Detecting the electric-field waveform of an optical pulse from the terahertz to the visible spectral domain provides a complete characterization of the average field waveform and holds great potential for quantum optics, time-domain (including frequency-comb) spectroscopy, high-harmonic generation, and attosecond science, to name a few. The field-resolved measurements can be performed using electro-optic sampling, where a laser pulse is characterized through an interaction with another pulse of a much shorter duration. The measured pulse train must consist of identical pulses, including their equal carrier-envelope phase (CEP). Due to the limited coverage of broadband laser gain media, creating CEP-stable pulse trains in the mid-infrared typically requires nonlinear frequency conversion, such as difference frequency generation, optical parametric amplification, or optical rectification. These techniques operate in a single-pass geometry, often limiting efficiency. In this work, we demonstrate field-resolved analysis of the pulses generated in a resonant system, an optical parametric oscillator (OPO). Due to the inherent feedback, this device exhibits a relatively high conversion efficiency at a given level of input power. By electro-optic sampling, we prove that a subharmonic OPO pumped with CEP-stable few-cycle fiber-laser pulses generates a CEP-stable mid-infrared output. The full amplitude and phase information renders dispersion control straightforward. We also confirm the existence of an exotic “flipping” state of the OPO directly in the time domain, where the electric field of consecutive pulses has the opposite sign.

Mode-locked lasers emit a sequence of almost identical light pulses, albeit with a varying phase shift of the oscillating wave with respect to the pulse envelope, termed as the carrier-envelope phase (CEP). In the frequency domain, this pulse train corresponds to a comb-like structure, defined by two parameters: the line spacing set by the pulse repetition rate (fr) and the frequency shift from the origin, the carrier-envelope offset (CEO) frequency fCEO. Achieving the sensitive control of both, i.e., introducing the optical frequency comb, was a breakthrough that revolutionized optical precision spectroscopy.1–3 

A subsequent development, realizing a frequency comb with fCEO set to zero, produced an exceptional type of laser source—a train of pulses with identical electric-field waveforms.4,5 Importantly, such CEP stability is a necessary condition for direct detection of the electric field transient of a pulse train through nonlinear techniques used to explore new physics in the time domain.6–9 Moreover, controlling the CEP was the catalyst for entirely new research fields, including electron transport in nanoscopic systems10–13 and attosecond science.14 Such phase-locked combs may be obtained by using active stabilization schemes15–17 or feedforward18 methods. Here, excess noise may be introduced at frequencies above the cutoff caused by a finite locking bandwidth. In comparison, a fully passive approach implemented by a difference frequency generation (DFG) process covers the entire stabilization bandwidth without the requirement for electronic feedback.5,19–21

Another continuously evolving field in laser technology is the frequency conversion of established laser sources in the visible and near-infrared (NIR) to cover the electromagnetic spectrum from terahertz (THz) frequencies22 through the mid-infrared (MIR)23 all the way to the (extreme) ultraviolet.24 This capability is of paramount importance for numerous applications, such as THz time-domain spectroscopy25,26 and molecular fingerprinting.27,28 Typically, single-pass non-resonant frequency conversion processes, e.g., difference frequency generation and optical parametric amplification (OPA), achieve high conversion efficiencies for kHz pulse repetition rates where very high pulse energies are available.29 

Nevertheless, considering the signal-to-noise ratio, most applications favor MHz repetition rate laser sources. Efforts based on nonlinear interactions within bulk crystals or periodically poled waveguides demonstrate promising capabilities in the conversion of NIR combs with a MHz pulse rate to the MIR,30–35 although typically either with moderate efficiencies or over a narrow frequency band. In a recent demonstration, a custom-built high-power laser oscillator at a wavelength of 2.3 µm was efficiently converted to a broadband MIR source through a non-resonant nonlinear interaction.36 

An alternative route to achieve notable conversion is by harnessing a resonant system in a multi-pass geometry. For example, MIR optical parametric oscillators (OPOs) can operate with an 80% quantum efficiency in the continuous wave mode.37 In the femtosecond pulse mode, conversion efficiency to the subharmonic may exceed 60%, even at relatively low (nJ-range) pulse energies.38 

However, achieving efficient frequency downconversion in a resonator, while maintaining CEP stability, remains an open problem as nonlinear processes within the OPO do not generally conserve the CEO frequency.39–41 Here, we demonstrate resonant frequency conversion that produces a CEP-stable MIR output at a 50 MHz repetition rate through a combination of two concepts. First, we pump an OPO with a passively CEP-stable NIR comb. Second, tuning the OPO to its degenerate regime inherently locks its phase and frequency to the pump source and thus results in a CEP-stable output.39–41 The electro-optic sampling (EOS) measurement provides, for the first time, a detection of the electric-field output of an OPO, directly in the time domain. Finally, harnessing these measurements as a feedback signal, we compress the pulse duration to 3.5 cycles of the carrier frequency.

