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Abstract
We report, to the best of our knowledge, the first fully referenced Cr:ZnS optical frequency comb. The comb features few cycle output pulses with 3.25 W average power at 80 MHz repetition rate, spectrum spanning 60 THz in the middle-IR range 1.79–2.86 µm, and a small footprint (0.1 m2), The spectral components used for the measurement of the comb’s carrier envelope offset frequency were obtained directly inside the polycrystalline Cr:ZnS laser medium via intrinsic nonlinear interferometry. Using this scheme we stabilized the offset frequency of the comb with the residual phase noise of 75 mrads.
© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Optical frequency combs in the middle-IR (MIR) spectral range (2–20 µm, 15–150 THz) enable a large number of applications related to the study and non-intrusive diagnostics of complex molecular systems. Notable examples include various versions of dual comb spectroscopy in the molecular fingerprint region [1,2,3]. This powerful method combines parallelism (simultaneous access to 105–106 spectral components) with high measurement speed (video rates), and with high spectral resolution (limited by a Hz-to-kHz linewidth of the combs’ teeth). MIR frequency combs can also be combined with other spectroscopic techniques, e.g. conventional Fourier-transform spectroscopy (FTS) [4], dynamic phase-controlled FTS [5], and photo-acoustic spectroscopy [6]. Additionally, MIR fs laser sources and frequency combs are in great demand for nano-imaging and studies of ultrafast dynamics [7], coherent control experiments, and atto-science [8].
The standard approach to generating MIR femtosecond (fs) pulses and frequency combs is based on the use of χ(2) media for nonlinear down-conversion of readily available near-IR (NIR) fs lasers [9]. Many successful practical implementations of MIR combs rely on mode-locked Yb-, Er, and Tm-doped fiber lasers, which are now mature [10,11,12] and commercially available technologies. Popular schemes for down-conversion of NIR combs include fs optical parametric oscillators (OPO) [3,13,14] and intrapulse difference frequency generation (IDFG) setups [1,2,15]. The significant gap between NIR and MIR wavelengths imposes limitations on the achievable efficiency of the down-conversion process. Therefore, systems based on NIR combs often require additional fs laser amplifiers and nonlinear stages for post-compression of NIR fs pulses.
Conversely, there have been a number of recent reports on fs lasing directly in the MIR, including: Ho:YAG thin-disk oscillators [16], fs lasers and amplifiers based on Cr:ZnS and Cr:ZnSe [17,18], and fs MIR fiber lasers [19]. Specifically, ultrafast Cr:ZnS(Se) laser technology is appealing because it enables direct generation and amplification of few-cycle pulses in the range of 2–3 µm, and is power scalable [20,21]. Therefore, mode-locked Cr:ZnS(Se) lasers are of high interest for the frequency comb community. Proof-of-principle experiments with free-running oscillators were already carried out, shortly after realization of the first mode locked Cr:ZnSe lasers [22].
Importantly, the relatively large 2.5 µm central wavelength of mode-locked Cr:ZnS(Se) lasers greatly enhances the efficiency of down-conversion of the laser’s output in highly nonlinear χ(2) materials with broad MIR transparency. Therefore, super-octave MIR fs pulses with Watt-level power can be obtained in relatively simple and compact lasers setups: the wavelength range of 3–8 µm can be addressed with sub-harmonic OPOs [23,24], while the adjacent range of 6–12 µm can be accessed via IDFG in ZGP crystals with record-breaking efficiency [25]. Further, tandem arrangements of fs Cr:ZnS lasers with GaSe crystals enabled fs pulses with exceptionally broad and coherent instantaneous spectra that cover the whole MIR range [26,27].
