Generating ultrashort visible light pulses based on multidimensional solitary states in gas-filled hollow core fiber

Laser sources producing ultrashort pulses in the VIS spectral range (400–750 nm) serve important applications in ultrafast spectroscopy and biophotonics. In pump-probe spectroscopy, such ultrashort pulses can photoexcite various chemical species or materials. On the other hand, ultrashort broadband ultraviolet-visible (UV-VIS) pulses can be used to probe the reaction intermediates as well as the dynamics of photoexcited molecules.^1–5 Over the past two decades, Titanium:Sapphire (Ti:Sa) lasers, with emission wavelength around 800 nm, have been instrumental in developing tunable sources in this spectral range by nonlinear-frequency conversion of visible and infrared pulses.⁶ These methods include harmonic generation, sum-frequency mixing, four-wave mixing (FWM), and spectral broadening in gas-filled capillaries.⁷ Noncollinear optical parametric amplification (NOPA) driven by UV pump pulses is another widely used technique to generate tunable sources in the visible region.^8,9 Using Ti:Sa-based fs pump pulses (around 60–180 fs), sub-20 fs pulses can be obtained using NOPA⁹ in a multi-stage setup. The generation of shorter pulses requires additional spectral phase compensation techniques based on the pulse wavefront tilting,¹⁰ such as the use of deformable mirrors, prism pairs, or chirped mirrors.^11,12 However, the shortest wavelength generated with single-stage Ti:Sa laser-based NOPA is often limited to ∼450 nm. Alternatively, ultrashort pulses with wavelengths down to ∼200 nm can be generated by a powerful yet more complex approach that includes frequency doubling of the spectral components in the frequency domain.¹³ 

Over the last two decades, hollow core fiber (HCF)-based pulse compression techniques have frequently been utilized to generate high-energy few-cycle to single-cycle pulses.^14,15 These two-stage techniques involve nonlinear spectral broadening in a gas-filled fiber followed by spectral phase compensation using chirped mirrors¹¹ or bulk materials.¹⁶ Usually, HCF-based compressors rely on the spectral broadening of ultrashort pulses in noble gases due to self-phase modulation (SPM). Recently, molecular gases have been used as promising alternative nonlinear media for spectral broadening in HCF.^17–22 Unlike noble gases, molecular gases have a delayed nonlinear response that arises due to the alignment of molecules and the stretching of bonds upon interaction with intense laser fields.²³ The dominant rotational nonlinear response in linear molecules (N₂, N₂O, etc.) can be enhanced upon interaction with pulses of a few hundred fs duration.^21,23

Recently, a peculiar study utilizing sub-picosecond (ps) near-infrared (NIR) pulses and the rotational nonlinearity of molecular gases demonstrated the creation of Multidimensional solitary states (MDSS)²² in a nitrogen-filled HCF. To create these self-sustaining light wavepackets in multimode fibers, the required conditions include low modal dispersion along with nonlinear propagation to balance diffraction and dispersion.^22,24 When the high-energy driving pulses with peak power close to the critical power of self-focusing are coupled into a gas-filled HCF, it leads to the creation of solitary states at the beginning of the HCF. The presence of Raman-active gas in the HCF promotes stimulated Raman scattering (SRS) and prevents the diffraction of these states, thus attaining spatial localization. On the other hand, these localized multimode states do not spread in time due to the ultralow modal dispersion of large core HCFs. As these wavepackets propagate along the length of the HCF, they experience enhanced nonlinearity and result in a broadband, redshifted spectrum at the HCF output.^22,25 The generated NIR output possesses an atypical negative quadratic spectral phase arising from the delayed Raman response.^25,26 The temporal evolution of the refractive index and the intensity envelope of long pulses (sub-ps duration) coincide at the leading edge of the pulse. Contrary to SPM-based pulse compressors, where the spectral phase compensation of a positively chirped output requires additional care, such as adapted chirped mirrors, the MDSS output with its intrinsic negative chirp can be conveniently compressed by simple linear propagation through a piece of glass with positive dispersion.