Schemes that capture electric-field transients of optical pulses in the time domain rely on nonlinear sampling of the signal waveform.6–9,34,35,42 In the most established of these, EOS, the output of a second-order nonlinear interaction between the signal and an ultrashort probe pulse is measured. A sensitive detection scheme relies on sequentially scanning the signal-probe delay time and averaging over multiple shots. This evaluation of the electric field directly in the time domain is only possible if its waveform is identical in all signal pulses, that is, only with CEP stability. Spectrally, such a frequency comb features fCEO = 0, i.e., comb lines occur at integer multiples of the pulse repetition rate. Even though CEP-stable laser sources have become commercially available in the recent years, despite extensive efforts, their expansion into the entire optical spectrum is an ongoing endeavor.20,36,43,44

OPOs provide efficient conversion of laser wavelength by taking advantage of a multi-pass interaction of the input and output pulses with a nonlinear crystal. While the signal and idler pulses emitted by a synchronously pumped OPO have an identical repetition rate to that of the pump (fr(OPO)=fr(pump)), their CEO frequencies are only partially constrained by energy conservation but not necessarily identical.39–41,45 As a result, even when pumped with a zero-CEO-frequency laser, the output of the OPO is generally not CEP stable (fCEO(OPO)0), and the field transient of subsequent pulses are different from one another [see Fig. 1(a)].

FIG. 1.

Achieving CEP stability in the output of an OPO. Conceptual depiction of the input and output of an OPO under three different experimental conditions: (a) a non-degenerate OPO pumped with a CEP-stable pulse train (fCEO(pump)=0), (b) a degenerate OPO pumped with a non-CEP-stable pulse train, and (c) a degenerate OPO pumped with a CEP-stable pulse train. Each panel depicts the energy diagram of the OPO process (left), a schematic of the electric fields of the pump pulse train (center), and the output pulse train (right). The highlighted areas emphasize the occurrence of pulses with identical CEPs.

FIG. 1.

Achieving CEP stability in the output of an OPO. Conceptual depiction of the input and output of an OPO under three different experimental conditions: (a) a non-degenerate OPO pumped with a CEP-stable pulse train (fCEO(pump)=0), (b) a degenerate OPO pumped with a non-CEP-stable pulse train, and (c) a degenerate OPO pumped with a CEP-stable pulse train. Each panel depicts the energy diagram of the OPO process (left), a schematic of the electric fields of the pump pulse train (center), and the output pulse train (right). The highlighted areas emphasize the occurrence of pulses with identical CEPs.

Close modal

A case of particular interest is that of an equal division of photon energy between signal and idler, a subharmonic OPO. Parametrically excited resonant systems exhibiting a subharmonic response are known in acoustics,46 microwaves,47 and optics.39 The main feature of such degenerate parametric oscillators is that the subharmonic oscillations are phase locked to the driving force. In the case of optics, a degenerate OPO coherently downconverts and augments the spectrum of the pump frequency comb. This feature allows one to achieve OPO pulses that are shorter than the pump. In addition, the intracavity peak power may noticeably exceed that of the pump, which can be exploited for resonantly enhanced high harmonic generation as well as other nonlinear-optical and quantum-optical effects.

The subharmonic operation imposes the following constraints on the OPO output: its CEO frequency can either be (A) fCEOOPO=fCEOpump/2 or (B) fCEOOPO=fCEOpump/2+fr(pump)/2.41 As a result, pumping with a non-zero-CEO-frequency source still produces pulses with a non-constant CEP—the electric field of consecutive pulses is not identical [see Fig. 1(b)]. Only when combining the two regimes: (i) operating the OPO in the degenerate mode, scenario (A) and (ii) pumping it with a CEP-stable pump (fCEO(pump)=0), produces a CEP-stable (fCEO(OPO)=0) output [Fig. 1(c)].

