–1.93 μm.

Another mission designed to precisely measure the radial velocities of objects in the center of the Milky Way using the Doppler shifts of absorption lines is GAIA (Global Astrometric Interferometer for Astrophysics).83 Such measurements allow, for example, the discovery of objects that are otherwise hidden from observers, such as double systems containing a stellar-mass black hole paired with a star. GAIA’s spectrometer is designed to measure small shifts of the Ca+-triplet, typical for stars of spectral types G (yellow stars, including the Sun), K (orange stars), and M (red stars), in the range of 845–872 nm with a resolution of 11 700.

There are many other proposed, planned, and ongoing space missions with various targets. An example of a mission targeted at exploring the mineral composition of asteroids using near-IR spectrometers is Hayabusa-2.84 Some of the missions are studying planetary formation by determining metallicity and O/C ratios, which include the Fast Infrared Exoplanet Spectroscopy Survey Explorer (FINESSE),85 which aims to measure visible to mid-IR absorption spectra (0.5–5 μm) with a moderate resolution (80 at 1.2 μm, 300 at 3 μm). Other missions have the goal of investigating objects in our solar system like Venus, in projects like VERITAS86 and EuropaClipper.87 The latter, EuropaClipper, will carry two spectrometers called MISE (mapping imaging spectrometer for Europa) and Europa-UVS (ultraviolet spectrograph) operating in the IR and ultraviolet (UV) spectral ranges (55–210 nm, R = 220). They will analyze the light reflected from the surface of Europa and seek trace concentrations of simple molecules like H2, O2, OH, CO2, CH4, and C2H6 venting through the small cracks of the planetary icy shell.

Space missions are often supported by observations from ground-based large telescopes equipped with high-resolution spectrometers. The main challenge for ground-based observation is the Earth’s atmosphere, where absorption and emission have to be taken into account when analyzing spectra. Typically, Earth-based spectrometers for space observation operate in so-called “atmospheric transparency windows,” where the absorption of atmospheric compounds is minimal. Therefore, Echelle spectrometers like HARPS (High Accuracy Radial velocity Planet Searcher) at La Silla Observatory46 and ESPRESSO aim to precisely measure the radial velocities of planetary objects (R ≈ 150 000) and work in the visible transparency windows between 378 and 691 nm and between 380 and 788 nm, respectively.

The near-IR and mid-IR windows between 0.93 and 5.3 μm are used by the CRIRES (CRyogenic high-resolution InfraRed Echelle Spectrograph) spectrometer88 at the European Southern Observatory and allow investigation of the chemistry, volcanic activity, and stellar evolution of objects in the solar system. The VLT alone facilitates 12 optical spectrographs, which register light from the UV (300 nm) to the LWIR (21 μm).

For obvious reasons, missions targeting interstellar objects use natural sources of light like the brightest lines of a star’s emission or the thermal radiation of colder objects. However, satellites looking down on Earth and launched to other objects in the solar system may use short-wave infrared solar radiation (0.7–3 μm) or thermal infrared planetary radiation (4–15 μm) for Earth (see Fig. 1). Some satellites even carry active light sources, such as heterodyne near-IR spectrometers designed for Venus missions,89 laser light detection and ranging (LIDAR) like MERLIN (Methane Remote Sensing LIDAR Mission),90 or tunable laser diode-based narrowband high-resolution spectrometers91 to study the night-time dynamics of aerosols, cloud formation, or the daily evolution of sources and sinks of various GHG, volatile organic compounds (VOCs), and pollutants in the Earth’s atmosphere.

The compact size, robustness, and low power consumption of mid-IR tunable laser diode (TDL)-based spectrometers have allowed for their installation on space rovers like Curiosity, which landed on the surface of Mars on August 5, 2012.92 Curiosity is equipped with the Sample Analyst at Mars (SAMs) multi-tool instrument, including a multi-pass Herriott cell and two CW lasers emitting at 2.87 and 3.27 μm. The resolution of the spectrometer is above 6.5 × 106, which allows measurement of the isotopic ratios of D/H, 18O/16O, 17O/16O, and 13C/12C in water and carbon dioxide molecules in the Martian atmosphere, enabling tracking of the origins of molecules. Moreover, a space-compatible dual-comb Er:fiber laser system that provides a link to absolute frequency standards was recently developed and tested in zero-gravity conditions during a parabolic flight as part of the FOKUS-II project.93 

The Copernicus satellite constellations94 orbit Earth and monitor global warming and climate change by measuring the thickness of the ozone layer, the densities of aerosols, and concentrations of reactive gases. This provides high-quality data for precise weather forecasting and even helps winemakers better understand the factors influencing the taste of grapes.95 Of the so-called 54 essential climate variables defined by the World Meteorological Organization (WMO), 23 (including stratospheric concentrations of GHG) can exclusively be observed from space. Among the primary targets of these space missions are the mid-IR and LWIR absorption bands of NH3, O3, NOx, CO2, CH4, SO2, HCHO, and VOCs and of secondary organic aerosols (SOAs), the near-IR lines of CO2 (1602–1619 nm, 2037–2065 nm),96 O2 (764–768 nm, 1270 nm), and methane between 1660 and 1672 nm or at 1645 nm,90 and the UV-scattering coefficients of aerosols.

Spectroscopic data from satellites are used to monitor not only atmospheric content but also vertical and horizontal temperature profiles in order to gain a better understanding of global processes. An example is the MetOp mission,97 which is equipped with the IASI (Infrared Atmospheric Sounding Interferometer) and measures spectra in the 3.62–15.5 μm range with a resolution of R = 5500–1290 (corresponding to 0.5 cm−1 at all wavelengths) and has vertical and horizontal resolutions of 1–2 and 25 km, respectively. The MetOp-mission is anticipated to adopt a Sun-synchronous orbit at an altitude of about 817 km. It will soon be complemented by the far-IR mission FORUM (Far-infrared-Outgoing-Radiation Understanding and Monitoring), which aims to cover a spectral range of 6.25–100 μm with a resolution of 3.200–200 (corresponding to 0.5 cm−1 at all wavelengths), which was never observed from space before now.

Once launched, space missions require the validation of the gathered data (on molecules such as CO, O3, CO2, HCl, N2O, NO2, NO, H2O, HNO3, CH4, HCHO, and 13CO2), which can be performed using balloon-borne short-term scientific measurements with a vertical resolution of 2–5 m. Typically, the validation measurements are performed with high-resolution spectrometers consisting of an active light source and a multi-mass cell or a moderate finesse cavity (ring-down spectroscopy). Therefore, for example, multiple missions between 2001 and 2011 were performed with the SPIRALE (SPectromètre Infra Rouge d’Absorption à 6 diodes Lasers Embarquées) instrument carrying six quantum cascade lasers (QCLs) centered at 3419, 4803, 5376, 5879, 6825, and 7923 nm, and a Herriott cell with 300–500 m of optical path length. The diodes have a power of roughly 10 mW, a spectral range of 0.5 cm−1, and a resolution of 34–13 × 106 (corresponding to 0.0001 cm−1 at each wavelength).98 

The monitoring of air quality can also be performed at distances of several meters to several kilometers without the need for satellites, large aircraft, or air balloons.2,99 In this case, a remote sensing instrument can also use thermal sources of radiation (active, like Globar’s silicon carbide elements, and passive, like Sun or Earth radiation coupled with an open-path FTS). However, instruments relying on passive radiation often lack reliability, stability, brightness, spatial coherence, and the possibility for targeted beam delivery over long distances. Using laser-based sources with spatially coherent low-divergence beams and higher spectral brightness helps to overcome these issues and create sensitive and accurate tools for particular applications. Depending on the target and the application, different detection schemes are possible. One of the common strategies for laser-based stand-off detection is the collection of light back-reflected from mirrors, road signs, and other reflecting surfaces. Another possibility is recording light scattered from aerosols and dust particles as a result of Mie and Rayleigh scattering, which is an approach widely employed in LIDAR measurements. In addition, more exotic solutions such as the use of drones carrying retroreflectors100 and exploiting the waveguiding properties of bundles of laser-ignited filaments101 have been suggested.

For monitoring a single chemical species, it is possible to use a single-frequency narrowband low-power laser tuned to resonance with a well-isolated absorption line. At present, CW laser diodes [distributed feedback (DFB) tunable laser diodes (TLDs), interband and intersubband quantum cascade (ICL and QCL) lasers, and external cavity (EC)-QCL] with a sufficiently narrow spectral bandwidth of less than 3 MHz (order of 0.01 ppm) and optical powers of 1–30 mW are commercially available and span a spectral range from 760 nm to 14 μm.102–105 These lasers are in use for the measurement of ppm/ppb variations in the concentrations of small molecules such as H2O, O2, CO, CO2, NH3, O3, NOx, CH4, C2H4, and C2H6.

Broadband detection techniques allow for the simultaneous registration of multiple absorption lines, providing chemical resolution and an increased dynamical range of detection. Recently, near-IR dual-comb spectroscopy across a 2-km open path was demonstrated with sub-1 kHz accuracy and R > 106, permitting the resolution of short-time variations in the CO2, CH4, and H2O concentrations at less than the percent level from average ambient concentrations.16 The simultaneous development of unmanned aerial vehicle technology brought remote spectroscopy to a new level of flexibility—three-dimensional distributions of the same GHG were simultaneously measured by registering the light sent back by a retro-reflector installed on a drone with a GPS tracker.12 Using 200-MHz dual-comb sources based on nonlinearly broadened femtosecond pulses originating from a fiber laser resulted in a resolution of >108 in the 1.57–1.66 µm spectral range. Switching from near-IR to mid-IR OFC sources permitted the open-path remote detection of trace gases such as acetone, isopropanol, and ethane in ppb concentrations.14 Note that despite acetone and isopropanol being relatively large organic molecules with broadband absorption features [similar to the spectrum in Fig. 1(e)], a resolution of R > 105 is required for accurate contraction retrieval due to interference with the absorption spectra of small, more abundant atmospheric molecules. Note that in most countries, the average power of lasers that can be employed for open-path outdoor measurements without regulation is limited to several mW (USA <5 mW, European Union <1 mW).106 

In contrast to fundamental research, space and environmental spectroscopic studies are focused not only on well-isolated absorption lines of molecules at low temperatures and pressures but also on molecular hot bands, collisional information, and the absorption spectra of gaseous media under high temperatures and pressures, plasmas, aerosols, and rocks.

Information on small molecules, which are of interest for astrophysics and planetary science, can be found in the MARVEL database42 (TiO, VO, etc.), VPL Molecular Spectroscopy Database77 (specialized on terrestrial and exoplanet research and including data from HITRAN25 and NIST Chemistry WebBook107), and Leiden Atomic and Molecular Database (LAMDA)64 [containing input data for models of interstellar media, comets, star-forming regions, and diluted atmospheres of exoplanets using non-local thermal equilibrium (LTE) calculations].

Ab initio calculations and potential surface energies based on the experimental and theoretical pressure broadening parameters are summarized in the ExoMol database,61,62 specializing in astronomical objects cold enough for the formation of molecules (brown dwarfs, exoplanets, and comets), as well as on flames and discharge plasma.

Spectra (spectroscopy of atmospheric gases) database72 compiles the data relevant to Earth’s atmosphere research from HITRAN25 and GEISA27 with original experimental data from V.E. Zuev Insitute of Atmospheric Optics (IAO)108 and simulated spectra from other research groups, like.109 

Chemical reactions and collisions important for the physics of interstellar space and the upper layers of the atmosphere are listed in the Kinetic Database for Astrochemistry (KIDA)110 and BASECOL (Ro-Vibrational Collisional Excitation Database and Utilities),55 respectively.

Ab initio calculated rotationally resolved spectra of four-to-six atomic molecules and isotopes at temperatures of up to 2000 K (like hot methane for example) are provided by Theoretical Reims-Tomsk Spectra Database (TheoReTS).75 Some of the hot bands of the small molecules are displayed in HITEMP111 (high-temperature version of HITRAN).

Extinction IR-spectra of dispersed powders and particulate matter in space, taking into account absorption and scattering, can be found in the database of aerosol spectra for cosmic dust,57 HITRAN,25 and GEISA,27 while the Aerosol InfraRed Spectroscopy analysis (AIRSpec) platform provides a tool to work with complex multi-species FTIR-spectra of atmospheric particulate matter.54 

Spectroscopic properties and photometric data of meteors, lunar rocks, and various organic and carbonized solids and liquids are provided by the Mineral Spectroscopy Server and Solid Spectroscopy Hosting Architecture of Databases and Expertise (SSHADE).74 The ECOSTRESS spectral library,60 developed as a part of the Earth’s surface observation mission, contains vegetation and non-photosynthetic vegetation spectra, as well as spectra of various natural and artificial materials.

Multiple industrial processes would benefit from exact knowledge of underlying chemical reactions, including exact kinetics pathways and short-lived intermediates. Chemical reactions often happen at high temperatures and in the presence of electrical discharge and can include toxic and dangerous compounds, which significantly complicates in situ sensing. Optical absorption and emission spectroscopy can offer a solution for remote non-invasive sensing inside the reaction chamber. However, the short timescales of chemical reactions require a fast detection scheme, which often excludes mechanical scanning (a characteristic of FTS and grating spectrometers) or spectral temperature tuning, which is typical for narrowband laser systems.