In recent times, the ultrafast laser community has increased interest in ytterbium (Yb) laser technology. Such lasers produce sub-ps duration pulses. While several studies involving SPM-based pulse compression driven by near 400 nm ultrashort pulses (∼20–50 fs) from amplified Ti:Sa laser systems have demonstrated tunable sources in the UV-VIS spectral region,^27,28 the implementation of such sources based on sub-ps driving pulses remains little known. Here, we demonstrate the MDSS-mediated pathway in a large-core HCF to generate ultrashort, tunable sources in the visible spectral region. We show the versatility of this method by experimentally investigating the MDSS formation in the high-dispersion regime driven by near 400 nm pulses of a few hundred fs duration in an N₂O-filled HCF.

The experiments were carried out at the Advanced Laser Light Source (ALLS) user facility using the 50 Hz Ti:Sa chirped pulsed amplifier (CPA). The fundamental CPA output was frequency-doubled using a 500 μm thick β-barium borate (BBO, EKSMA Optics) crystal to generate pulses near 400 nm. The remaining fundamental beam was filtered using a pair of dichroic beamsplitters. A schematic of the experimental setup is shown in the supplementary material, Fig. S1.

At first, we investigated the effect of the input pulse duration on the spectral broadening of frequency-doubled Ti:Sa CPA pulses (near 400 nm) in an N₂O-filled HCF. The pulse duration of the fundamental output of the CPA was varied by changing the separation between the compressor gratings, and this pre-chirped fundamental beam resulted in a chirped second-harmonic beam. Keeping the peak intensity constant at the fiber input, we recorded the spectral broadening for different input pulse durations with positive and negative chirps, respectively. In both cases, the pulse energy was correspondingly varied between 76 and 570 μJ for different input pulse durations (80–600 fs) to maintain a constant peak intensity of ∼2.9 TW/cm² at the HCF input.

The spectrum of the HCF output was recorded using a visible spectrometer (USB4000, Ocean Optics, Inc.). The dependence of the spectral broadening on different input pulse durations is shown in Fig. 1. The spectral shapes in both the positively and negatively chirped input pulses depict a strong red shift. The spectral broadening is maximum for input pulse durations between 150 and 220 fs. Even though we observed ∼5% more broadening for negatively chirped pulses, the overall dependence of the spectral broadening as a function of pulse duration is very similar for the positive and negative chirps. We identified two possible causes of the differences in the spectral broadening for input pulses of the same duration but opposite chirp sign: the N₂O dispersion and the asymmetry in the temporal profile of chirped input UV pulses [for example: Fig. 3(b)]. In multidimensional simulations, based on previous studies^22,25 and the Sellmeier equation for N₂O,²⁹ we observe that the group-velocity dispersion and the third-order dispersion are sufficient to explain the variation. The parameters considered for 3D simulations are summarized in the supplementary information. However, a complete wavelength dependence of N₂O’s nonlinear refractive index would be required to model MDSS with an N₂O-filled HCF, which is beyond the scope of this work.

To characterize the measured broadband, red-shifted MDSS output, we chose the Transient Grating Frequency Resolved Optical Gating (TG-FROG) configuration over the most commonly used Second Harmonic Generation (SHG)-FROG because the operation of Si-based UV-VIS spectrometers is often limited in the deep-UV due to their poor detection sensitivity in this spectral region. In addition, SHG-FROG has stringent phase-matching requirements. Moreover, TG-FROG provides very intuitive FROG traces.^30,31

As demonstrated previously, the MDSS output has a characteristic negative frequency chirp.^22,32,33 Using TG-FROG, the negative chirp can be inferred directly from the FROG traces. The experimental FROG trace of the HCF output, shown in Fig. 2, indicates that >80% of the energy in the output pulses is contained in the negatively chirped part, thus confirming that the spectral broadening originates from multidimensional interactions. On the contrary, when the spectral broadening originates from 1D interactions, both positively and negatively chirped parts have roughly the same energy.²⁰ 

For the measurement shown in Fig. 2, positively chirped input pulses (∼350 fs, ∼100 μJ) were used, and the N₂O pressure in the 0.9 m long gas cell at the fiber output was 1400 mbar. For the same gas pressure, input pulses with higher energy resulted in more spectral broadening. As these self-trapped states with a broadband spectrum propagate through the gas cell and its output glass window, the negatively chirped component gets compressed as both the N₂O and the glass window add positive dispersion in this spectral region. The use of spectral filters to select the desired bandwidth from the broadband output further adds positive dispersion, and pulses of sub-30 fs duration can be produced.