The experimental setup can be divided into the three parts, as shown in Fig. 2: (i) generation of the NIR pump frequency comb (purple frame), (ii) its resonant frequency conversion to the MIR within an OPO (red frame), and (iii) time-domain measurement of the output via EOS (green frame).

FIG. 2.

Schematic of the experimental setup. An ultrabroadband Er:fiber laser (100 MHz repetition rate) system (top left) serves as an input for the generation of the OPO pump (purple frame). As a result of the DFG process (ω3 = ω1 − ω2) between the two spectral portions of the input (dispersive wave and soliton), a frequency comb of around 193 THz with fCEOpump=0 is generated. An electro-optic modulator (EOM) reduces the repetition rate of the comb to 50 MHz before it is amplified in an Er:fiber amplifier. The beam is then coupled to an HNF fiber, in which a χ(3) process splits the spectrum into dispersive and solitonic bands (spectral broadening). The latter, centered around 155 THz, is spectrally separated from the residual pump and dispersive portions and fed into the OPO cavity (red frame). When above threshold, the OPO produces a degenerate spectrum at half of the pump center frequency of around 78 THz. A CaF2 wedge outcouples 1 mW of average power into an EOS characterization setup (green frame), where the beam is overlapped with a NIR broadband pulse centered at a 270 THz frequency (FWHM 113 THz) and focused into a nonlinear electro-optic crystal (EOX). An ellipsometer (see the supplementary material, Note 1) reads out the polarization changes in the NIR pulse induced by the MIR OPO output. BC: beam combiner, a 500 μm Si wafer.

FIG. 2.

Schematic of the experimental setup. An ultrabroadband Er:fiber laser (100 MHz repetition rate) system (top left) serves as an input for the generation of the OPO pump (purple frame). As a result of the DFG process (ω3 = ω1 − ω2) between the two spectral portions of the input (dispersive wave and soliton), a frequency comb of around 193 THz with fCEOpump=0 is generated. An electro-optic modulator (EOM) reduces the repetition rate of the comb to 50 MHz before it is amplified in an Er:fiber amplifier. The beam is then coupled to an HNF fiber, in which a χ(3) process splits the spectrum into dispersive and solitonic bands (spectral broadening). The latter, centered around 155 THz, is spectrally separated from the residual pump and dispersive portions and fed into the OPO cavity (red frame). When above threshold, the OPO produces a degenerate spectrum at half of the pump center frequency of around 78 THz. A CaF2 wedge outcouples 1 mW of average power into an EOS characterization setup (green frame), where the beam is overlapped with a NIR broadband pulse centered at a 270 THz frequency (FWHM 113 THz) and focused into a nonlinear electro-optic crystal (EOX). An ellipsometer (see the supplementary material, Note 1) reads out the polarization changes in the NIR pulse induced by the MIR OPO output. BC: beam combiner, a 500 μm Si wafer.

Close modal

An ultrabroadband spectrum (see the supplementary material, Fig. S1) is generated by coupling the pulsed output of an amplified Er-doped fiber laser (fr = 100 MHz) into a highly nonlinear fiber (HNF).48,49 Subsequently, passive stabilization of the CEP is achieved through a DFG process between dispersive and soliton combs within the broad spectrum (purple frame in Fig. 2).5,19 Since the two combs originate from the same oscillator, their CEO frequencies are identical. Thus, the DFG signal, generated at frequency differences between lines, corresponds to a comb with fCEO = 0. Since the DFG product is tuned to the telecom band (center frequency 193 THz), it can be amplified in a standard Er-doped fiber amplifier (EDFA). Subsequently, the central frequency of the pulse train is shifted to 155 THz (λ = 1.935 µm) in a second HNF, maintaining 50 mW of the average power.

This beam serves as the input of part (ii) of the setup (red frame in Fig. 2), the OPO. The design of the subharmonic OPO is similar to that described in Ref. 50. In the center of the cavity, built in a bow-tie configuration, a parabolic mirror focuses the beams into a 500-μm-thick orientation-patterned GaAs (OP-GaAs) crystal. Tuning the cavity length to support a degenerate OPO process produces a signal and idler of around 78 THz (3.86 µm wavelength). A CaF2 wedge compensates for the round-trip second-order dispersion and outcouples a portion of the generated MIR CEP-stable comb (see the supplementary material, Note 1).