One of the important fundamental chemical reactions, significant for combustion and atmospheric processes, is the formation of carbon dioxide and atomic hydrogen from OH radicals and carbon monoxide. Recent broadband (≈70 cm−1) spectroscopic time-resolved studies using a mid-IR frequency comb originating from an optical parametric oscillator (OPO) and a VIPA (virtual imaging phase array) sensor have allowed the observation of reaction kinetics on a microsecond timescale with a spectral resolution of around 105, suitable for resolving the individual pressure- and temperature-broadened absorption lines of small molecules (CO, CO2, HOCO, DOCO, H2O, and D2O).9,112

The time-resolved kinetics of the formation of acetylene in a gas cell filled with a CH4/He mixture in the presence of high-voltage electric discharge were investigated with a dual-comb mid-IR OPO-based system with a power of 200 mW in each comb, a temporal resolution of 20 µs, and a spectral resolution of 6 GHz at 3.3 μm (R = 16500). The measurements were performed within a spectral range of 300 nm,6 simultaneously covering the C2H6 and CH4 absorption lines, including the CH4 hot bands.

A similar spectral and temporal resolution was demonstrated with a QCL-based dual-comb spectrometer at 8 μm, which was used to study the oxidation of propyne in shock tube experiments.11 The environmental conditions change quickly inside such shock tubes—low-pressure room-temperature gas can be heated and pressurized to ≈700 K and a sub-atmospheric pressure within several tens of microseconds. If necessary, dual-comb time-resolved spectroscopy can be conducted at a significantly higher spectral resolution of R ≈ 5 × 108 at the expense of simultaneous spectral coverage (a few cm−1), allowing the retrieval of the pressure and temperature coefficients of individual absorption lines and quantitative spectral analysis of the short-lived intermediates.113 

A common technique for the spectroscopic analysis of non-gaseous samples (rocks, solids, aerosols, and liquids) is laser-induced breakdown spectroscopy (LIBS), in which a small fraction of the investigated substance is ionized and evaporated into a plasma state. LIBS is widely employed in isotopic analysis for archaeological and anthropological studies, nuclear waste monitoring,114 geology, and food analysis. Typically, the laser-induced plasmas are characterized by their emission spectra, which contain information exclusively about the excited species and states. The emission spectrum of the plasma consists of lines, Stark-broadened to a several-GHz bandwidth due to the locally high electric fields, and a broadband continuum Bremsstrahlung background that complicates the analysis of the spectrum. Moreover, the transient nature of the laser-induced ablation plumes and the fast recombination time of the laser-induced plasma in ambient air (a few ns115) require high temporal resolution and detection sensitivity. A combination of emission spectroscopy with tunable laser diode absorption spectroscopy allows the extension of the investigation of the temporal laser-induced breakdown-plasma evolution to later and colder stages and increases the precision of, for example, uranium isotope ratio characterization.114,116 A temporal resolution of a few μs and a spectral resolution of R = 35 000 were recently experimentally demonstrated.116 Dual-comb spectroscopy (DCS) has also been applied to study ablation plasma plumes induced by energetic nanosecond laser pulses.15,117,118

The capabilities of DCS in registering various excited states, as well as the temporal evolution of their populations and plasma temperatures, were demonstrated on a stainless steel target. The absorption of Fe ions at 533 nm was registered in a range of 1 nm with a spectral resolution of R = 70 000 (0.0076 nm) and a temporal resolution of 20 µs.119 Later, the method was extended to more complex molecular species (CeO)120 and simultaneous multi-species (Fe, Gb, and Nd) detection.117 Moreover, the characterization of plasma induced by high-peak-power ultrashort laser pulses and the scaling of the plasma temperature, volumetric content, and density with changes in the driving laser wavelength, pulse duration, and energy are ongoing research topics. Among the applications of plasma ignited in the atmosphere by ultrashort pulses are guiding lightning discharge,121 the triggering of air photochemistry, which leads to the formation of clouds,122,123 and clearing paths through fog for free-space optical telecommunication.124 

The spectroscopy of plasma and aerosols is not only of interest for industrial monitoring but also has a significant impact on the development of novel medical treatments, the monitoring of diseases and the metabolic status of patients, and the detection of health hazards. For instance, atmospheric pressure plasma jets (APPJs) are in use for skin treatment and the inactivation of viruses and bacteria. However, their properties, such as plasma density, temperature, and spatial profile, can be further optimized.125 

Particulate (aerosol) matter is known to have a strong effect on human health and wellbeing because its fine particles can penetrate the lungs and rapidly access the blood vessels. Aerosols also have a large impact on the climate due to their ability to reflect, scatter, and absorb light. Studying the formation of plumes of aerosols could reveal the presence of military warfare and toxic or explosive materials. Aerosols are particles with diameters ranging from 10 nm to several millimeters formed by the condensation of water molecules on highly oxygenated VOCs or other hydrophilic molecules. Aerosols exhibit broadband absorption features, which are also typical for liquids or solids. Broadband measurements in the mid-IR and LWIR spectral regions can be used to identify the chemical composition of aerosols. Some of the optical approaches for aerosol characterization are summarized here.124,126 Recently, the broadband remote detection of aerosols utilizing scattered light was demonstrated. Broadband (∼100 nm) LWIR and mid-IR optical parametric oscillators (OPOs) (see also Sec. V B) tunable to the resonance of aerosol absorption features were used with the FTS detection scheme.3,4

Analysis of the scattered or reflected light from a powdered or solid sample can be used to detect explosives and control pharmaceutical drug production.1,5 A broadband spectrum at 8.2–8.9 μm from a 200-fs OPO and a low-resolution FTS (R ≈ 500) allows one to distinguish between various white powders like aspirin, caffeine, and paracetamol. Scanning dual-comb spectroscopy with QCLs, covering 1200–1280 cm−1 and 1280–1320 cm−1, allows the detection of cyclotrimethylenetrinitramine (RDX) and pentaerythritol tetranitrate (PENT) in the light reflected from a blackened aluminum surface stained with surface concentrations of 5 and 2 μm/cm2 at a distance of 3 m.1 

Another important application of laser absorption spectroscopy is medical breath analysis for the diagnosis of diseases and changes in metabolic status. Breath samples are often analyzed by means of mass spectroscopy—a precise but expensive and time-consuming technique that requires collection and storage of the sample, which can lead to its contamination or the dissipation of active agents. On the contrary, optical spectroscopy allows for real-time and time-resolved monitoring of the breath content without the need for sample collection.8 Among the species of interest for breath analysis are isotopes of carbon, which signal the presence of cancerogenic bacteria; acetone, which points toward an abnormal metabolic status such as diabetes; and NOx, which exposes inflammation of the airways.127 The detection of VOCs, ammonia, and CO2 is of interest for the investigation of the breath cycle. The presence of methane and H2, O2 (detected simultaneously using an additional electro-chemical technique) can be related to gastrointestinal disorders.127 The simultaneous detection of CO2 isotope ratios, CO, and NH3 in human breath samples was demonstrated with broadband (1.5–1.6 μm and 1.6–1.7 μm) near-IR optical frequency combs. 40- and 300-mW Er:fiber lasers, a high-finesse enhancement cavity, and a VIPA-spectrometer provided a system with a spectral resolution of 800 MHz, which could distinguish the individual absorption lines of trace gases on the background of H2O, CO2, and CH4 absorption.8 Recent work has extended the scope of this work with a focus on ultrasensitive multi-species detection.128 

Industrial and medical applications benefit from knowledge about major and trace atmospheric gases (ammonia and volatile organic compounds) since they are important species for pollution monitoring, industrial processes, and breath analysis. Specific data on the spectra of organic compounds can be found in the Spectral Database for Organic Compounds (SDBS).69 Spectroscopic information on plasma compounds can be found on the webpage of Weizmann University,129 and the hot lines of combustion-related gases are tabulated in the EM2C database.33 The spectra of gases emitted during the combustion of biomass at an atmospheric pressure in the 600–6500 cm−1 spectral range and with a resolution of 0.11 cm−1 can be found in the Pacific Northwest National Laboratory (PNNL) SERDP (Strategic Environmental Research and Development Program) database.68 FPbase63 contains the fluorescence and absorption spectra of proteins. Deep4Chem58 is an (artificial intelligence) neural network that predicts the optical properties (absorption, emission, quantum yield, and lifetime) of newly designed large organic molecules (chromophores) employed in the production of optoelectronics, OLEDs, fluorescent dyes, and biomarkers. The spectra of various liquids can be found in the IARPA (Intelligence Advanced Research Projects Activity)67 PNNL database.

In the following, we will discuss line strengths and the line-broadening mechanisms that govern the shapes and widths of absorption lines. For our examples, we will use the P(9) transition in the ν3 band of acetylene located at 3054.974 nm or 3273.350 cm−1. The ν3-band is a cold band (meaning the transition starts from the ground state) and corresponds to the antisymmetric stretching mode. The discussion below loosely follows those in the textbooks “Spectra of atoms and molecules” by Bernath130 and “Laser Spectroscopy: Vol. 1 and Vol. 2” by Demtröder37,131 and takes input from the HITRAN database.25 

Let us consider a transition between state 0 and state 1 (or, more generally, state i and state j) with respective populations Ni and Nj. The absorption of light in matter is governed by Beer’s Law,
I = I 0 e α l = I 0 e σ ( N i N j ) l ,
(3)
where I is the transmitted intensity through a sample, I0 is the incident intensity, l is the length of the sample, and α is the absorption coefficient. The absorption coefficient α can also be expressed as a cross-section σ multiplied by the difference in the state populations. The cross-section σ can be directly linked to the transition dipole moment μij or the Einstein coefficient Aij of the transition,
σ ( ν ) = 2 π 2 μ i j 2 3 ε 0 h c ν i j g ( ν ν i j ) = A i j c 2 8 π ν i j 2 g ( ν ν i j ) .
(4)
Here, c is the speed of light, ɛ0 is the vacuum permittivity, h is the Planck constant, and ν is the frequency. The central frequency of a transition is typically labeled as νij, which is the transition frequency from state i to state j. The connection between the Einstein coefficient Aij and the dipole moment μij130 is
A i j = 16 π 3 ν i j 3 3 ε 0 h c 3 μ i j .
(5)
A schematic of an absorption line is shown in Fig. 3(a). The shape of the transition is described by the normalized line shape function g = g(ννij). The full width at half maximum (FWHM) of a transition is called Δνij.
FIG. 3.

(a) A schematic diagram of an absorption line. The FWHM of a transition is called Δνij. The strength of the transition corresponds to the area under the absorption line and is typically labeled Sij. (b) A comparison of pressure-broadened (Lorentzian) and Doppler broadened (Gaussian) line shapes with the same FWHM and the resulting Voigt line shape, all profiles are normalized to peak absorption.

FIG. 3.

(a) A schematic diagram of an absorption line. The FWHM of a transition is called Δνij. The strength of the transition corresponds to the area under the absorption line and is typically labeled Sij. (b) A comparison of pressure-broadened (Lorentzian) and Doppler broadened (Gaussian) line shapes with the same FWHM and the resulting Voigt line shape, all profiles are normalized to peak absorption.

Close modal
The strength of the transition132 corresponds to the area under the absorption line and is typically labeled Sij [Fig. 3(a)],
S i j = σ ( ν ) d ν ,
(6)
with units of cm2 Hz. In the field of spectroscopy, the frequency unit is typically wavenumber (1/λ) in units of cm−1, which leads to an additional factor of 1/c when converting from frequency to wavenumber. The conversion to wavenumbers leads to the unintuitive units of cm2 cm−1, which are sometimes just given as cm.

A full model of a given molecular absorption spectrum involves many transitions with their respective transition strengths and line widths and also includes weighing factors for the respective population levels (partition sums) and statistical weights, which lead to the introduction of spectral line intensities defined for a single molecule. Inconveniently, line intensities are also labeled Sij, so caution must be exercised when comparing different sources. For example, the HITRAN database tabulates spectral line intensities at a reference temperature of 296 K in units of cm−1/(molecule cm−2), which corresponds to cm/molecule.25 

The linewidth of a given transition is determined by the natural linewidth and various broadening mechanisms. Broadening mechanisms are either homogeneous (H), affecting all molecules equally and leading to identical line shape functions for all molecules, or inhomogeneous (IH), when they affect only a sub-group of the available molecules. In the following brief overview of line widths and broadening mechanisms, we will use γij to indicate the FWHM of transitions in terms of angular frequency ω (which is often used for Lorentzian-broadened line shapes) and Δν to indicate the FWHM of transitions in terms of frequency.

1. Natural linewidth (H)

The unperturbed isolated linewidth of an isolated molecule with zero velocity is given by the transition lifetime and can be described by a Lorentzian line shape
g ( ν ν i j ) = γ i j ( γ i j / 2 ) 2 + ( 2 π ) 2 ( ν ν i j ) 2 ,
(7)
which is directly linked to the Einstein coefficient Aij,
γ i j = A i j .
(8)
The FWHM Δν1/2 can then be calculated as
Δ ν 1 / 2 = A i j 2 π = 1 2 π τ sp .
(9)
For our rovibrational P(9)-transition in the ν3-band of acetylene, we have an Einstein coefficient of 23.6 s, which corresponds to a radiative lifetime of τsp = 424 ms, a natural linewidth of Δν1/2 = 3.76 Hz, or 1.25 × 10−10 cm−1, and a dipole moment of 1.55 × 10−31 D.

2. Pressure broadening (H)

Pressure broadening or collisional broadening is homogeneous and can be well approximated by a Lorentzian line shape. A fully analytical treatment of pressure broadening is very involved since it depends on the intermolecular potential between the colliding molecules.130 For practical purposes, pressure broadening is approximated by a Lorentzian line shape with an FWHM γ(p, T) that depends on pressure p and temperature T,25,
γ ( p , T ) = T ref T n air ( γ air ( p p self ) + γ self p self ) .
(10)
If γ(p, T) is known, it is straightforward to calculate the pressure-broadened Lorentzian line shape gD using Eq. (7). The air- and self-broadened Lorentzian FWHM coefficients γair and γself are given at the reference temperature Tref. In HITRAN,25 the coefficient is tabulated as HWHM (half width at half maximum), the frequency axis is given in wavenumbers, and the pressure in atmospheres is tabulated in units of cm−1/atm.