The output of a mode-locked oscillator is described by the comb equation fn = n·fR + fCEO where fR and fCEO are the oscillator’s pulse repetition frequency and carrier envelope offset frequency respectively, and fn is the frequency of the nth comb tooth [8,28]. Thus, the transformation of an oscillator to a comb requires measurement and control of two parameters. There are a number of different options for comb stabilization as discussed, e.g., in [10]. The simplest, albeit not ideal, approach is based on stabilization of fR and fCEO to a radio frequency (rf) reference. It is important to note that the fluctuations and changes in fR and fCEO are correlated. Therefore, servo-control of one frequency affects another frequency and vice versa.
Locking of the fR to a rf reference is very straight forward. This frequency can be measured directly with a sufficiently fast photodetector and then controlled by adjusting the length of the optical cavity. The standard scheme for fCEO measurement — termed as f–2f method — is based on a nonlinear interferometer that requires input pulses with a super-octave spectrum [8,28]. A spectral-broadening stage (i.e. a specially designed nonlinear fiber or waveguide) and the interferometric setup itself add complexity to the laser system and make it susceptible to coupling instabilities, external noise, and misalignment. Therefore, robust fCEO stabilization with f–2f interferometry is a demanding task that remains a subject of ongoing research. For instance, it has been demonstrated that octave-spanning oscillators and monolithic fCEO detection schemes can result in frequency combs with improved performance [29,30].
In our recent report [31] we utilized to its full extent the unique combination of laser, optical, and physical properties of polycrystalline Cr:ZnS. This material features superb ultrafast laser capabilities, high χ(2) and χ(3) nonlinearity, and polycrystalline microstructure that enables three-wave mixing of spectrally broad fs pulses via random quasi phase matching (RQPM) [32,33]. Thus, polycrystalline Cr:ZnS laser medium allows for simultaneous amplification of a pulse train from a fs oscillator, spectral broadening of pulses to an octave, and generation of optical harmonics. We termed this regime as “intrinsic nonlinear interferometry” there all the interactions occur in a single pass through a microscopic volume of bulk laser material. This approach to the fCEO measurement is insensitive to fluctuations of the environment and does not require any alignment. In a proof-of-principle experiment, we measured the fCEO of a mode-locked Cr:ZnS laser as easily and reliably as its pulse repetition frequency fR. Here we report the first fully stabilized optical frequency comb based on a mode-locked Cr:ZnS laser with intrinsic nonlinear interferometry.
2. Experimental setup
The schematic of the experiment is illustrated in Fig. 1. The laser part of the setup is very similar to the system described in [31]. A few-cycle Kerr-lens mode-locked Cr:ZnS oscillator is coupled to a single-pass Cr:ZnS amplifier at full repetition rate (fR = 80 MHz). The oscillator and amplifier are based on the designs described in [34,35]. The oscillator is optically pumped by a commercial low-noise single-frequency Er-doped fiber laser (EDFL-SF), while the amplifier is pumped by a conventional EDFL. The Cr:ZnS amplifier is optimized for supercontinuum generation that is enhanced by generation of optical harmonics from second (2f) to fourth (4f). The 2f signal generated in the oscillator’s Cr:ZnS gain element is separated with a broadband dichroic mirror (DM) and is used for the fR measurement. Another 2f signal is generated in the amplifier’s gain element with 0.3 W average power. It is separated by another DM and outcoupled to an auxiliary NIR port. The 3f and 4f signals, which are partially transmitted through one of the MIR high reflectors (HR), are used for the fCEO measurement. The 2f–3f and 3f–4f spectral bands of the continuum are selected with band-pass filters (BP) at 633 nm and 865 nm central wavelengths.
Fig. 1. Experimental setup. EDFL, pump lasers for the fs oscillator and the single-pass Cr:ZnS amplifier-&-nonlinear converter; L, plano-convex lenses; DM, dichroic mirrors (see main text); HR, MIR high reflectors; OC, oscillator’s output coupler. The oscillator’s pump is modulated with an AOM and the length of the optical cavity is controlled with a piezo (PZT). The fR is measured in 2f band with an InGaAs detector (PD). The fCEO is measured in 2f–3f–4f band with a Si avalanche detector (ADP) equipped with a band-pass optical filter (BP). Detected rf signals are fed to the phase-locking electronics and to the test equipment via 50:50 resistive splitters (S). For simplicity, only the end mirrors HR and OC are shown in the oscillator’s cavity; the other four HR mirrors are used to fold the laser beams for footprint reduction.