The quantum efficiency of the OPO (8%), while well below that of record-holding implementations of a femtosecond OPO,38 is reasonably high compared to single-pass conversion of high repetition rate sources. The following two main factors limit the efficiency: (1) to keep the cavity compact while matching the time between pump pulses (20 ns), a total of 12 mirrors are necessary. Implementing broadband operation with gold-coated mirrors results in a considerable loss of about 25% per roundtrip. (2) Only ∼24% of the pump photons are converted to the MIR (see the supplementary material, Note 2). This is, in part, due to the mismatch of the pump spectral width to that of phase matching of the OP-GaAs crystal. Within the latter, 42% of the photons are frequency converted. These facts leave a significant room for improving the efficiency of the system in the future designs.

To retrieve the MIR field transient directly in the time domain, it is sampled by an ultrashort probe pulse in an EOS setup depicted in the green frame shown in Fig. 2 [part (iii)]. In order to produce a sufficiently broad probe spectrum, a portion of the CEP-stable NIR comb is amplified in another EDFA and a supercontinuum is generated in an HNF. The spectral components of the fundamental and soliton are removed, keeping only the dispersive wave with a center frequency of 270 THz (λ = 1.11 μm). Dispersion compensation is obtained through a pair of SF10 prisms, shortening the pulse duration to 8 fs. Importantly, as required by EOS,51 the bandwidth of this pulse train (FWHM 113 THz) is larger than all frequency components of the OPO output (see the supplementary material, Fig. S3). The OPO signal and probe pulses spatially and temporally overlap in a 10 µm thick GaSe electro-optic crystal. The resulting nonlinear polarization variations in the probe beam are sensitively detected with an ellipsometer. Scanning the relative delay time analyzes the entire electric-field waveform of the OPO output in the time domain. To suppress the systematic noise, EOS is performed in a lock-in protocol by reducing the repetition rate of the OPO pump to fr(pump)=50 MHz with an electro-optic modulator (EOM). Further details of the experimental implementation, e.g., on the average power of the different stages, are given in the supplementary material, Note 1.

In an OPO cavity, a pump photon is downconverted into two photons, signal and idler, respectively. Not only must the round-trip time of the downconverted pulse match the periodicity of the pump pulse train but also due to the doubly resonant operation (for signal and idler), the OPO lases only at distinct cavity lengths. Thus, the energy splitting between the signal and idler photons depends on the nm-scale (interferometric) sensitivity on the cavity length52 (see the supplementary material, Note 3).

Figure 3(a), presenting the OPO output spectra vs cavity-length detuning δL within one cavity-length resonance, can be divided into three regimes. Regime I covers the detuning range δL0.16,0.1μm, presenting a purely degenerate OPO performance with the center frequency of around 78 THz [for example, spectra Ia and Ib in Fig. 3(b)]. On further shortening the cavity length, the energy splitting between the signal and idler photons grows due to the intracavity third-order dispersion and the spectrum splits into two (see also the supplementary material, Fig. S5). In regime II, δL centered around −0.18 μm [the purple dashed line shown in Fig. 3(a) and the spectrum shown in Fig. 3(b-II)], the OPO output splits into two distinct signal and idler bands with different fCEO, respectively, indicating non-degenerate operation. Surprisingly, even at a shorter cavity length, corresponding to regime III, δL centered around −0.25 μm [the green dashed line shown in Fig. 3(a) and the spectrum shown in Fig. 3(b-III)], the OPO output collapses to a continuous and broadband degenerate spectrum. We note that the merged frequency combs for idler and signal share the same fCEO despite the distinguishable spectral peaks. The rich physics of the nonlinear interactions between the combs in the transition from non-degenerate to degenerate operation involving χ(3), and possibly higher-order nonlinearities in GaAs, is yet to be studied comprehensively. At δL < −0.27 μm, the output splits once more into distinct signal and idler combs. Altogether, regimes I and III are the two cavity length ranges supporting the degenerate operation suitable for EOS, with the latter providing the broadest OPO spectrum. We note that the clear asymmetry in the measured intensity between signal and idler results from the declining sensitivity of our spectrometer (S4, Miriad Technologies) below 75 THz. In addition, the dip at 70 THz across all spectra arises from CO2 absorption in the path from the output of the purged OPO cavity to the spectrometer.

FIG. 3.