The temperature-dependent exponent nair is typically tabulated for air and, if unknown, the self-broadened coefficient γself is approximated with γair.

In addition to pressure broadening, the transition will experience pressure-dependent shifts of the order of 1 kHz/mbar. Pressure shift data in spectroscopic databases are often completely lacking or reported with high uncertainties, 20 % .

3. Doppler broadening (IH)

Doppler broadening is caused by the well-known Doppler effect, which relates the velocity of a molecule to a shift in its transition frequency. In gas-phase spectroscopy, the analyte will have a Maxwell–Boltzmann velocity distribution. Combined with the Doppler effect, this causes inhomogeneous broadening with a Gaussian line shape, gD,
g D ( ν ν i j ) = 1 ν i j m c 2 2 π k B T 1 / 2 e m c 2 ( ν ν i j ) 2 / ( 2 k B T ν i j 2 ) ,
(11)
with FWHM νD,
Δ ν D = 2 ν i j 2 k B T ln ( 2 ) m c 2 = 7.2 × 1 0 7 ν i j T M ,
(12)
where M is a molar mass in atomic mass units u.
Doppler and pressure broadening are typically the most prominent broadening mechanisms. In most databases, the calculation of the absorption coefficients considers both mechanisms, which leads to a convolution of the line shape functions gp and gD. The convolution of a Lorentzian and a Gaussian function leads to the well-known Voigt line130 with FWHM,
Δ ν Voigt = Δ ν D 2 + Δ ν p 2 .
(13)

A comparison of line shapes that are dominated by pressure broadening, Doppler broadening, and their combination is given in Fig. 3(b).

The Voigt profile, while describing the absorption line affected by both pressure and Doppler broadening, does not describe higher order effects, such as speed dependence of the pressure-broadening parameters, Dicke narrowing, or asymmetry due to the finite duration of the molecular collisions. An introduction to those effects and an appropriate profile can be found in Refs. 133 and 134.

4. Transit-time broadening (H)

Transit-time broadening is caused by the finite interaction time τ between a molecule and the radiation. This effect leads to a sinc-line shape function gTTB originating from the Fourier transform of a rectangle function describing the finite interaction time,
g TTB ( ν ν i j ) = 1 π 2 τ sin 2 ( 2 π ( ν ν i j ) τ / 2 ) ( ν ν i j ) 2 .
(14)
The FWHM is ΔνTTB ≈ 0.89/τ.

5. Saturation broadening of homogeneously broadened transitions

When an optical transition is pumped with high-power radiation, the pumping rate can exceed the relaxation rates. At sufficiently strong pumping rates, the population in the excited state Nj equals the population in the absorbing state Ni. Consequently, the absorption coefficient reduces to zero (absorption equals stimulated emission), and the material becomes transparent.

For the treatment of this effect, it is convenient to introduce the saturation parameter S, which is defined as the ratio of the pump-rate to the average relaxation rate. For our two-level system, relaxation occurs via spontaneous emission only, and S can be expressed as
S ( ν ) = 2 σ i j I ( ν ) h ν A i j .
(15)
Together with simple rate equations (see also Ref. 37), we can express the saturated absorption coefficient αS as
α S ( ν ) = α 0 ( ν ) 1 + S ,
(16)
with α0(ν) being the unsaturated absorption coefficient. Considering homogeneously broadened Lorentzian line shapes and assuming that the relaxation rate is independent of ν allows us to explicitly write down the frequency dependence of S,
S ( ν ) = S 0 ( γ / 2 ) 2 ( γ / 2 ) 2 + ( 2 π ) 2 ( ν ν i j ) 2 ,
(17)
with
S 0 = S ( ν i j ) .
(18)
The Lorentzian frequency dependence of S reduces the strength of the absorption and leads to a Lorentzian profile with an increased saturated FWHM γS,37 
γ S = γ 1 + S 0 .
(19)
This type of broadening is often called power broadening or energy broadening.

6. Saturation of inhomogeneously broadened transitions

The Maxwell velocity distribution in combination with the Doppler effect leads to inhomogeneous Doppler broadening, as discussed earlier. At high pump power, the saturated absorption coefficient can be calculated as131 
α S ( ν ) = α 0 ( ν i j ) 1 + S 0 exp ν ν i j 0.6 Δ ν D 2 .
(20)
Scanning over the Doppler broadened transition, the high-power pump radiation “burns” a so-called Bennett hole into the velocity distribution. Interestingly enough, the Bennett hole cannot be detected simply by tuning the high-power laser through the absorption profile. The high-power radiation simply reduces the saturation coefficient by a constant factor of ( 1 + S 0 ) 1 / 2 at each of the probed frequencies. To observe the Bennett hole, a second laser beam is used to probe the saturated part of the transition. Typically, a counter-propagating beam is used for this purpose. This situation can be experimentally implemented by reflecting the high-power pump laser back through the sample. The dip occurring in the middle of the absorption line (where the two counter-propagating laser beams probe the same velocity class of molecules) is called the Lamb dip. The effect of saturation and the Bennett hole on the form of a Lamb dip is shown in Fig. 4.
FIG. 4.

The absorption spectrum of the P(9) transition in the ν3 band of C2H2 under the same conditions as outlined in the caption of Fig. 5. The Lamb dip in the center of the absorption line appears when the laser power starts to saturate the transition. Note the decrease in line strength and the simultaneous broadening of the absorption line due to power broadening (see also Sec. II B 6).

FIG. 4.

The absorption spectrum of the P(9) transition in the ν3 band of C2H2 under the same conditions as outlined in the caption of Fig. 5. The Lamb dip in the center of the absorption line appears when the laser power starts to saturate the transition. Note the decrease in line strength and the simultaneous broadening of the absorption line due to power broadening (see also Sec. II B 6).

Close modal
The saturated absorption coefficient for two counter-propagating beams can be derived as131 
α S ( ν ) = α 0 ( ν ) γ / 2 B 1 2 ( ν ν i j ) A + B 2 1 / 2 ,
(21)
with A = [ ( ν ν i j ) 2 + ( γ / 2 ) 2 ] 1 / 2 and B = [ ( ν ν i j ) 2 + ( γ / 2 ) 2 ( 1 + 2 S ) ] 1 / 2 .

Evaluating the saturated absorption coefficient at the line center and for (ννij) ≫ γ allows the calculation of the maximum depth of the Lamb dip, which occurs at S0 ≈ 1.4.

7. Saturation spectroscopy

Overcoming the Doppler broadening limit and, hence, increasing the accuracy and precision of line-center measurements is a cornerstone of precision spectroscopy.135 One possible tool for this is saturation spectroscopy or, in other words, Lamb dip spectroscopy. A typical setup consists of an absorption cell, a strong pump laser, and a weaker probe laser. Lamb dip spectroscopy was first demonstrated simultaneously around 1970 by Smith and Hänsch,136 Hänsch et al.,136 and Bordé.137 Since then, it has been a valuable tool for precision measurements ranging from hydrogen hyperfine structure measurements to the stabilization of lasers on hyperfine transitions in Rubidium.

The typical width of a Lamb dip is of the order of well below 1 MHz, 2–3 orders of magnitude smaller than the regular Doppler broadened absorption feature in which it appears (Fig. 4). Typically, the depth of the Lamb dip is a few percent of the transition peak value. Saturation spectroscopy probes only the homogeneously broadened transition line and can increase the precision of line-center frequency measurements by 2–3 orders of magnitude135 for a given signal-to-noise ratio (SNR) by reducing systematic sources of measurement errors. Such sources of systematic errors for line-center measurements include line-center shifts caused by nearby lines not adequately included in the fit. These disturbing lines can be caused by a weaker band, by sample contamination,138 by spectral baseline distortions caused by etalons,135 or by the asymmetry of Doppler broadened absorption profiles due to the speed-dependent impact of intermolecular collisions.135,139 Fitting the Lamb dip enables the absolute determination of the line-center frequency and collision shift coefficients.140 

8. Saturation power

The saturation power PS, which is calculated for a saturation parameter S = 1 and includes the effects of standing waves,141 can be analytically calculated. For a given transition, this yields
P S = 1 4 c h π w 2 6 Γ 2 k 3 A i j ,
(22)
with Γ being the FWHM of the transition, k the wave vector, and w the beam waist. This equation can be rewritten for narrow absorption features in the low-pressure regime (p ≈ 1 × 10−3 mbar), where collisional broadening is negligible compared to transit-time broadening,141,
P S = 1 4 π c h 48 k B T M k 3 A i j .
(23)
The need for high average power is mitigated by moving to stronger fundamental transitions in the mid-IR instead of working with weaker overtones (see Fig. 5). The necessary saturation power can be reduced from several Watts down to tens to hundreds of microwatts by probing fundamental transitions, which are typically located in the mid-IR spectral region. Examples include the typical C–H-stretch absorption around 2500–3300 cm−1, the region between 2400 and 2000 cm−1 that contains, among many others, the stretches of C≡C, C≡N, or C=C=C. To date, the drastic increase in the dipole moments when moving to the mid-IR spectral region has allowed for many successful saturation experiments and sub-Doppler experiments. Some recent highlights are given in Refs. 23, 41, 142, and 143.
FIG. 5.

Calculated room temperature absorption spectrum of acetylene (light blue) with N2 as a buffer gas, volume mixing ratio 500:1. The total pressure of 10−3 mbar is low enough that transit-time broadening dominates over pressure broadening.141 The absorption spectrum was calculated for an enhancement cavity with a length of 56.7 cm and a finesse of 5000. The average power required to saturate the corresponding transitions is indicated in the graph at the top. The saturation power does not reflect the enhancement in the cavity. Hot bands are marked in black, and cold bands are labeled in color. The selection of bands and overtones shows the decrease in transmission dipole moment (and the increase in saturation power) when probing weaker overtone bands in the near-IR.

FIG. 5.

Calculated room temperature absorption spectrum of acetylene (light blue) with N2 as a buffer gas, volume mixing ratio 500:1. The total pressure of 10−3 mbar is low enough that transit-time broadening dominates over pressure broadening.141 The absorption spectrum was calculated for an enhancement cavity with a length of 56.7 cm and a finesse of 5000. The average power required to saturate the corresponding transitions is indicated in the graph at the top. The saturation power does not reflect the enhancement in the cavity. Hot bands are marked in black, and cold bands are labeled in color. The selection of bands and overtones shows the decrease in transmission dipole moment (and the increase in saturation power) when probing weaker overtone bands in the near-IR.

Close modal

Most measurements involving molecular spectroscopy primarily employ broadband incandescent light sources, readily accessible coherent light sources, and laser diodes. These conventional, well-established techniques are widely accessible for most applications, offering broad spectral coverage with moderate resolution or exceptionally high spectral resolution, albeit at the expense of significantly reduced spectral bandwidth. In this section, our goal is to acquaint the reader with frequency comb-mode-resolved spectroscopy, which presents an elegant solution for achieving both broad spectral coverage and high spectral resolution simultaneously, although it does entail increased technical complexity and higher costs.

OFCs can be produced by various types of mode-locked lasers, as well as by exploiting external devices based on the nonlinear Kerr electro-optical effect.144 In the frequency domain, OFCs are represented by a set of sharp equidistant spectral lines. The position of each line can be described by two radio frequencies,
f N = f CEO + N f rep ,
(24)
where N is a large natural number, fCEO is the frequency of the carrier-envelope offset, and frep is the repetition rate of the laser or modulation frequency in the case of electro-optical combs.
In many comb-based spectroscopy experiments, the OFC is coupled to an enhancement cavity by carefully matching the repetition rate of the OFC to the free spectral range (FSR) of the cavity.145 The FSR of a cavity is the distance (in Hertz) between two neighboring cavity resonances in the frequency domain. It is defined by the cavity length L,
F S R = c 2 L .
(25)
The FWHM ΔνEC of each cavity mode grows linearly with the FSR of the cavity and decreases when increasing the cavity finesse F (Fig. 6),
Δ ν EC = F S R F .
(26)
The cavity serves two purposes. First, it elongates the interaction path length, drastically increasing the SNR and sensitivity of the experiment. The path-length enhancement E path of a two-mirror cavity with finesse F is given by
E path = β F π ,
(27)
with 1 ≤ β ≤ 2 being a factor depending on the coupling scheme.145 
The second purpose of a cavity can be to enhance the average power circulating in the resonator. For a tight-locked cavity, the power enhancement E power of a two-mirror cavity with mirror transmission T and excess optical losses L (defined as the sum of absorption and scatter losses on each mirror) is given by141,146
E power = T F 2 π 2 = T ( T + L ) 2 .
(28)
The intensity at the waist w0 of the cavity spatial mode is given by
I EC = C EC P in F π 2 w 0 2 ,
(29)
where CEC is the cavity coupling coefficient.

Efficient enhancement in the enhancement cavity requires the comb lines to be aligned with the cavity’s transmission modes. In contrast to the frequency comb lines, the modes of the enhancement cavity (i) do not have a tunable offset, and (ii) are only equidistant for zero cavity dispersion, which is generally difficult to achieve in a real cavity due to dispersion in the mirror coatings and the gas sample. There are two approaches that can be used to address this issue and couple a comb with a cavity: a tight lock (β = 2) between the cavity modes and the frequency comb lines based on the Pound–Drever–Hall (PDH) scheme,147 which couples a part of the OFC to the cavity,145 or a swept coupling (β = 1) scheme. The swept coupling scheme, or “dither-lock,” is a method used to overcome the adverse effects of dispersion by rapidly dithering the cavity modes across the comb modes. In this approach, all corresponding mode pairs come to resonance one after the other. This approach allows the full laser spectrum to be transmitted when averaging over one sweep but at the cost of transmitted average power.145 

There are a few established approaches for the acquisition of comb-mode-resolved spectra, such as VIPA,112,148,149 DCS,150–152 and comb-mode-resolved FTS.153,154 VIPAs are ideal for applications requiring time-resolved spectral acquisition.112 Here, we will briefly review DCS and comb-mode-resolved FTS since both of them offer access to broadband, comb-mode-resolved spectra.