The fCEO of the oscillator is controlled by pump power modulation with a free-space acousto-optic modulator (AOM), i.e. we relied on a classical scheme that was developed for Ti:sapphire oscillators [8,29,30]. The fR is also controlled in a standard way by a piezotransducer (PZT). The estimated bandwidths of the actuators are, approximately, 250 kHz (AOM) and few hundred Hz (the piezo assembly). Most likely, the bandwidths can be further improved. Commercial phase-locked loop (PLL) controllers are used to stabilize the fCEO and the fR to a 10 MHz rf standard. The piezo assembly is combined with a motorized translation stage (not shown in Fig. 1 for simplicity) and the laser’s control system is programmed for automatic compensation of slow drifts in the oscillators’ cavity. In this way it is possible to keep both parameters fCEO and fR in phase-lock for an extended time. The laser setup was is in a dust-tight case and purged with dry air. Most experiments were carried out at low relative air humidity RH < 1%.
3. Results and discussion
Obtained laser parameters are summarized in Fig. 2. Figure 2(a) shows spectra of pulses measured at MIR output (curves f, f*) and auxiliary NIR output (curve 2f) of the system. The spectrum f* was acquired with the amplifier’s pump turned off, while the spectra f and 2f were acquired with the amplifier active. Comparison of the spectra f and f* confirms significant nonlinear broadening of pulses in the amplifier’s 9 mm long polycrystalline Cr:ZnS gain element. The second harmonic spectrum continuously spans all the way to the fundamental band. Bandwidth measurement of the MIR spectra is limited by the dynamic range of our optical spectrum analyzer (OSA). Most likely the MIR spectrum also spans an octave as was demonstrated in [27,31].
Fig. 2. (a) Measured spectra of pulses presented in log scale. f*, seed pulses; f, amplified pulses; 2f, signal at the second harmonic output of the source. Numbers near the spectra show measured average power (P) and pulse-widths (Δτ(S), derived from the spectra assuming flat phase). Relative humidity (RH) inside and outside of the laser enclosure is <1% and ∼40%, respectively. Dashed line shows noise floor of the MIR optical spectrum analyzer. Insert shows measured beam profile. (b, c) Interferometric autocorrelations (IAC) that correspond to the spectra f* and f, respectively. Δτ(IAC) are pulse-widths derived from the IACs using sech2 fit.
The autocorrelations of pulses, which were measured both with the amplifier’s pump turned off and with the amplifier active, are compared in Figs. 2(b) and 2(c), respectively. We explain the discrepancy between the pulse-widths derived from the spectra (Δτ(S)) and from the autocorrelations (Δτ(IAC)) by (i) uncompensated third order dispersion of bulk optics (about 9000 fs3), and (ii) significant additional chirp that is acquired due to nonlinear interactions in the amplifier’s gain element. We believe that improved pulse metrology (e.g. SHG FROG), will allow us to design and implement an additional stage for re-compression of output pulses and thus achieve a 2-cycle regime of the laser.
Parameters of the pulse train detected at 2f output of the oscillator with a fast InGaAs photo-detector are illustrated in Fig. 3. Optical pumping of the oscillator by a single-frequency fiber laser results in high spectral purity of the generated pulse train. The integrated phase noise of the free-running oscillator (1.8 mrads accumulated in the 102–106 Hz bandwidth) corresponds to a timing jitter of 3.5 ps. Thus, we easily achieve phase-locking of the oscillator’s fR to a rf reference. Comprehensive characterization of the pulse trains emitted by EDFL-pumped few-cycle Kerr-lens mode-locked Cr:ZnSe oscillators, which are similar to their Cr:ZnS counterparts, was carried out in [36].