Output spectra of the OPO for one resonance of the cavity. (a) OPO intensity spectrum vs cavity length detuning, δL. (b) Four spectral cross sections are indicated by the dashed lines in (a) at δL = 0 μm (Ia), −0.11 μm (Ib), −0.18 μm (II), and −0.25 μm (III) in black, red, purple, and green, respectively. (Ia), (Ib), and (III) present degenerate output spectra, whereas (II) shows a non-degenerate spectrum. A dip in the measured spectra, occurring at 70 THz (4.3 μm), results from the absorption by CO2 molecules during propagation through the ambient atmosphere between the OPO and the spectrometer.

FIG. 3.

Output spectra of the OPO for one resonance of the cavity. (a) OPO intensity spectrum vs cavity length detuning, δL. (b) Four spectral cross sections are indicated by the dashed lines in (a) at δL = 0 μm (Ia), −0.11 μm (Ib), −0.18 μm (II), and −0.25 μm (III) in black, red, purple, and green, respectively. (Ia), (Ib), and (III) present degenerate output spectra, whereas (II) shows a non-degenerate spectrum. A dip in the measured spectra, occurring at 70 THz (4.3 μm), results from the absorption by CO2 molecules during propagation through the ambient atmosphere between the OPO and the spectrometer.

Close modal

In this section, we show that applying a CEP-stable pump, the degenerate output of the OPO is CEP stable, enabling the measurement of its electric field directly in the time domain in a pump–probe configuration. To enhance the sensitivity of such a pump–probe setup, it is advantageous to halve the repetition rate of the pump and filter the signal with a lock-in amplifier at the Nyquist frequency of the probe fr/2.53,54 This scheme is graphically shown in Fig. 4(a): the probe intensity (blue) has twice the repetition rate of the CEP-stable OPO output (orange). Thus, only every second probe pulse interacts with a signal pulse and undergoes a polarization change. A lock-in amplifier with the reference frequency set to fmod = fr(OPO)=fr/2 (solid black line) extracts the average difference between two successive probe pulses, thus isolating the pump-induced polarization change in the most sensitive way.

FIG. 4.

Field-resolved detection of both the degenerate states of the OPO. (a) Illustration of the electric field transients of the CEP-stable (orange) and flipping (green) state of the degenerate OPO in the time domain and their detection with a lock-in scheme. (b) Electro-optic sampling (EOS) transients of both the states for a narrow output spectrum within regime I [Fig. 3(b-Ia)]. Inset: zoomed-in view of the detected electric field for a shorter time scale. (c) Fourier transform of (b). Spectral amplitudes (solid lines) and phases (dashed lines) with the same color code.

FIG. 4.

Field-resolved detection of both the degenerate states of the OPO. (a) Illustration of the electric field transients of the CEP-stable (orange) and flipping (green) state of the degenerate OPO in the time domain and their detection with a lock-in scheme. (b) Electro-optic sampling (EOS) transients of both the states for a narrow output spectrum within regime I [Fig. 3(b-Ia)]. Inset: zoomed-in view of the detected electric field for a shorter time scale. (c) Fourier transform of (b). Spectral amplitudes (solid lines) and phases (dashed lines) with the same color code.

Close modal

The detected electro-optic signal of the degenerate OPO output is shown in Fig. 4(b) (orange line). In this measurement, the resonator length is within regime I, set to support a narrow degenerate output spectrum as the one shown in Fig. 3(b-Ia). The electric-field waveform consists of an oscillating carrier wave with a period of 13 fs, matching the degeneracy frequency of 78 THz. It is nearly free of frequency chirp. The Fourier transform shown in Fig. 4(c), exhibits a Gaussian peak for the amplitude (solid orange line) matching the one observed in Fig. 3(b-Ia) and a relatively flat spectral phase (dashed orange line) around the peak position. We stress that this measurement already demonstrates the CEP stability of the degenerate-state output—a non-zero average electric-field waveform, in line with the conceptual discussion around Fig. 1(c) shown above. A more quantitative and detailed discussion of CEP stability is provided in the supplementary material, Note 4.

In the following, we present a measurement of the electric-field waveform of the so-called “flipping state” of the OPO output. Here, we operate the OPO in regime I in the degenerate state (B) (see above) for which the frequency comb obtains fCEO(OPO)=fr(OPO)/2, when using the same phase-stable pump (fCEO(pump)=0), instead of fCEO(OPO)=0 as in the previous measurement. This regime is achieved by switching to a neighboring cavity-length resonance and fine tuning the dispersion with the CaF2 wedge.45,52 In this state, two consecutive pulses are identical, apart from an alternating sign of the field [Fig. 4(a), green]. For this reason, we term this configuration the “flipping state.”