1. Dual-comb spectroscopy

Recent progress in laser development has pushed the limits of standoff trace gas detection to parts per billion (ppb) with sub-second temporal resolution.12 In particular, this became possible due to DCS.155 In DCS, two lasers with slightly different repetition rates, frep + δ and frep, interfere on a photodiode, which leads to a periodic beating in the registered signal. The interferogram can be recorded with an oscilloscope and Fourier transformed into a radio frequency (RF)-spectrum located between zero and frep/2 Hz. Each comb line of the RF spectrum can be converted into an optical frequency using a scaling factor α given by α = frep/δ. However, since each optical comb line of the laser interferes with each comb line of the other laser, only a limited spectral bandwidth ΔvNA can be unambiguously mapped from the optical to the RF domain,
Δ v NA α f rep 2 = f rep 2 2 δ .
(30)
The position of the center of the RF spectrum is defined by the difference between the fCEO of the two combs. When ΔfCEO = 0, the RF spectrum is centered at zero, and part of the information in the optical domain is lost. The acquisition time of a dual-comb system is inversely proportional to the difference in the repetition rates and can be as small as tens of microseconds.

Since the dual-comb signal can be registered with a single photodiode and the spectral resolution of the technique is mainly limited by the optical linewidth of the individual comb teeth and the comb spacing, the obtainable resolution varies from several GHz to sub-MHz (see also Fig. 1) for uninterleaved spectra acquired with free-running, independent OFCs. In these systems, the maximum acquisition or averaging time is limited by the temporal coherence of the free-running OFCs. On the high-resolution end, kHz resolution and accuracy are possible when the two OFCs are mutually phase-locked and referenced to a frequency standard (optical clock). Mutual coherence between the combs can be achieved in different ways: the OFCs can be locked to an external reference or passively stabilized by, for example, sharing their lasing cavity, gain media, and pump, which can lead to effective noise cancellation.155 

The sensitivity of a dual-comb system can be estimated by using the scaling law of the SNR in the shot-noise regime. The scaling law states that the SNR is proportional to the square root of the acquisition time and is inversely proportional to the number of measured comb lines (due to the distribution of the optical power and registered signal over the total number of elements).155 However, in reality, the SNR is also limited by the minimal power that can be recorded with a particular detector, the individual power of each OFC, and the dynamic range of the detector.

2. Comb-mode-resolved Fourier transform spectroscopy

OFC-based FT spectrometers can surpass the path-limited resolution of traditional Fourier transform spectroscopy.153 The underlying idea is to use the comb-line structure of the OFC. When the total scanning length of the spectrometer exceeds c/frep, it becomes possible to resolve individual comb lines. Crosstalk via the instrumental line shape (ILS) between each spectral element (comb line) can be eliminated by carefully matching the length of the interferogram to c/frep.153 Comb-mode-resolved FTS enables spectroscopy at a resolution given by the individual comb-mode stability while only needing a physical scanning range of about a meter for an OFC with frep ∼ 100 MHz. When the interferogram is recorded and truncated to the correct length, it is possible to calculate the accurate line position of the comb lines by accounting for the offset frequency of the comb (fCEO)153,154 and using precise knowledge of frep (with a relative accuracy of typically 10−11). Similar to other techniques, the absorption features of molecular transitions can then be measured by interleaving spectra from various interferograms taken for several different values of frep or fCEO, scanning the frequency space between individual comb lines.

The majority of spectroscopic measurements of molecules are performed in the linear, Doppler broadened regime. In many cases, the spectral resolution available is often sufficient, and numerous experiments do not face limitations related to it. However, within the field of frequency metrology, there is a demand for higher spectral resolution. Lamb-dip measurements based on CW-light sources are a very established approach and have recently been employed in various experiments to significantly enhance measurement precision and accuracy. For instance, Aiello et al. utilized Lamb-dip measurements to drastically increase measurement accuracy in their work at the kHz-level.20 Lamb-dip measurements have also been applied to obtain the high-resolution spectra necessary for a comprehensive understanding of the HD hyperfine structure156 and to perform frequency metrology of acetylene in the visible spectral region.138 

Here, we propose a novel experimental approach of frequency comb-mode-resolved saturation spectroscopy, which could enable broadband precision spectroscopy in a plethora of molecules such as H2O, CO2, CH4, CO, CHN, SO2, C2H4, C2H6, and PH3. Accessing this novel spectroscopy regime will require progress in mid-IR laser technology. Some of the recent advances in this field are summarized further down in this article. It should be stressed that suitable light sources for the proposed experiment will require excellent phase and amplitude stability in addition to a high output power per comb line.

In the case of a broadband frequency comb spectrum consisting of multiple lines, the power of an individual comb line Pcomb needs to be above Psat to saturate the transition. The power per comb line can be approximated by dividing the average laser power Pav by the number of comb lines M that fit under the spectral envelope Δν at FWHM level,
P comb = P av M = P av f rep Δ ν .
(31)

In many saturation experiments driven by continuous wave lasers, the necessary average power is provided by combining a stable laser source of moderate-high average power in the mW range with a high-finesse enhancement cavity. The enhancement cavity reflects the incoming beam back and forth many times, resulting in two perfectly overlapping, counter-propagating high-power waves, as needed for Lamb dip spectroscopy.

In the context of comb-mode-resolved saturation spectroscopy, all essential technological prerequisites are now within reach, allowing the pursuit of this novel approach.

Recent progress in the field of mid-IR mirror coatings has made low-loss, high-Finesse cavities accessible also in the mid-IR spectral region,157,158 where the strongly absorbing fundamental transitions are located (Fig. 5), which allows for significant power enhancement factors of the necessary average power per comb-line [Eq. (28)].

Comb mode resolved spectrometers, such as those discussed in the work by Rutkowski et al.,154 are crucial to the success of this spectroscopy technique. These instruments allow for the instrumental line-shape free probing of individual comb-modes, enhancing the resolution and sensitivity of the measurements.

The primary challenge that remains is the development of a dedicated, stable, low-noise, high-average power mid-IR OFC. The generation and maintenance of such a comb are pivotal for achieving reliable and consistent results.

To harvest the benefits of comb-mode-resolved saturation spectroscopy, it will be necessary to conduct massively parallel precision measurements of transitions with similar transmission dipole moments and saturation powers. These measurements will be performed by interleaving spectra of different values of frep. These measurements bear a resemblance to the approach detailed in the work of Foltynowicz et al.,23 where double-resonance spectroscopy was used to provide broadband sub-Doppler measurements based on a combination of a high-average power CW-pump and a low-power OFC.

The pursuit of comb-mode-resolved saturation spectroscopy is poised to make significant advancements, opening up new avenues for research and applications in the field of broadband precision spectroscopy.

Typically, a light or laser source for an experiment is selected based on several parameters, for example, spectral coverage, pulse energy, pulse duration, and pulse repetition rate. An overview of the different technologies and their parameter spaces is given in Sec. V. We now point out the less obvious but equally important noise properties of light sources, which often influence the selection in favor of weaker and more stable sources over sources providing a higher average power or a shorter pulse duration.

FIG. 6.

Parameters of enhancement cavities and their dependence on the mirror reflectivity R and the cavity FSR.

FIG. 6.

Parameters of enhancement cavities and their dependence on the mirror reflectivity R and the cavity FSR.

Close modal

Noise, or the fluctuation of laser parameters, enters any laser system through any channel one can imagine. For example, the cavity length of a laser might change due to acoustic vibrations, resulting in a variation in the phase or repetition rate of the laser. The fluctuation of the pump current results in a change in the power of the pump laser or diodes, which in turn leads to a change in the output power and offset frequency of the laser. A slight thermal drift of opto-mechanical elements might also cause similar behavior. The goal of this section is to give the reader an idea of the physical quantities describing these fluctuations and how to compare the stability (noise) performance of different laser systems. The broad topic of reducing noise either passively by design or actively via feedback loops to the light sources is deemed outside the scope of the current work.159,160

The following short introduction to and overview of amplitude noise (also known as relative intensity noise, RIN), phase noise, line widths, and long-term measurements is loosely based on a recently published book chapter by Keller,161 the book “Quantum Electronics for Atomic Physics” by Nagourney,162 a comprehensive summary of phase noise by Rubiola and Vernotte,163 and the IEEE Standard on the topic.164 The latter is the go-to resource for experimental work in this field, as it clearly defines measurement terminology.

In the following, we give definitions for one-sided spectral density functions (an overview of different spectral density definitions is given in Ref. 164), as they are used throughout the above-mentioned IEEE standard and are found in most publications. For clarity, we will use ν for carrier frequencies (note these can be either optical or RF frequencies) and f for frequencies defined relative to the carrier frequency. These are in the RF range and are usually termed “Fourier frequencies.”

Moving forward, we consider a signal with amplitude fluctuations α(t) and phase fluctuations ϕ(t),
E ( t ) = E 0 ( 1 + α ( t ) ) exp [ i ( 2 π ν 0 t + ϕ ( t ) ) ] .
(32)

For clarity, we discuss the two main types of noise separately: In Sec. IV A, we only consider amplitude noise [setting ϕ(t) = 0 in Eq. (32)], followed by a discussion of pure phase noise [setting α(t) = 0] in Sec. IV B. There, we discuss the basic concepts underlying stable CW carriers [as indicated by Eq. (32)]. These can be extended to mode-locked lasers (modeled as an infinite series of δ functions).161 

A well-known parameter for describing the fluctuations of a physical quantity q is the variance σ q 2 , which is the squared deviation of a variable from its mean q ̄ ,
σ q 2 = 1 n i = 1 n ( q i q ̄ ) 2 .
(33)
A power spectral density (PSD) is an extension of the variance, which tells us the frequency distribution of the fluctuations of q. A PSD is usually denoted as Sq(f) and is linked to the variance by
σ q 2 = 0 S q ( f ) d f .
(34)
PSDs are a key element for describing the noise properties of (light) sources.
The power distribution P(ν) of the signal in Eq. (32) is given by the normalized power spectral density SE(ν),
P ( ν ) = S E ( ν ) = 1 E 0 2 | E ( ν ) | 2 ,
(35)
with E(ν) being the Fourier transformation of E(t). SE(ν) can be directly calculated using Eq. (32),
S E ( ν ) = | δ ( ν ν 0 ) + α ( ν ν 0 ) | 2 ,
(36)
with α(ν) being the Fourier transformation of α(t). This is an interesting result, as it shows that the noise sidebands, given by |α(ν)|2, occur around the carrier frequency ν0 (the mixed term vanishes for νν0). In the case of an infinite δ comb, the amplitude noise sidebands end up around every harmonic of the fundamental repetition rate frep (see Fig. 7). The observation that α(f) adds sidebands around the carrier frequency now motivates the definition of Sα(f) = 2|α(f)|2, which is the power spectral density of the normalized amplitude noise,
S α ( f ) = 2 | α ( ν ν 0 ) | 2 = 2 | α ( f ) | 2 .
(37)
Note that we have transitioned from the optical domain ν to the Fourier frequency f = (νν0). We can now write the normalized line shape centered around the carrier frequency as
P α ( f ) = S α ( f ) = 2 | α ( f ) | 2 .
(38)
The factor of two in front of |α(f)|2 is necessary because Sα(f) is defined as a one-sided spectral density. Omitting it would violate the conservation of energy. The power spectral density of amplitude fluctuations Sα(f) can also be expressed via its autocorrelation function Rα(t) using the Wiener–Khintchine theorem.165,166 This theorem states that the power spectrum of a function α(t) is the Fourier transform of its autocorrelation function. In essence, this is the correlation theorem of Fourier transform calculus assuming infinite integration times, i.e.,
S α ( f ) = 2 + R α ( t ) e i 2 π f τ d τ ,
(39)
with
R α ( t ) = lim T 0 1 T 0 T 0 / 2 T 0 / 2 α ( t ) α ( t + τ ) d τ ,
(40)
where Sα(f) is given in units of dBc/Hz, signifying the relative power in dB with respect to the carrier (hence dBc) in a 1-Hz bandwidth.
FIG. 7.

(Left) A schematic diagram of pulse-to-pulse output power variations in an ultrafast laser, and (right) the resulting broadening of the repetition rate and its harmonics indicated in red.

FIG. 7.

(Left) A schematic diagram of pulse-to-pulse output power variations in an ultrafast laser, and (right) the resulting broadening of the repetition rate and its harmonics indicated in red.

Close modal
The power spectral density Sα(f) can also be integrated over an arbitrary Fourier frequency range, giving the integrated root-mean-square (rms) value
| S α ( f ) | rms = σ α [ f low , f high ] = f low f high S α ( f ) d f ,
(41)
which is typically stated in percent.

The concept of phase noise is typically used to describe fast fluctuations (≥1 Hz) in the phase of a signal. Slower fluctuations are usually accounted for by a concept called Allan deviation (AD), as outlined below.

Random irregularities in the phase of an oscillator are described by the spectral density of the phase noise Sϕ(f), which is simply the power spectrum of ϕ(t). As for the RIN, this can be obtained by applying the Wiener–Khintchine theorem,162 
S ϕ ( f ) = 2 | ϕ ( f ) | 2 = 2 R ϕ ( τ ) e i 2 π f τ d τ ,
(42)
with
R ϕ ( t ) = lim T 0 1 T 0 T 0 / 2 T 0 / 2 ϕ ( t ) ϕ ( t + τ ) d τ ,
(43)
where ϕ(f) is the Fourier transformation of ϕ(t).