Fig. 3. (a) Rf spectrum of the NIR pulse train detected at the 2f output of the free-running oscillator. (b) Phase noise power spectral density (PSD) for the free running (solid curve) and locked oscillator. Dashed curve: only the fR lock was engaged; doted curve: both fR and fCEO locks were engaged. The cross-couplings between two servo loops are also illustrated in Fig. 5 and discussed in the main text.
Variations of the fCEO in a free-running oscillator were characterized using the 2f–3f band of the supercontinuum. We obtained the fCEO beat note with 40 dB signal to noise ratio (SNR) using a BP with 55 nm bandwidth at 865 nm central wavelength, as illustrated in Fig. 4(a). We observed a 9 MHz variation of the fCEO during the adjustment of the oscillator’s pump power between 7.2 and 7.7 W. Within this range, the dependence was linear with the slope of 22.3 MHz·W−1 (4.4%·%−1 in relative terms). Reduction of pump power below 7.1 W resulted in modulation instabilities in the pulse train, while increasing pump power above 7.8 W resulted in the appearance of a continuous wave (cw) component in the oscillator’s optical spectrum. The spectrogram in Fig. 4(b) illustrates short-term fluctuations of the fCEO that occur within the range 0.4 MHz (assuming ± 2σ) and, hence, can be compensated by modest 18 mW pump power modulation.
Fig. 4. (a) Rf spectrum of the signal in 2f–3f band of the intrinsic nonlinear interferometer. (b) Spectrogram of the fCEO fluctuations near 57 MHz acquired for a free-running oscillator during 5 s in 2 MHz span with 50 kHz RBW. (c) Measured dependence of the fCEO vs RH inside the laser enclosure.
We measured a close-to-linear dependence of the fCEO on the RH inside the laser enclosure with the slope 0.77 MHz·%−1 (we monitored the fCEO beat note during several hours while the enclosure was slowly purged with dry air). Most likely, the fCEO variation is related to the dependence of the oscillator’s central wavelength (λC) on the air humidity inside the optical cavity: we measured the red shift from λC = 2.34 µm at RH = 40% to λC = 2.4 µm at RH = 0%. This, in turn, can be explained by variation of the intracavity losses due to water vapor absorption occurring in the 2.5–3 µm region. Observations over several days show that the dependence of the oscillator’s fCEO on pump power and air humidity is reproducible (up to few MHz). Thus, the fCEO of a few-cycle Cr:ZnS oscillator can be set to any desired value by a combination of the oscillator’s pump control and air humidity control.
We then engaged the servo control and characterized in-loop performance of the laser. With the conventional pump power modulation scheme we have achieved stable phase-locking of fCEO in the broad range of air humidity RH = 0–40%. After optimization of the PID terms of the PLL controller we obtained the rf spectrum with a small servo bump at about 250 kHz, as illustrated in Fig. 5(a). Measured phase noise PSD is represented in Fig. 5(c) by solid curves. We estimate integrated phase noise of 0.075 rad (shown in Fig. 5(c) by dashed curves). Obtained phase error corresponds to the timing jitter of 95 attoseconds.
Fig. 5. (a, b) In-loop rf spectra of phase-locked fCEO signal acquired with different resolution. (c) Phase noise PSD (solid curves) and accumulated phase error of the signal (dashed curves, integrated from 106 Hz). Black curves: only the fCEO lock was engaged; red curves: both fR and fCEO locks were engaged. Vertical arrows show the couplings from the fR servo loop.
Figures 3 and 5 also show that the cross-coupling between the fR and the fCEO servo loops is insignificant. Engagement of the fCEO servo-loop results in a slight reduction in phase noise of the phase-locked fR signal (see dashed and dotted curves in Fig. 3(b)). The coupling from the fR servo-loop appears in the rf and in the noise spectra of the fCEO signal as weak narrow peaks (marked in Fig. 5(b) and Fig. 5(c) by vertical arrows).