To demonstrate that our OPO can indeed be tuned to the flipping state, we introduce a new measurement scheme. Using the same optical setup, we only change the demodulation frequency of the lock-in amplifier from fr(OPO) to fr(OPO)/2. In this configuration, instead of estimating the average waveform of the pulses, the lock-in outputs the waveform difference between consecutive pulses of the OPO [Fig. 4(a), black dashed line]. If successive pulses have just an opposite sign, this difference produces the same waveform as that of each pulse, multiplied by two. Indeed, the resulting field-transient difference [Fig. 4(b), green] is remarkably similar to the average field of the CEP-stable state [Fig. 4(b), orange]. This similarity demonstrates the unique selectivity in the OPO output—the ability to switch the CEO frequency (between 0 and fr(OPO)/2) without altering the shape of the pulse. The inset of Fig. 4(b) highlights the similarity of both field oscillations on a shorter time scale. Naturally, the spectral amplitude and phase of the flipping state is also nearly identical to that of the CEP-stable state [Fig. 4(c), green]. A more in-depth analysis and further data on the detection of the flipping state are provided in the supplementary material, Note 5.

It should be noted that the flipping state opens up interesting opportunities to enhance time-resolved coherent spectroscopy. Applying it as a pump beam would modulate any field-dependent interaction with a sample without varying the total power impinging on it. This feature inherently suppresses any parasitic background from, e.g., transient thermal effects or pump-induced strain waves that often overwhelm weak nonlinear signals.55 

Finally, we note that the small quadratic spectral phase of both the measurements already indicates that the output is not perfectly compressed in time. For the relatively narrow spectrum supported by the OPO cavity within regime I, the nonlinear spectral phase only slightly influences the pulse shape in the time domain. However, for broader spectra [e.g., Figure 3(b-Ib)], this phase dependence can significantly elongate the duration of the pulse. This topic is addressed in Sec. III D of the article.

The generation of ultrashort pulses relies on two key components: producing a broadband spectrum and compressing it in the time domain through dispersion control. As shown in Fig. 3(a), the OPO supports various resonant conditions, including the generation of broadband spectra by adjusting the intracavity dispersion and the cavity length. With an increasing OPO output bandwidth, higher-order dispersion within the resonator becomes more influential, although resulting in a chirp of the electric field transient. We demonstrate below how EOS can supply the feedback for temporal compression of the OPO pulse.

For this purpose, we set the cavity length of the OPO to −0.11 μm, generating the most broadband output supported in regime I, as shown in spectrum Ib of Fig. 3(b). The detected electro-optic signal for this configuration constitutes the blue graph in Fig. 5(a). The spectral amplitude, obtained from a Fourier transform of the EOS signal, is shown in Fig. 5(b). Indeed, this spectrum is very similar to the one presented in Fig. 3(b-Ib) when accounting for the response function of the two measurement methods (see the supplementary material, Fig. S8). The main lobe of the intensity envelope in the time domain [Fig. 5(a), inset, blue] is characterized by a full width at half maximum (FWHM) duration of 59 fs. The FWHM of the spectral amplitude is 17 THz , which can optimally support pulses with a 43 fs FWHM duration [Fig. 5(b), inset, black dashed line].

FIG. 5.

Temporal characterization and compression of broadband OPO outputs. (a) EOS transients of the OPO output (blue) and the compressed output (red) in the broadband region of regime I. (b) Spectral amplitudes (solid lines) and phases (dashed lines) of (a). inset: the temporal intensity envelope for both the measurements compared to the bandwidth limit (black dashed line). (c) EOS transient measured for the broadband emission state of the OPO (regime III) temporally compressed via propagation through 3 mm of CaF2. (d) The spectral amplitude of the OPO output operated in regime III (back) and regime I [blue, same spectrum as in (b)].

FIG. 5.

Temporal characterization and compression of broadband OPO outputs. (a) EOS transients of the OPO output (blue) and the compressed output (red) in the broadband region of regime I. (b) Spectral amplitudes (solid lines) and phases (dashed lines) of (a). inset: the temporal intensity envelope for both the measurements compared to the bandwidth limit (black dashed line). (c) EOS transient measured for the broadband emission state of the OPO (regime III) temporally compressed via propagation through 3 mm of CaF2. (d) The spectral amplitude of the OPO output operated in regime III (back) and regime I [blue, same spectrum as in (b)].