The factor of two between the PSD of the phase noise and |ϕ(f)|2 takes into account that we defined Sϕ(f) as a one-sided spectral density.163 

The units of Sϕ(f) are rad2/Hz. Experimental measurements often give a quantity called the “script-L of f,” L ( f ) = 1 2 S ϕ ( f ) , in units of dBc/Hz. The “c” in dBc refers to an angle and not the carrier power, as in the case of amplitude noise. More details on the units of Sϕ(f) can be found in Ref. 163.

The phase-noise behavior of a laser is often characterized in terms of the integrated phase noise, defined as
σ ϕ [ f low , f high ] = f low f high S ϕ ( f ) d f ,
(44)
and given in units of rad. From this definition, it is straightforward to calculate the timing jitter
σ x [ f low , f high ] = 1 2 π f rep f low f high S ϕ ( f ) d f ,
(45)
in units of s.
The instantaneous frequency is the derivative of the phase f = 1 2 π ϕ ( t ) ̇ , which can be used to reformulate the spectral density of the phase noise Sϕ(f) to obtain the power spectral density of frequency fluctuations
S ν ( f ) = f 2 S ϕ ( f ) ,
(46)
in units of Hz2/Hz (Fig. 8).
If it becomes necessary to compare oscillators at different frequencies, we use the spectral density of fractional (or normalized) frequency fluctuations, Sy(f), normalized by the carrier frequency ν0,
S y ( f ) = f 2 ν 0 2 S ϕ ( f ) .
(47)
From the power spectral density of the frequency fluctuations Sν(f), the mean square frequency deviation is calculated as
σ ν 2 = 0 S ν ( f ) d f ,
(48)
where 1.18 σ ν 2 is the HWHM of the frequency excursion of the oscillator, assuming a normal distribution of frequency excursions with a standard deviation σν. When integrating experimental results, this integral generally diverges, so in practice, the linewidth is often stated for a finite integration time. The long-term linewidth stability is better assessed using the Allan variance, which is discussed in Sec. IV C.
FIG. 8.

(Left) A schematic diagram of pulse-to-pulse output timing jitter over time in an ultrafast laser and (right) the resulting spectral broadening of the repetition rate and its harmonics indicated in red.

FIG. 8.

(Left) A schematic diagram of pulse-to-pulse output timing jitter over time in an ultrafast laser and (right) the resulting spectral broadening of the repetition rate and its harmonics indicated in red.

Close modal
The phase-noise broadened line shape of a laser is directly calculated from the frequency noise spectral density Sν(f) of the laser light field, as given in Eq. (32),165,167 neglecting amplitude fluctuations (α(t) = 0). Again, the Wiener–Khintchine theorem allows us to calculate the power spectrum
P ( f ) = S E ( f ) = 2 + e i 2 π f τ R E ( t ) d t ,
(49)
via the autocorrelation function, with
R E ( t ) = E 0 2 e i 2 π ν 0 t e 2 0 S ν ( f ) sin 2 ( π f t ) f 2 d f ,
(50)
calculated for E(t).167 

To sum up, the observed noise of a laser system is the result of both amplitude and phase noise. These contributions originate from a wide variety of sources, such as electrical noise, mechanical noise (e.g., entering via cavity-length fluctuations), temperature fluctuations, or spontaneous emissions. All noise sources will change the amplitude and/or phase of a laser or oscillator and broaden the spectral line, thereby reducing the precision of any measurement. An example can be seen in Fig. 9, where the frequency noise PSD of a fCEO measurement was used to reconstruct the line shape of the offset frequency.

FIG. 9.

(a) The measured and reconstructed linewidth of a free-running fCEO. (b) The frequency noise power-spectral density measurement that was used to reconstruct the fCEO. Data from Ref. 168.

FIG. 9.

(a) The measured and reconstructed linewidth of a free-running fCEO. (b) The frequency noise power-spectral density measurement that was used to reconstruct the fCEO. Data from Ref. 168.

Close modal

Proper design of the laser oscillator can help to minimize the influence of noise sources on the laser linewidth, as was demonstrated by Refs. 168 and 169. In general, the noise performance of the laser and parametric amplifiers differs from the noise performance of the seed laser. However, it is possible to preserve or even improve the noise properties of the system if certain requirements are fulfilled.170,171 Furthermore, measurements of the laser noise can be used for feedback schemes, effectively stabilizing the linewidth and mitigating the detrimental effects of phase and amplitude noise on a given system.

Assessing the long-term stability of a frequency needs to take frequency drifts into account. This is a challenge since the standard statistical tool used to access deviations from a mean value (the variance) diverges when the central frequency drifts. To solve that issue, the Allan deviation172 has been introduced, which converges for most noise types. The concept of AD originates from a comparison of the mutual stability of two oscillators used as clocks. More details on the calculation of ADs and related functions can be found in Ref. 164.

In order to obtain the AD, a (long) series of instantaneous, normalized frequency deviations y(t) is measured. It is important that no dead time occurs between the frequency measurements. Often, y(t) is obtained from a measurement of instantaneous phase deviations expressed in units of time, x(t) = ϕ(t)/(2πν0). In this case, y(t) is given as the derivative of x(t).

The value of the AD for a given averaging time τ is calculated as a variance-like value of normalized frequency deviations averaged over τ. To compute this, one first needs to calculate the averaged frequency deviations,
y ̄ k ( τ ) = 1 τ t k t k + 1 y ( t ) d t = x ( t k + 1 ) x ( t k ) τ ,
(51)
with tk = and k N , assuming a time origin of zero.
The AD now compares neighboring averages for a given averaging time τ and is given by
σ y ( τ ) = 1 2 ( M 1 ) k = 1 M 1 ( y ̄ k + 1 ( τ ) y ̄ k ( τ ) ) 2 1 / 2 ,
(52)
where M is the number of averaged frequency measurements that can be obtained from the measurement series. This function is also called the non-overlapped AD and compares averages with longer and longer averaging times. If the signal were to average nicely, then the AD would constantly decrease. However, there are noise sources that cause frequency drifts, which become visible as an increase in the AD for longer averaging times.
The AD can be calculated from the spectral density of the phase noise, or more precisely, from the spectral density of normalized frequency fluctuations Sy(f) (one-sided),164,
σ y ( τ ) = 2 0 f high S y ( f ) sin 4 ( π τ f ) ( π τ f ) 2 d f 1 / 2 ,
(53)
with fhigh being the high-frequency cutoff. The obvious challenge is that Sy(f) will not extend to zero but start at a measurement frequency flow, so the implementation of Eq. (53) will be an approximation. A schematic displaying the relationship between Sy(f) and the Allan variance can be found in Fig. 10. Note that even the AD can diverge for certain noise types, leading to the introduction of the modified version of the AD.163 
FIG. 10.

A schematic representation of a fractional frequency spectrum and the corresponding Allan variance. For more details, please see Ref. 163.

FIG. 10.

A schematic representation of a fractional frequency spectrum and the corresponding Allan variance. For more details, please see Ref. 163.

Close modal

Peter Werle introduced the AD to spectroscopic analysis,173 particularly to assess the noise and stability of individual spectrometers.174,175 Hence, the AD is called the “Werle” deviation when quantifying the spectroscopic instruments.

In summary, the linewidth of a signal is the typical measure of the short-term stability of the system over the chosen integration time. In contrast, the AD provides a tool to judge long-term stability. Both the AD and the linewidth can be calculated from the spectral density of the phase noise, Sϕ(f). The aforementioned summary by Rubiola and Vernotte provides a good starting point163 for readers further interested in the topic of phase noise and its link to AD.

The development of laser sources for spectroscopic applications branches in multiple directions, spanning from CW narrow linewidth tunable laser diodes with a spectral range of a few nm through parametric amplifiers with a bandwidth of hundreds of nm and a tunability range of several μm to octave-spanning supercontinuum sources.

For the scope of this review, it is important to separate the sources into two pillars: (i) tunable sources, such as OPO, OPA (optical parametric amplification), and DFG (difference frequency generation), and (ii) non-tunable sources, such as solid-state and fiber laser systems, optical parametric chirped pulse amplifiers (OPCPA), OPOs working at degeneracy, and QCLs. We exclude low-repetition rate and octave-spanning supercontinuum sources as both provide very little power per comb line.

Figure 11 shows the variation in the power per comb line over the spectral bandwidth (a) and central wavelength (b) of current state-of-the-art laser systems and optical parametric frequency converters. As one can see from Eq. (31), the power per comb line grows with the total average power of the laser pulse and the laser repetition rate (corresponding to a higher spacing between comb lines) and decreases at larger spectral bandwidths. Looking at the plots in Fig. 11, one can keep in mind several areas of interest for different applications: (1) high power per comb line (Pcomb > 0.1 mW), moderate spectral bandwidth (∼100 nm), mid-IR spectral region (λ > 2.5 μm) for precision spectroscopy of fundamental rovibrational transitions; (2) moderate power per comb line, moderate spectral bandwidth for remote spectroscopy and ranging; (3) low power, very broad near-IR-LWIR spectrum for out-of-lab chemical analysis; (4) narrowband, high power per comb line for single species monitoring (near-IR/mid-IR/LWIR); (5) pump lasers for broadband frequency conversion (high power, narrow bandwidth (1–10 nm), near-IR, sub-ps pulse duration).

FIG. 11.

State-of-the-art optical frequency comb sources mapped onto the power per comb line Pcomb vs the FWHM of the useable spectrum and Pcomb vs the central wavelength spaces. Hollow dots represent non-tunable laser systems, and solid dots represent tunable parametric systems of various configurations. The bars represent the tuning range.

FIG. 11.

State-of-the-art optical frequency comb sources mapped onto the power per comb line Pcomb vs the FWHM of the useable spectrum and Pcomb vs the central wavelength spaces. Hollow dots represent non-tunable laser systems, and solid dots represent tunable parametric systems of various configurations. The bars represent the tuning range.

Close modal

1. Tunable laser diodes

For monitoring a single chemical species, it is possible to use a single-frequency narrowband low-power laser tuned to resonance with a well-isolated absorption line. Commercial external cavity diode lasers (EC-DL) are readily available, ranging from the visible to the near-IR spectral region, with average power levels in excess of 10 mW.176 CW-DFB TLDs, QCLs, and ICLs, as well as external cavity (EC) QCLs with a narrow spectral bandwidth of fewer than 3 MHz (on the order of 0.01 pm) and optical powers of up to 130 mW, are available in a spectral range spanning from 760 nm to 14 μm.177–180 

These lasers are in use for the measurement of ppm/ppb variations in the concentrations of small molecules such as H2O, O2, CO, CO2, NH3, O3, NOx, CH4, C2H4, and C2H6, for example, to detect gas leaks along pipelines100,181 or to monitor air and natural gas quality.182–184 TDLs, ICLs, and QCLs are small, have low power consumption, and have high insensitivity to mechanical vibrations, which makes them suitable for loading onto automotive vehicles, helicopters, and other aerial vehicles, as well as small-scale satellites and even extra-terrestrial rovers.84,92,185,186 Typically, the spectral tunability of TLDs and EC-QCLs spans from a fraction of a nm to several nm.

Since all of the optical power of narrowband CW sources is concentrated in a single line, they can also be applied to precision spectroscopy. Therefore, Lamb dip features in the ν2 + ν3 + 2ν4 cold band of acetylene in the range of 1.5–1.63 μm were resolved with kHz level accuracy and a spectral resolution of 10 kHz.135 The measurements were performed by coupling a single-frequency laser with a linewidth of 5 MHz with a high-finesse cavity, F > 100 000, and measuring the ring-down time for each cavity mode. The corresponding intra-cavity intensity was around 1.5 kW/cm2. Scanning over a single Lamb dip feature takes 3.3 min in such a configuration. A 0.4-MHz-wide Lamb dip feature with an HD-absorption overtone at 1381 nm was investigated with a 15-mW laser diode and a 1.2 × 105-finesse cavity. The intra-cavity power was 200 W and the beam waist was 0.46 mm, leading to a saturation parameter S of 0.2, a regime that allows saturation broadening to be neglected. A single scan had a bandwidth of 10 GHz (0.063 nm) and required 12 hours of signal acquisition. Later, a resolution of 100 kHz was achieved at 1524 nm with a cavity finesse of F = 57000, Pin = 30 μW, an intra-cavity intensity of 14 W cm−1, and a single-line measurement time of 10 min.20 

Ongoing research efforts have pushed ICL and QCL technologies further toward on-chip OFC sources with 1–10 GHz repetition rates, enabled by small cavity lengths and spectral bandwidths of several tens of nm.187–191 The generation of broadband ICL and QCL-based OFCs is facilitated by low cavity group delay dispersion and nonlinear four-wave-mixing (FWM) happening directly within the gain media. On-chip OFCs can increase the dynamic range of sensors and unlock the possibility of the simultaneous detection of small organic molecules with overlapping absorption features, such as ethane and ethylene at 3.4 µm, or Freon F152a, F134a, and N2O2 in the vicinity of 8.6 μm.

Although on-chip OFCs exhibit exceptional power per comb line, the task of coupling broadband ICLs and QCLs with enhancement cavities remains highly challenging. This challenge partially undermines the advantages derived from their high repetition rate and power per comb line. To date, the reported broadband ICLs and QCLs have failed to produce narrow optical comb line widths that align with the eigenmode of the enhancement cavity. Furthermore, achieving a narrow cavity linewidth within the desired frequency range of 1–10 GHz is notably difficult. Consequently, both the quality of the mode and the linewidth significantly impact the coupling efficiency with optical cavities.