In Subsection II C, we demonstrate the universality of such temporal pulse compression and wavelength manipulation in the visible spectral range by discussing two cases of different input pulse durations resulting in outputs at different central wavelengths.

We compare two different scenarios for MDSS-based pulse compression. In the first case (Fig. 3), positively chirped blue input pulses (220 μJ, ∼600 fs) were coupled into the HCF filled with 1300 mbar of N₂O at the fiber output. The spectrally broadened output extends to 480 nm. The MDSS part in the visible spectral range from 420 to 480 nm contains a pulse energy of 24.6 μJ. The red part of this output was spectrally filtered using FELH0450 (Thorlabs, Inc.) and characterized using TG-FROG with a 1 mm thick sapphire window as the nonlinear medium. The experimental TG-FROG traces for the input and spectrally filtered output are shown in the supplementary material, Fig. S3. The retrieved pulse duration of this MDSS output, with a central wavelength of 468 nm, is 26 fs (FWHM). The retrieved spectral and temporal profiles are shown in Figs. 3(c) and 3(d), respectively.

In the second case (Fig. 4), negatively chirped input pulses (350 μJ, ∼250 fs) were coupled into the HCF. The spectrally broadened output at 1400 mbar of N₂O at the fiber output extends to 535 nm. The generated MDSS output in the visible spectral range from 450 to 530 nm has a pulse energy of 24.9 μJ. The red part of this output was spectrally filtered using FELH0500 (Thorlabs, Inc.) and was characterized by TG-FROG. The experimental TG-FROG traces for the input and spectrally filtered output are shown in the supplementary material, Fig. S4. The retrieved pulse duration of the MDSS output, centered around 515 nm, is ∼27 fs (FWHM), as shown in the retrieved spectral and temporal profiles in Figs. 4(c) and 4(d), respectively.

Therefore, MDSS-based HCF pulse compressors can help in achieving a temporal compression factor of up to ∼20 while red-shifting the wavelength to the visible spectral regime.

Besides the pulse compression discussed so far, another interesting aspect is the quality of the spatial beam profile. Spatial beam cleaning based on Raman^34,35 and Kerr nonlinearities³⁶ has been previously reported in multimode graded-index (GRIN) fibers in numerical and experimental investigations.^37,38 Here, we observe that the spectral broadening due to MDSS results in a red-shifted output beam with a clean spatial profile at wavelengths longer than that of the pump beam.

The beam quality at the HCF output depends on the input coupling conditions. Efficient coupling into the fundamental LP₀₁ mode of an HCF can be achieved when the beam waist diameter (1/e²) is 0.64 times the inner diameter of the HCF. Large deviations in the beam diameter from the specified value lead to coupling into higher-order modes (HOMs). This is the case here, where we coupled the input beam (∼398 nm) into the HOMs of a 400 μm HCF. The beam profile at the fiber input is shown in Fig. 5(a).

When the fiber is under vacuum, the beam undergoes diffraction as it propagates through the HCF, as shown in Fig. 5(b). Coupling into HOMs of a gas-filled HCF provides multiple pathways to various nonlinear phenomena, such as intermodal FWM (IFWM), dispersive waves, and modulation instability, which compete with SRS.²² In GRIN fibers, the SRS-based pulse cleaning is by virtue of the competition between different modes for Raman gain.^34,37 In such multimode fibers, the SRS gain depends on the phase mismatch for the FWM. As it is difficult to maintain phase matching over long fiber lengths, FWM can be suppressed by employing longer GRIN fibers.³⁵ In our case, the phase mismatch to suppress intermodal FWM is created by fine-tuning the HCF coupling angle and position with respect to the input beam while monitoring the bandwidth of the MDSS output.^22,25 As these self-trapped states are created and IFWM is suppressed, the MDSS spectrum extends to longer wavelengths with prominent Raman peaks. Consequently, a clean beam profile is observed at the HCF output for wavelengths greater than that of the input beam (in this case, >450 nm), as presented in Fig. 5(c). Unlike in the Kerr-based beam self-cleaning,³⁶ the residual pump remains fluctuating in the HOMs (other than the LP_0n modes family) of the HCF.^22,25