Close modal

With this information at hand, we set out to compensate for the intracavity dispersion through propagation in a material characterized by anomalous dispersion at the OPO wavelength, namely, CaF2. Using two windows, each with a 1.5 mm thickness, we obtain the compressed pulse, as shown in red in Fig. 5(a). After compression, the FWHM duration of the intensity envelope [Fig. 5(b), inset] is reduced by 20% to 47 fs – only 4 fs longer than its bandwidth limit. As expected, the spectral phase [Fig. 5(b), red dashed line] is now significantly flatter and exhibits only some residual third-order dispersion. In fact, the direct measurement of the phase, enabled by the EOS of the CEP-stable output, can facilitate a precise correction even for higher-order dispersion, which is typically difficult to perform.56,57

To explore the most broadband output of the OPO, we operate it in regime III. Passing the output pulse through two 1.5 mm CaF2 windows to compensate for second-order dispersion, we obtain the EOS transient shown in Fig. 5(c), presenting a double-peaked waveform typical in the presence of considerable third-order dispersion. Nevertheless, the duration of each of these temporal peaks is only 36 fs FWHM (∼2.7 optical cycles). This value is substantially shorter than the compressed pulse duration obtained in regime I [red lines shown in Fig. 5(a)], 47 fs, and only slightly longer than the corresponding bandwidth limit of 33 fs. The broadband nature of the resonance in regime III becomes even clearer when comparing its spectral amplitude to that of regime I [Fig. 5(d)]: the output of the former (black) is clearly broader than that of the latter (blue). In fact, the spectral amplitude above the noise floor spans more than an octave, ranging from 40 to 90 THz. This illustrates the potential of this source for broadband linear and nonlinear spectroscopy in the MIR.

This potential is further highlighted when considering the SNR of the current EOS measurements. Each time-domain measurement, containing 6500 sampling points, is recorded within an overall acquisition time of just 2 s, demonstrating an excellent SNR of 250 in the spectral amplitude (6.25 × 104 in spectral intensity). This is a testament to the potential of an OPO MIR source in the detection of small perturbations directly in the time domain,53,54,58 such as quadrature squeezing of the electric field.

This work presents and implements a novel concept for measuring the electric-field waveform emitted from a resonant system directly in the time domain. Such a measurement is possible, thanks to the CEP-stability-maintaining nature of the resonant system—a degenerate OPO. In our experiments, the OPO efficiently transforms a NIR frequency comb with only nanojoule-scale pulse energies into a CEP-stable comb in the MIR. This development paves the way to a significant expansion of CEP-stable sources with MHz repetition rates into new spectral bands for which broadband gain materials do not exist. The capability to implement an “optical oscilloscope” for high repetition rate sources in the MIR holds great potential in advancing optical spectroscopy by performing field-resolved measurements. In addition, we have shown that even when the CEP alternates by π in a flipping state, the field transient can be sampled in the time domain via a modified lock-in scheme. The well-controlled variation of the CEP opens up new opportunities to study coherent light–matter interactions through pump–probe spectroscopy.

The supplementary material contains extra notes and figures to strengthen the claims made in this paper. In particular, a thorough description of the experimental setup and the construction of the laser source, a discussion of the wavelength conversion efficiency, and characterization of the OPO system.

The authors thank the Deutsche Forschungsgemeinschaft (DFG) – Project-ID 425217212 – SFB 1432 and the Alexander von Humboldt Foundation for the financial support. R.T. acknowledges the support of the Minerva Foundation.

The authors have no conflicts to disclose.

Hannes Kempf: Formal analysis (equal); Investigation (equal); Writing – original draft (equal). Andrey Muraviev: Investigation (equal); Methodology (equal). Felix Breuning: Investigation (supporting). Peter G. Schunemann: Investigation (equal); Resources (equal). Ron Tenne: Supervision (equal); Writing – review & editing (equal). Alfred Leitenstorfer: Conceptualization (equal); Supervision (equal). Konstantin Vodopyanov: Conceptualization (equal); Supervision (equal).

The data that support the findings of this study are available within the article and its supplementary material.

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Supplementary Material