2. Broadband sources: supercontinuum

One set of attractive tools for broadband remote sensing are the various nonlinear supercontinuum sources, featuring extremely large bandwidths, high spatial coherence, and excellent beam quality.192–195 A supercontinuum can be produced with relatively narrowband low-peak-power laser pulses in various nonlinear media such as printed waveguides and photonic-crystal or micro-structured optical fibers.192,195–197 The underlying mechanisms of supercontinuum generation in isotropic transparent dielectric media are self-phase modulation (SPM), stimulated Raman scattering (SRS), self-steepening, and FWM.198 These rely on the intensity-induced modulation of the refractive index n(I) and the accumulation of the nonlinear phase,
ϕ nl ( t ) = ω 0 t 2 π λ n ( I ) L ,
(54)
where λ is the central wavelength, L is the propagation distance, and I is the time-dependent laser pulse intensity. The change in phase leads to a variation in the instantaneous angular frequency ω(t),
δ ω ( t ) = δ ϕ nl δ t .
(55)
Depending on the temporal intensity profile of the driving laser and the response of the medium, the acquired nonlinear phase change results in the generation of novel spectral components and/or the shift of the central frequency. Consequently, efficient supercontinuum (SC) generation requires high peak power, intensity, or/and a long interaction length.

Photonic crystal fibers (PCF) can be used to ensure long interaction lengths with high beam confinement in the fiber core, but they tend to limit the temporal coherence of the generated white light.192,195 PCFs can be designed to optimize dispersion, making the generation of supercontinua in PCFs a reliable and reproducible technique.

Driving SC generation in PCFs with femtosecond lasers leads to improved stability and temporal coherence compared with nanosecond and picosecond laser sources. However, the stability of SC sources is still limited due to intensity-to-phase noise coupling and the amplification of quantum noise caused by intensity-induced modulation instabilities. By utilizing highly birefringent ANDi fibers that have their zero dispersion point at the central wavelength of the driving laser, it is possible to attain stability improvements compared to commonly used PCFs.195 

SC sources have found their application in near-IR research on fuel and combustion, where the simultaneous registration of multiple species (e.g., CH4, C2H2, C3H8, H2O) is necessary and high-resolution spectrometers (0.02 nm, R = 75 000) are available.193 Atmospheric research and spectroscopy of unknown gas mixtures can also benefit from the extreme bandwidth of SC sources. Finally, SCs are often used for seeding OPA and DFG stages for the generation of more stable and energetic pulses or in f-2f interferometers for stabilization purposes.199 

3. Laser systems: oscillators

Over the past few years, the performance of low-noise mode-locked lasers has been significantly improved by the development of fiber-based oscillators. Fiber lasers offer many advantages in that respect: for common gain media such as ytterbium (Yb)- and erbium (Er)-doped glass fibers, pump light from low-cost 976/980-nm semiconductor diode lasers can be delivered to the gain fiber through all-fiber components, thus avoiding pump misalignment. Moreover, most of the cavity components are inexpensive, durable, and widely commercially available. The large surface-to-volume ratio of optical fibers eases thermal management, and even long oscillator cavities can be spooled to fit within very small footprints.

However, the robustness and reliability of such systems are also affected by the employed mode-locking mechanism. In particular, lasers based on non-polarization-maintaining fibers tend to be very sensitive to environmental perturbations such as temperature changes, humidity, or mechanical stress. Nevertheless, mode locking based on nonlinear polarization rotation (NPR) in such fibers has been one of the most common techniques to achieve pulsed operation, as it is simple to implement with off-the-shelf optical components and allows for large flexibility in cavity design.

The use of polarization-maintaining fibers significantly increases their robustness against environmental effects. One attractive method of achieving stable self-starting mode locking in polarization-maintaining fiber lasers is the use of a nonlinear-amplifying loop mirror (NALM) mechanism.168,200,201 These devices are based on the superposition of two waves counter-propagating in a fiber loop that can be formed by connecting the output ports of a conventional fiber coupler. The transmission/reflection of the loop mirror depends on the difference in the nonlinear phase shift ΔΦNL between the two counter-propagating pulses. Since the nonlinear phase shift is intensity-dependent, these devices can act as instantaneous saturable absorbers and thus support mode locking if the NALM is implemented such that the total laser cavity round-trip losses decrease with an increase in ΔΦNL. In a NALM, ΔΦNL is additionally increased by an active fiber asymmetrically placed inside the loop.

A modification of this scheme has recently been proposed,202,203 in which the NALM is implemented in reflection (i.e., containing a straight arm with a mirror at its end). Due to the straight arm, the scheme has been named the “figure-9 laser” (F9L) and has been demonstrated both with a NALM entrance featuring a fixed splitting ratio200–202 and using a variable splitting configuration.203 The concept was applied to lasers based on Yb-, Er-, and thulium–holmium (Tm/Ho)-doped gain fibers.203 Repetition rates as high as 700 MHz have been demonstrated in a Yb-fiber laser using this type of architecture.204 

Due to their robustness as well as their reliable and reproducible self-starting behavior, all-polarization-maintaining NALM lasers have rapidly turned into ideal candidates for a large variety of applications where reliable and maintenance-free mode-locked lasers are desirable.203 In particular, they have raised considerable interest as sources of low-noise optical frequency combs. First of all, a full-frequency comb stabilization (i.e., stabilization of both the carrier-envelope offset frequency fCEO and comb repetition rate frep) is possible.200,201 Second, the F9L can operate in different mode locking regimes, which allows for the minimization of phase and amplitude noise in the frequency regions where active stabilization is not possible.

Furthermore, even all-polarization-maintaining NALM-based dual-comb configurations have been demonstrated, where the two pulse trains are generated within the same laser cavity.205–207 

Typically, mode-locked fiber oscillators deliver low average powers on the order of tens of mW and, therefore, require further amplification to achieve high power per comb line. It is, however, possible to scale up the power to several Watts directly out of the oscillator.208 

Recently, fiber oscillators operating in the mid-IR spectral range (around 3 and 3.5 μm) were implemented on the base of Dy3+-, Ho3+/Pr3+-, and Er3+-doped fibers using various mode locking mechanisms with repetition rates of the order of tens of MHz, average powers up to several hundred mW, and picosecond to femtosecond pulse duration.

Around 2.8 μm, a moderate power per comb line of tens of μW in combination with a broadband (200 nm) spectrum was achieved with Er-doped fluoride-fiber lasers.209,210

Although powers above 10 W were demonstrated in CW, as well as the possibility for tuning of the central wavelength over 300 nm,211 most of the mode-locked lanthanide-doped fluoride-fiber lasers emitting in the 2.8–3.5 μm spectral region are limited to a few hundred mW and have a spectral bandwidth below 10 nm.212–214 There have been attempts to extend the central wavelength toward the LWIR region using alternative host materials (chalcogenide glasses215), co-doping with different lanthanide-ions215 or Fe2+ metal ions,216 or gas-filled hollow-core fiber lasers.217 

Nevertheless, low-power mid-IR oscillators on their own are of interest for monitoring GHG and air pollutants since they operate in a spectral window that also contains CH-bond stretch, NOx, and NH3 resonances. Another potential application of such lasers is the stabilization of externally seeded OPA and DFG stages.218,219

4. Laser systems: high power oscillators and amplifiers

The highest Pcomb is delivered by Yb-fiber-based chirped pulse and self-similar amplifiers (CPA and SSA)113,220–225 operating at around 1-μm wavelength with a typical spectral bandwidth of 2–20 nm, repetition rate above 100 MHz, and tens of Watts of average power. The spectral region around 1 µm is of limited interest for spectroscopy on its own, but Yb-doped lasers are often employed as pumps for parametric frequency converters into the mid-IR, UV/x-ray HHG, and for strong field phenomena applications and industrial processing.

Therefore, the recent development of the semiconductor saturable absorber mirror (SESAM)-mode-locked Yb:CALGO oscillators resulted in ≈12 W of average power at a 10 GHz repetition rate and Pcomb > 1 mW.226 Nevertheless, the potential of thin-disk laser technology for low-noise applications has not yet been studied. Like other solid-state lasers, the amplitude fluctuations of thin-disk lasers are affected by technical noise, coming from cavity vibrations and air turbulence. Moving thin-disk lasers into vacuum227 enclosures should mitigate noise sources and allow for record-high pulse energies directly from the oscillator.228 

Despite significant advancements in the field of high-power solid-state lasers, they continue to face limitations compared to fiber-based systems. One major challenge is the presence of thermal issues, which require complex and costly cryo-cooling systems.121,228–232 Moreover, in the crystalline matrix, the amplification bandwidth of Yb ions is limited to several nm, resulting in a picosecond pulse duration and often requiring an external spectral broadening and a post-compression stage, increasing the overall noise, cost, and footprint of the system.233,234 Recent progress on cross-polarized pumping schemes for thin-disk lasers has resulted in significant progress toward shorter pulses at high average powers.235 For now, recent developments in the field of multi-pass cell broadening233 and post-compression technology are the standard routine for the generation of sub-100-fs pulses from Yb-based sources, making them appealing as pump sources for ultra-broadband DFG236 and intrapulse DFG.237 

The frequency comb community takes particular interest in Yb-doped fused silica optical fibers due to their wide availability, the low costs of their high-power components (compared with solid-state systems), their easy thermal management, their robustness, and their possibility to operate at room temperature with a repetition rate well above 100 MHz, along with a broadband amplification bandwidth that allows for the generation of 100 fs-pulses without nonlinear spectral broadening.225 Remarkably, Yb:fiber-based CPAs demonstrated a kW-level of average power at sub-MHz repetition rates238,239 and have the potential for further up-scaling due to the small quantum defect of Yb ions, the large surface-to-volume ratios of optical fibers, and coherent pulse stacking technologies. Moreover, due to the amorphous structure of the fiber material, pulses with a duration of 60–100 fs can be routinely generated.

Short energetic pulses without post-compression stages are of interest for cavity-enhanced HHG targeting the vacuum ultraviolet (VUV) and extended ultraviolet (XUV) spectral regions64 for the investigation of long-living nuclear transitions in 229mTh. Importantly, even at 100 W of average power amplification, the low-phase noise of the seed oscillators can be preserved in Yb:CPA systems when amplification is linear and the influence of technical noise is minimized by the amplifier design.170 

There are multiple overtones of the important atmospheric gases (H2O, O2, CO2, CH4, HCl, and HF) in the near-IR window of atmospheric transparency in the vicinity of 1.2 μm that are beyond the reach of Yb-doped lasers. A promising material with which to fill this gap is Cr4+:forsterite.240 Lasers using it as the active medium are tunable to between 1196 and 1380 nm and support a high average power (Watt-level) and a broad spectrum (few to a few tens of nm) in CW operation at room temperature using only water cooling.241 In the mode-locked regime pulses, with a bandwidth of 250 nm at 1.3 μm and average powers of 80 mW at repetition rates of 100 MHz are available.242 Cr:forsterite243,244 was also used as the active medium, which boosted the average power to 1.4 W at an 85 MHz repetition rate.245 

Even though the spectral region around 1.55 μm is of great interest for multiple applications (easier mid-IR continuum and parametric generation when used as a pump, telecommunication wavelength, window of atmospheric transparency surrounded by molecular resonances, eye-safety spectral region, LIDAR, and in biomedical and micromanaging applications), Er:fiber lasers deliver significantly less average and peak power compared to their Yb- and Tm-doped fiber counterparts. The main problem is the high quantum defect of the Er-based systems, and as a consequence, thermal issues, a low conversion efficiency, and the necessity for higher doping concentrations.246,247 Conveniently, Er:fiber lasers can be pumped by the same widespread and relatively cheap laser diodes that are used for pumping Yb-based systems with a central wavelength of 976 nm. However, the emission wavelength of Yb is at around 1030 nm, while Erbium has an amplification maximum at 1560 nm, providing a conversion efficiency of only 10%–20%, significantly worse than that of Yb (∼50%).

The low conversion efficiency of Er-based lasers can be counterbalanced by longer fiber lengths, an increase in the pump wavelength, or the co-doping of the fiber with other ions that absorb pump light more efficiently and transfer it to the Er-ions.248 A long fiber length leads to an accumulation of nonlinearities and fosters a Raman-shift of the central wavelength, which again limits its suitability for high-average power operation. Using a pump at 1460–1532 nm results in a higher conversion efficiency but also increases the amplified spontaneous emission (ASE) level due to the lower population inversion. Co-doping with Yb ions improves the conversion efficiency, but ASE at 1030 nm prevents high average power operation beyond 10 W.249 Similarly, high doping levels result in a high refractive index, which limits the core diameter of the active fibers and increases nonlinear effects already at lower peak-power levels.

Typical power levels are 10 times lower than for state-of-the-art Yb-based CPA systems delivering 3–8 W, with a repetition rate typically limited to 50 MHz. Few systems offer a repetition rate above 100 MHz.250 However, few-GHz systems251 have been demonstrated with an average power of 10 W and femtosecond–picosecond pulse duration.

In the vicinity of 2 μm, a similar power per comb line Pcomb to that of Yb-based systems was achieved with Tm-doped fiber-based CPA.252,253 After a nonlinear broadening step, these sources are of interest for the remote sensing of CO2, methane, and water vapor. Moreover, high-power Tm-based CPAs could pave the way for more efficient parametric conversion due to their smaller pump/idler photon energy ratio and could permit the use of other nonlinear crystals, such as zinc germanium phosphide (ZGP), which are opaque at 1 µm (see also the overview given below in Sec. V B).

An interesting alternative for pumping mid- and LWIR generators at 1.9–2.5 μm is given by solid-state lasers based on Cr:ZnS and Cr:ZnSe laser media. Recently, attractive OFC sources with a bandwidth of a few hundred nm at a central wavelength of 2.4 μm have delivered a Watt level of average power at repetition rates ranging from sub-100 MHz to 2 GHz.254,255 using 1.55-μm Er:fiber amplifiers256 as pump sources.