In the next experiment we replaced the BP filter and measured fCEO beatings in 3f–4f band of the supercontinuum. We obtained similar SNR of the beat (about 40 dB) using the BP with 12 nm bandwidth at 633 nm central wavelength. We also phase-locked the fCEO of the oscillator using this 3f–4f beating and obtained the phase error of 0.125 rad accumulated in 1–106 Hz bandwidth. We expect that fine-tuning of the fCEO detection stage (i.e. optimization of the bandpass filter’s central wavelength and bandwidth) will allow for further improvement of the beat note’s SNR. That, in turn, can result in further reduction of the phase noise of the frequency comb.
We do not have a conclusive explanation for the observed build-up of phase noise at Fourier frequencies above 106 Hz. We tentatively attribute it to the excess noise in the rf path and to the limitations of the noise measurements with an rf spectrum analyzer. Therefore, we integrated the phase noise within the bandwidth 1–106 Hz. We consider the obtained results as preliminary because the in-loop measurements usually underestimate the actual phase noise. Comprehensive characterization of the phase noise will require an additional stage for out-of-loop fCEO detection and a dedicated test bench, as described, e.g., in [29,30].
4. Conclusion
We implemented a compact (length×width×height = 400×225×70 mm3) MIR optical frequency comb that outputs few-cycle pulses with 3 W average power at the central wavelength 2.4 µm, and with the spectrum spanning 60 THz at -20 dB level with respect to the main peak. We demonstrate that intrinsic nonlinear interferometry in the polycrystalline Cr:ZnS laser medium is a robust approach for measurement and stabilization of the comb fCEO. Pumping of the Cr:ZnS oscillator with low-noise single-frequency fiber laser at 1567 nm results in a frequency comb with low timing jitter and with low fluctuations of the offset. Therefore, we reliably phase-locked the comb to an rf reference.
The fully-locked comb exhibits good long-term stability: 0.6% power variation was measured during the 7 h work day. Estimated in-loop phase noise — about 0.075 rad integrated from 1 Hz to 1 MHz — is sufficiently low for many practical applications, e.g. for precision dual-comb spectroscopy. The auxiliary 2f output of the comb can be used for its referencing to readily available NIR narrowband lasers and optical frequency standards. The spectrum of the Cr:ZnS laser can be extended to the whole MIR range with high conversion efficiency using OPO and IDFG techniques. The Cr:ZnS laser’s average power can be scaled to tens of Watts in the spinning ring Cr:ZnS(Se) amplifiers.
The obtained results enable a new class of frequency combs and open a new avenue of research and development, including exploration of the limits of comb stabilization via intrinsic nonlinear interferometry, comprehensive noise analysis and determination of fixed points of the Cr:ZnS(Se) frequency combs, as well as the application of Cr:ZnS(Se) frequency combs for spectroscopy.
Note
The experiments were carried out using off-the-shelf laser gain elements, fiber lasers, and PLL controllers. NIR and MIR optical spectra were measured with an ANDO AQ6317B OSA and a Thorlabs OSA207C Fourier transform OSA, respectively. Temporal parameters of MIR pulses were measured with a custom 2nd order IAC with two-photon detection, manufactured by APE. Pulse widths were evaluated using the autocorrelator’s control software. Optical signals were acquired with a TimeBase PD1800 InGaAs photodetector (fR frequency) and a Thorlabs APD430A Si Avalanche photodetector (fCEO frequency). Rf spectra and phase-noise of the detected signals were characterized with a Keysight N9010B signal analyzer.
Funding
DARPA (W31P4Q-15-1-0008); AFOSR (FA9550-13-1-0234); DOE (DE-SC0018378).
Acknowledgments
We thank Vladimir Fedorov at UAB for useful discussions and Randy Smith with Keysight for equipment loans.
Disclosures
S.M. declares competing financial interests.
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