Therefore, MDSS allows for easing the experimental requirements on input beam size and quality to obtain a clean beam profile at the output of large core HCFs. In another example of a spatially clean MDSS beam, the energy build-up from different modes to the LP_0n mode family upon filling the fiber with N₂O gas can be seen in the supplementary material, Fig. S5.

In conclusion, we have experimentally shown that the creation of MDSS using near 400 nm driving pulses in an N₂O-filled HCF can produce tunable μJ-level, sub-30 fs pulses in the VIS spectral region. The pulses possess broadband spectra and an inherent negative chirp at the HCF output. This intrinsic negative chirp of the output pulses facilitates pulse compression, as such pulses can be compressed by linear propagation through glass windows , which have positive dispersion in the UV-VIS spectral range. We demonstrate that the MDSS-based pulse compression technique can help achieve temporal compression up to a factor of 20. For a given peak intensity of input UV-VIS pulses, spectral tuning can be achieved by changing the gas pressure at the fiber output. Besides temporal compression and spectral tunability, we have also shown that the MDSS process can lead to spatial beam cleaning of the redshifted output. The MDSS process relaxes the stringent requirements for input beam size and quality for HCF-based pulse compression systems to provide spatially clean visible light sources. The conversion efficiency of this method is about ∼16%–17%, similar to that offered by NOPAs in the visible spectral region. In the future, the efficiency could be improved by better coupling the input beam to the LP₀₁ mode since the LP₀₁ mode has the highest Raman gain with the MDSS part, and the pump could efficiently transfer to MDSS and increase the efficiency up to 50%–60%.²² Therefore, this work presents a novel approach to developing compact and spatiotemporally engineered UV-VIS ultrafast light sources. Using sub-ps Yb laser systems, MDSS can be scaled to high repetition rates to provide high-power ultrashort pulsed sources for a variety of spectroscopic applications.^25,33 Our results further provide a promising route for compressing frequency-doubled and tripled Yb laser systems. The MDSS process in an appropriate Raman-active gas-filled fiber can be driven by 515 nm and maybe even at 343 nm. The approach thus provides a robust and straightforward nonlinear frequency conversion technique to achieve ultrashort pulses spanning across the UV-VIS region of the electromagnetic spectrum.

The supplementary material provides details on the experimental setup, the parameters used for simulations, and the experimental and reconstructed FROG traces of the results presented in Subsection II C.

We thank the technical team of ALLS (Antoine Laramée, Loïc Arias, and Philippe Lassonde) for their support in the laboratory. M. Kumar acknowledges the financial support from the NSERC-CREATE program.

Natural Sciences and Engineering Research Council of Canada (NSERC); Fonds de recherche du Quebec—Nature et Technologies (FRQNT); Canada Foundation for Innovation (CFI); PROMPT; National Research Council of Canada's (NRC) “Quantum Sensors Program (QSP)”.

The authors have no conflicts to disclose.

Mayank Kumar: Data curation (lead); Formal analysis (lead); Investigation (equal); Methodology (equal); Writing – original draft (lead); Writing – review & editing (equal). Maghsoud Arshadipirlar: Data curation (supporting); Formal analysis (supporting); Investigation (equal); Methodology (equal); Writing – review & editing (equal). Reza Safaei: Software (lead); Writing – review & editing (supporting). Heide Ibrahim: Funding acquisition (supporting); Project administration (equal); Supervision (equal); Writing – review & editing (lead). François Légaré: Conceptualization (lead); Funding acquisition (lead); Project administration (equal); Supervision (equal); Writing – review & editing (equal).

The data that support the findings of this study are available on request from the corresponding authors. The data are not publicly available.