Despite significant advancements in the development of QCLs, mid-IR fibers, and solid-state lasers, as well as supercontinuum sources, these technologies still show worse performance in terms of spectral tunability and instantaneous bandwidth when compared with optical parametric amplifiers (OPAs) and oscillators (OPOs). Compared with supercontinuum sources, OPAs and OPOs provide superior spectral brightness, more power per comb line, and better stability and noise performance, which allow for a significant increase in SNR. The mode quality of parametric sources can be significantly better than that of QCLs. Moreover, parametric amplification is an instantaneous process. In contrast to laser amplification, parametric processes do not deposit energy into the nonlinear crystal (despite parasitic absorption), which eases thermal management.

A detailed description of parametric amplification can be found in books257,258 and review papers.259,260 Here, we aim instead to guide the reader through a few practical aspects that help one design or choose a parametric source using existing tools, such as the SNLO software from AS Photonics261 and the chi2D-code.262,263

1. Basics of optical parametric amplification

In the parametric process of DFG, a high-frequency (near-IR, in this case) pump-photon splits into two photons with lower frequencies, the signal (near- or mid-IR) and the idler (mid-IR or LWIR). This process adheres to the conservation of energy
ω pump = ω signal + ω idler ,
(56)
and the conservation of momentum
k pump = k signal + k idler .
(57)
Equation (57) can also be written in the form of a phase-matching (PM) equation
Δ k = k signal + k idler k pump .
(58)
Usually, the PM condition of Δk = 0 cannot be achieved in a transparent isotropic media due to the monotonic dependence of the refractive index on the wavelength. However, it can be fulfilled in non-centrosymmetric media, such as birefringent crystals, where the refractive index for the pump, signal, and idler waves depends on their polarization and direction of propagation. Furthermore, PM can also be achieved by periodically switching the sign of the electric dipole domains, such as in periodically poled crystals and orientation-patterned semiconductors. This process is known as quasi-phase matching (QPM) and transforms Eq. (58) into
Δ k = k pump k signal k idler 2 π Λ ,
(59)
where Λ is the period of the poling pattern.
When PM is achieved and Δk = 0, in the plane wave approximation, the parametric gain parameter Γ, that characterizes the growth of the signal and idler and also the depletion of the pump, can be calculated as258–260,
Γ 2 = 2 d eff 2 ω s ω i I p c 3 ε 0 n p n s n i ,
(60)
where deff is the effective nonlinear optical coefficient, calculated from the elements of the nonlinear susceptibility tensor χ(2), c is the speed of light in vacuum, ɛ0 is the electric permittivity of vacuum, Ip is the intensity of the pump wave, and np, ns, and ni are the refractive indices of the pump, signal, and idler, respectively, as
d eff χ eff ( 2 ) 2
(61)
and in accordance with Miller’s empirical rule, χ(2) can be written as257,264
χ ( 2 ) ( ω p , ω s , ω i ) = Δ ( χ ( 1 ) ( ω p ) χ ( 1 ) ( ω s ) χ ( 1 ) ( ω i ) ) ,
(62)
where Δ is Miller’s constant and χ(1) = n2 − 1. Therefore, approximating nnpnsni,
Γ ( n 2 1 ) 3 ( n 3 ) .
(63)
Taking into account that most of the nonlinear crystals exhibit normal dispersion in their transparency range, we come to the first important observation that parametric gain monotonically decreases for longer wavelengths.
Next, using Eq. (56), we can write ωi = ωpωs and, therefore, rewrite Eq. (63) to obtain
Γ 2 ( ω p ω s ) ω s .
(64)
From Eq. (64), one can see that (i) the most efficient parametric conversion can be achieved at ωs = ωp/2, and (ii) the gain is approaching zero in the vicinity of the pump wavelength (see also Fig. 12).
FIG. 12.

Parametric gain, Γ2, as introduced in Eq. (60), in relation to the signal wavelength ωs.

FIG. 12.

Parametric gain, Γ2, as introduced in Eq. (60), in relation to the signal wavelength ωs.

Close modal

In real crystals, the pump intensity is reduced by surface reflections, scattering, absorption, and parasitic light generation such as super luminescence or harmonic radiation. This leads to a familiar situation in which the parametric gain has to exceed the losses for a given frequency. This also limits the frequency tuning range of a crystal.

In addition, working with a broad spectral bandwidth, non-ideal polarization states, a deviation from the optimal direction, or temperature fluctuations leads to Δk ≠ 0. In this case, the phase-mismatching efficiency can be characterized by the function
s i n c 2 Δ k L 2 = sin 2 ( Δ k L ) / 2 ( Δ k L / 2 ) 2 ,
(65)
and the expression for parametric gain is transformed into
g = Γ 2 ( Δ k / 2 ) 2 .
(66)
In the case of non-perfect phase-matching, the intensities of the generated signal and idler waves are proportional to a term,259 
I s,i Γ 2 g 2 sinh g L 2 .
(67)
In Eqs. (65) and (67), L is the length of the nonlinear crystal.

While the intensities of the generated signal and idler grow with an increase in L (in the absence of back-conversion and absorption), their spectral bandwidths are narrowing [Eq. (65)], similarly to the case of laser amplification.

Furthermore, when propagating through any dispersive media, including the nonlinear crystal, the pump, signal, and idler pulses will experience a temporal walk-off due to the group-velocity mismatch (GVM) between them. This effect limits the effective crystal length,259,260
L jp = τ p v j 1 v p 1 ,
(68)
where τp is the FWHM pump pulse duration and j = s,i, with vp, vs, and vi being the group velocities in the crystal for the pump, signal, and idler waves, respectively.

In birefringent crystals, where phase matching is achieved via angular tuning for pulses of different polarizations, the effective interaction length is additionally limited by spatial walk-off. However, spatial walk-off does not occur in crystals where non-critical phase matching (based on temperature tuning of the refractive index, for example) is possible and all three waves are propagating along the principal optical axis.

Therefore, the efficiency of the parametric conversion depends on the length of a nonlinear crystal and on the intensity of pump pulses. Using longer crystals and higher intensities increases the parametric gain but eventually leads to undesired effects such as back conversion, accumulation of the B-integral, spectral narrowing, and walk-off, which are limiting the efficiency and result in a degradation of the beam and pulse quality.259,260

2. Nonlinear crystals

The choice of nonlinear crystal for a specific spectroscopic application depends on various parameters: (i) its efficiency based on the effective nonlinear coefficient, which can be expressed by the following figure of merit (FM):
F M = d eff n p n s n i ,
(69)
as is shown in Fig. 13 for the most popular mid-IR and LWIR crystals; (ii) the transparency range for all interacting wavelengths (signal, idler, and pump); (iii) its optical properties, such as laser damage threshold, photo-refractive effect, Kerr-lensing, and self-phase modulation (SPM) due to its nonlinear refractive index, and photo-darkening of the crystals under long-term pumping conditions at high intensity; (iv) practical properties, such as maximum available aperture and crystal thickness, homogeneity, defects, growing process, polishing process, coating, and poling procedures; (v) tolerance against spectral and intensity fluctuations and temperature variations.
FIG. 13.

The nonlinear figure of merit in the transparency region for the nonlinear crystals used in this review. The dashed lines show the crystals supporting QPM.

FIG. 13.

The nonlinear figure of merit in the transparency region for the nonlinear crystals used in this review. The dashed lines show the crystals supporting QPM.

Close modal

The parameters described under (v) can be characterized by calculating the spectral, angular, and temperature acceptance of the crystals and by comparing the reduction of the parametric conversion efficiency to the case of monochromatic plane-wave pumping under ideal phase-matching conditions.

First, let us consider the spectral acceptance of broadband femtosecond pump pulses with bandwidth Δλp. In this case, each spectral component of the pump will generate a slightly frequency-detuned signal and idler pairs within the phase-matching bandwidth, which leads to a broadening of the generated spectra. Due to the group velocity dispersion, the spectral edges will experience a larger temporal walk-off, lower the intensity and, therefore, reduce the conversion efficiency. Eventually, the edges of the spectrum will be lost due to absorption and scattering or will simply contribute too little intensity for further applications. Similarly, the angular acceptance Δθp is the maximal divergence of the pump beam, which can be efficiently phase-matched in the case of angular parametric tuning and which is limited by the spatial walk-off.265 

The spectral and angular acceptance of the crystal can be quantified by using a Taylor expansion of the PM condition around the central pump wavelength or the phase-matching angle
Δ k = Δ k 0 + Δ λ d Δ k d λ + 1 2 Δ λ 2 d 2 Δ k d λ 2 ,
(70)
Δ k = Δ k 0 + Δ θ d Δ k d θ + 1 2 Δ θ 2 d 2 Δ k d θ 2 ,
(71)
where Δk = 2.78/L defines the FWHM of the phase-matching curve [see Eq. (65)]. Since spatial walk-off does not occur in the case of non-collinear PM and QPM, when all three pulses are propagating along the principal optical axis, the crystals supporting these PM regimes allow tighter focusing, a feature that is especially important for OPO, optical parametric generation (OPG), and low-energy OPA stages.
The conversion efficiency in the case of a broadband pump or non-planar waves correspondingly drops to
η ( ν p ) η ( 0 ) Δ ν 2 Δ ν 2 + Δ ν p ,
(72)
where
Δ ν p Δ λ p c λ p 2 ,
(73)
with c being the speed of light. The conversion efficiency also depends on the divergence angle θp
η ( θ p ) η ( 0 ) Δ θ 2 Δ θ 2 + Δ θ p ,
(74)
with Δθp = 0.4λ/(πw0) being the divergence at the entrance of the nonlinear crystal of a Gaussian pump beam focused to a 1/e-beam-waist of w0.266 

3. OFCs and parametric amplification

For spectroscopic experiments that use an OFC generated by a parametric process as a light source, the design of the frequency converter is very important because it affects access to the offset frequency fCEO and the stability of the system.

OPG-based systems start with the spontaneous decay of a pump photon into a signal and idler; the phases of the signal and idler are random but satisfy a relation
ϕ CEO p = ϕ CEO s + ϕ CEO i + π / 2 .
(75)
The situation is different for signal-resonant synchronously pumped OPOs, in which case the phase of the signal wave is defined by the cavity length LOPO and the dispersion
d ϕ CEO s d t = 2 π ω L OPO 1 v g 1 v p .
(76)
fCEO is related to the carrier-envelope offset phase, ϕCEO, as
f CEO = 1 2 π d ϕ CEO d t .
(77)
Taking into account the phase relation between the pump, signal, and idler waves for DFG processes,
ϕ CEO i = ϕ CEO p ϕ CEO s + π / 2 ,
(78)
for f CEO i , we get
f CEO i = f CEO p f CEO s .
(79)
Therefore, some applications benefit from the “passive stabilization” of the idler wave, which happens via the cancellation of ϕCEO during the DFG between the signal and pump when the signal is seeded by a white-light supercontinuum,259,260 generated by a small energy fraction of the pump, or provided by a pulse generated in another laser amplifier, optically synchronized with the pump via a mutual oscillator.219,267 Other experiments rely on access to and, ideally, a wide tuning range of fCEO. Therefore, compared with parametric or laser systems, enhancement cavities do not have a tunable fCEO. Therefore, to match combs to the cavity modes, one needs to keep control over the fCEO of the parametric system, which can be performed either by using OPO-based setups with subsequent OPA stages if necessary or with the help of phase modulators.268 

1. Mid-infrared systems

Periodically poled lithium niobate (PPLN) is one of the most common QPM nonlinear crystals for the generation of high-average-power, low-energy near- and mid-infrared frequency combs. PPLN has a large FM, comparable to orientation-patterned gallium phosphide (OP-GaP), and is transparent in the 0.3–5 μm spectral region. At high pump intensities, PPLN suffers from photo-refractive damage and green-induced infrared absorption (GIIRA), which can be partially overcome by MgO-doping and operating at high temperatures. The useable aperture of periodically poled crystals is limited by the poling technique. In the case of easily commercially available crystals, it is around 1–3 mm.

PPLN-based synchronously pumped femtosecond OPOs usually have a bandwidth of a few to a hundred nm for the signal (1.3–2 μm) and a few tens to hundreds of nm for the idler (2–5 μm) with average powers of tens to hundreds of mW.208,269–275 The highest average power of the idler directly from a PPLN-based OPO of 1.5 W was demonstrated in 2009 by Adler and co-authors.276 GRIIRa, thermal lensing, and degradation of the OPO mode at larger beam sizes prevent further scaling of the technology.277,278

One possible solution to this would be using a single-pass OPA configuration or even splitting the parametric device into several stages, permitting independent optimization of several parameters (e.g., the beam quality, spectra, power, and noise properties). Therefore, using an additional OPA stage after the low power OPO allows for the generation of Watt-level idler radiation tunable between 2.2 and 4.1 μm with reduced amplitude noise compared to the pump laser.171 

Another option is to use a nonlinear crystal suitable for the spectral region but exhibiting higher photorefractive damage resistance and a smaller GRIIRA, such as KTA (potassium titanyl arsenate, KTiOAsO4) or PPSLT (periodically poled stoichiometric LiTaO3). Note that, additionally, PPSLT can have a larger size due to its lower coercive field, which allows us to periodically pole thicker samples. A sub-picosecond OPO with 19 W of average power at a wavelength of 1445 nm (FWHM ∼ 3 nm) was implemented using an uncoated 17.5-mm-long PPSLT crystal and a nearly 60-W thin-disk laser Yb:YAG-based pump with a repetition rate of 56 MHz.279 The maximum idler power was 7.8 W at a central wavelength of 3.57 μm.

Reference 280 reported on a singly resonant KTA-based OPO with an idler power of 1.3 W and a signal of 2.5 W at a pump power of 7 W, resulting in an overall conversion efficiency of 51.8% without saturation. The OPO has a high pump threshold of 3.11 W, which may explain the absence of saturation and suggests that higher signal and idler powers are possible if more pump power is available. Similar performance, also without saturation, was observed in the case of a potassium titanyl phosphate (KTP)-based OPO.281 The spectral bandwidth of OPOs, in turn, can be extended to 500–1000 nm by manipulating the intra-cavity chirp and using aperiodically poled crystals.208,273

Changing from an OPO to an OPA configuration results in an increase in the average power of the signal wave to 0.5–15 W with an idler power of 0.2–6.7 W, while keeping the spectral bandwidth at the same level as that of the previously discussed OPOs.213,218,219,274,282–286

A 1-µm pump (55 W) from a Yb:fiber CPA system and a 1.55-μm seed (290 mW) from an Er:fiber amplifier and a subsequent nonlinear PCF stage were recently optically synchronized by a 100-MHz oscillator and mixed in a two-stage OPA system to produce 6.7 W idler and 13.6 W signal waves.219 A comparable output power of an idler was generated in a single-stage OPA seeded by a supercontinuum generated in a PCF and pumped with a 50-W thin-disk oscillator.286 

For OFC applications, it is important to keep control over the offset frequency fCEO of the mid-IR pulses. However, the fCEO cancels to zero for systems based on DFG when the seed and pump lasers are based on the same source. One possible solution is to implement an acousto-optic modulator before combining the beams at the DFG stage. Roiz and co-authors suggested an f CEO idler -tuning scheme based on locking the signal-seeding supercontinuum to an independent CW-laser.218 

Since the KTA and KTP crystals have high damage thresholds and can be grown to large apertures and lengths, they are popular materials for high-power and high-energy systems, including OPCPAs.287,288 Typically, OPCPAs operate at lower repetition rates than systems designed for OFC spectroscopy.268,288 However, recent work has demonstrated significant progress toward systems simultaneously featuring high peak power, high average power, and a high degree of stability.199,289

2. Long-wave infrared systems

Among the crystals summarized in Fig. 13, GaSe (gallium selenide) has the broadest transparency range and one of the highest nonlinear figures of merit. GaSe is a negative uniaxial crystal consisting of multiple soft layers,258,290 which limits its thermal conductivity and, therefore, scalability to high peak and average powers. For the same reasons, GaSe cannot be cleaved under certain phase-matching angles and is known to be hard to polish and coat. The large birefringence of GaSe provides phase matching over a broad spectral region but also causes a strong spatial walk-off, which limits the usefulness of the crystal under the tight focusing conditions typical for OPOs. GaSe is often employed in DFG and intrapulse (IDFG) schemes, having low conversion efficiency and broadband spectra, for the generation of LWIR237,291–295 or even THz pulses.296 

Comparing the performance of GaSe with PPLN under similar pumping conditions, specifically by using pulses from a sub-ps few-Watt 47.5 MHz Yb:KGW oscillator, a GaSe single-stage OPA is three orders of magnitude less efficient than a comparable PPLN-stage, but GaSe produces a few hundred of μW of widely tunable, broad spectra between 4.85 and 9.33 μm.294 

Higher LWIR pulse power was demonstrated using a longer wavelength pump.291–293,297 When pumping with 100-fs pulses from a 360-mW, 40-MHz Er:fiber laser system, 1 mW of average power with a bandwidth of 700 cm−1 tunable between 4 and 7 μm were produced in 1-mm crystal.292 Later, a nearly 6-W mode-locked Cr2+:ZnS (77 MHz) laser system with a central wavelength of 2.5 μm and sub-20-fs pulse duration IDGF was used to produce 13 mW pulses at 9 μm in 1-mm GaSe with the spectral bandwidth reaching 12 μm at the 10−3-level.291 Recently, the generation of a 0.5-W broadband LWIR waveform centered at 11 μm was demonstrated via IDFG in a 1-mm-thick GaSe crystal.237 For this purpose, pulses from a Tm-doped fiber amplifier with an average power of 30 W were nonlinearly broadened in PCF and post-compressed to a pulse duration of 32 fs, then tightly focused into the crystal by a parabolic mirror. Despite the high average power and the high repetition rate of 50 MHz (burst mode), the power per spectral element was relatively low due to the extremely large spectral bandwidth of 4000 nm.

Interestingly, similar power per spectral element and similar spectra were achieved with an alternative choice of nonlinear crystal, LGS, and a 1-μm pump laser.236, LGS (LiGaS2, lithium thiogallate) is a negative biaxial crystal that significantly underperforms compared with semiconductor materials (e.g., GaSe, GaAs) in terms of its FoM but possesses a superior damage threshold (up to TW/cm2) and low linear and nonlinear absorption losses, making it compatible with higher intensity and peak power 1-μm sources.258 Unfortunately, similar to BGS (barium–gallium–selenide) and HGS (mercury thiogallate) crystals,298,299 LGS is expensive and not widely commercially available.

In Ref. 236, 250-fs pump pulses centered around 1 µm from a thin-disk Yb:YAG 100 MHz-oscillator were spectrally broadened in PCF and post-compressed to 19 fs. An average power of 50 W was focused on a 1-mm-thick LGS crystal to generate 0.1-W LWIR (12 μm) pulses. In a similar experimental setup, when DFG in an LGS crystal was seeded by a supercontinuum generated in PCF and pumped by 250-fs pulses directly from a thin-disk laser, the conversion efficiency increased by an order of magnitude, and the average power of the generated 8.2 μm pulses was around 1 W with a FWHM of ∼800 nm.286 

AGSe (silver gallium selenide, AgGaSe2) is a negative uniaxial crystal that is well established for mid-IR and LWIR generation.258 AGSe has a similar transparency range to GaSe (0.8–18 μm) and a slightly lower FoM (70 pm2/V2) but has a significantly smaller spatial walk-off. Moreover, unlike GaSe, which can be grown in one direction only, AGSe can be grown and cut in the desired orientation. It is also easier to coat AGSe than GaSe.300 AGSe can be grown to large sizes and thicknesses but has poor thermal conductivity, resulting in significant thermal lensing and therefore limiting AGSe applicability for high-average-power synchronously pumped OPOs.301 Furthermore, AGSe has a low damage threshold of ∼3 GW/cm2 for femtosecond pulses.

CSP (cadmium silicon phosphate, CdSiP2) exhibits an even higher nonlinear FoM than GaSE but has a smaller transparency range. CSP is a uniaxial negative crystal, supporting a broad phase-matching bandwidth, and is suitable for femtosecond pumping at 1 μm.258,290,302 CSP is only partially suitable for LWIR since its transparency is limited to 6.5 μm. The crystal permits non-critical phase matching (temperature-controlled PM instead of angular PM), allowing the avoidance of spatial beam walk-off and working in a tight-focusing geometry, improving the conversion efficiency of low-power OPOs.302 At the same time, CSP’s large birefringence supports the spectral acceptance of broadband femtosecond-pump pulses. CSP has a relatively low damage threshold when pumped with a 1-μm source, which is caused by linear and multi-photon absorption and, therefore, has limited usability for CSP in high-peak-power systems.303 

Typical femtosecond synchronously pumped CSP-based OPOs operate in a 5–8 μm spectral region, producing tens to hundreds of mW of average power when pumped with a Watt-level pump laser.302,304–306 The large spectral acceptance of CSP allows for the implementation of pump-wavelength tuning of the signal and idler central wavelength instead of traditional temperature, angular, and cavity delay tuning.302 CSP has good thermal conductivity, which makes it suitable for high-average-power applications: an OPO pumped with a 1-μm, 3.7-W pump produced 6–7 μm pulses with an average power of 300 mW.307 

When critically phase-matched, pumped by a 2 μm Tm/Ho fiber laser, and seeded by nonlinearly broadened and compressed pulses from an Er:fiber amplifier, a 1.5-mm CSP crystal produces a flat-top spectrum with a bandwidth of 2500 nm, which results in a factor of 50 improvement in the conversion efficiency compared with a 1-mm AGS (AgGaS2, silver thiogallate) crystal operating under the same conditions.308 In Ref. 309, LWIR pulses were generated in a similar fashion, with a pulse energy of 150 pJ (10 mW at 100 MHz). The pulses had a central wavelength of 7 μm and were used as a seed for a high-energy, low-repetition rate (100 Hz) ZGP-based OPCPA system.

ZGP (zinc germanium phosphide) is a positive uniaxial crystal, exhibiting significant nonlinearity, good thermal properties, and a high damage threshold of 4 J/cm2 at 20 ns.258,290 ZGP has a large absorption peak at 1 μm with a tail up to 2 μm, which limits the choice of pump sources. The absorption around 2 μm can be reduced by either controlling the composition and post-growth annealing or by electron beam treatment. However, the e-beam treatment penetration depth is only around 3 mm, which results in a maximum crystal thickness of 3 mm.310 

Usually, ZGP is used for high-energy femtosecond OPCPA at 0.1 to tens of kHz repetition rates287,309,311,312 and Q-switched nanosecond OPOs313 operating around 7 μm. At a high average power, a ZGP-based system typically suffers from thermal lensing and gain guiding, which limits the application space of ZGP for high-power frequency combs since these effects decrease stability and lead to beam degradation (M2 > 3), as has been shown in nanosecond Q-switched OPO experiments.313 At intensities higher than 40 GW/cm2, ZGP suffers from nonlinear absorption even when pumped at 2.5 μm. Nevertheless, a 3% conversion efficiency was achieved in a 3-mm type-I ZGP crystal in IDFG experiments, demonstrating octave-spanning spectra around 10 μm.291 

Quasi-phase-matched orientation-patterned (OP) semiconductor materials, such as GaP and GaAs, offer large nonlinear refractive indices and transparency ranges (0.57–12 μm and 0.85–18 μm, respectively). OP-GaP and OP-GaAs suffer from small aperture sizes and thicknesses that are limited by their growth methods.314 Recently, methods allowing for increased thickness of OP-GaAs up to a few mm were developed based on multiple-plate stacking315 and multiple sequential growth runs.310 For OP-GaP, the maximum thickness that can be reached without breakdowns using the hydride vapor phase epitaxy growth technique is around 1.2 mm.310 Despite the transparency range of GaAs starting at 0.85, the crystal suffers from two-photon absorption at pump wavelengths below 1.73 μm316 and three-photon absorption at 1.93 μm.317 

Typical tunable OPO and DFG devices based on OP-GaAs and OP-GaP operate in the 3–12 μm spectral range with an instantaneous spectral bandwidth of a few hundred nm and average powers below 100 mW at 50–100 MHz repetition rates.267,310,317–322 A high-average-power synchronously pumped picosecond OPO based on a 5-mm anti-reflection coated OP-GaAs crystal was demonstrated in Ref. 316, where an average power of 5.7 W for the signal (2.9–3.4 μm, with an FWHM of around 1 nm) and 4 W for the idler (4.9–6.4 μm, with an FWHM of around 5 nm) at 35 W of pump power were achieved before the onset of thermal issues. Moderate powers of 0.1–0.5 W broadband pulses (with an FWHM of ∼400–800 nm) were demonstrated in degenerative synchronously pumped OPOs based on OP-GaAs317,323,324 with a central wavelength of ∼4 μm and OP-GaP319 at 5.5 μm. Remarkably, the large nonlinear refractive index allows DFG in OP-GaP at a low peak power, which is of interest for the development of on-chip GHz sensors.325 

Current research on spectroscopy is gradually moving away from the traditional gold standard of broadband spectroscopy based on incoherent candescent light sources combined with FTS. It is instead moving toward more sensitive, high-resolution, high-precision, and high-accuracy experiments that find use in fundamental research, environmental science, space research, and medical applications. The price to pay for the drastic increase in sensitivity, resolution, and precision is usually a reduced spectral bandwidth. Each of the aforementioned fields of research features a sub-community that focuses on aspects of spectroscopy and on providing access to line lists and spectroscopic data via a vast number of (often freely accessible) databases.

Challenges to increasing the resolution, precision, and accuracy of experiments are plentiful, and we have reviewed some of the more spectroscopy-specific challenges, such as linewidth broadening due to pressure and the Doppler effect. We have also discussed the more general challenge of amplitude and phase noise and demonstrated how noise broadens the spectral response of any measurement. We have tried to give the reader possible solutions and tools to address specific challenges, such as the ubiquitous Doppler broadening or low-frequency sources of noise that are visible in the Allan deviation.

Last but not least, any modern spectroscopic system relies on a suitable laser source. With that in mind, we have made an effort to guide the reader through a large number of available coherent light sources by highlighting various types of lasers operating in wavelength regions of interest. In general, lasers rely on laser transitions in active media and can only operate in specific wavelength ranges. Often, the species of interest is not exactly at a wavelength for which a laser source is readily available. The way out of this dilemma is through the use of parametric sources, which are in principle able to provide any wavelength of interest if pumped by a suitable laser and if a suitable nonlinear medium can be found.

We hope that this overview of current technology for modern laser-based spectroscopy and the introduction to the basics of laser spectroscopy prove useful to researchers entering this field and help to foster mutual understanding between laser physicists and spectroscopists.

We would like to acknowledge Maximillian Prinz (University of Vienna), Dr. Robert Riedel (Class 5 Photonics), and Dr. Piotr Masłowski (Nicolaus Copernicus University, Torun) for carefully proofreading this article.

Financial support from the Austrian Federal Ministry of Labor and Economy, the National Foundation for Research, Technology and Development, and the Christian Doppler Research Association is gratefully acknowledged. This research was funded in part by the Austrian Science Fund (FWF) (Grant Nos. 10.55776/P33680, 10.55776/P36040, 10.55776/T1216, and 10.55776/ZK91). For open access purposes, the author has applied a CC BY public copyright license to any author-accepted article version arising from this submission.

The authors have no conflicts to disclose.

V. Shumakova: Conceptualization (equal); Writing – original draft (equal); Writing – review & editing (equal). O. H. Heckl: Conceptualization (equal); Funding acquisition (lead); Project administration (lead); Resources (lead); Supervision (lead); Writing – original draft (equal); Writing – review & editing (equal).

The data that support the findings of this study are available from the corresponding author upon reasonable request.

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