Coherent control of mid-infrared frequency comb by optical injection of near-infrared light

Quantum cascade lasers (QCLs) emitting frequency combs were first demonstrated in 2012¹ and have since become an established technology for fast and broadband mid-infrared (MIR) spectroscopic applications, such as time-resolved studies of microsecond-scale molecular dynamics,² high-pressure and temperature thermometry in shock tubes,³ or high-resolution measurements of molecular spectra.^4–6 Some of their key assets are their low footprint and large optical power compared to other types of MIR combs, especially in the 8–10 μm spectral range that is usually reached via nonlinear frequency conversion.^7–9 Indeed, QCLs are electrically driven devices that directly emit frequency combs in the MIR with a power that can reach 1 W.¹⁰ 

In the context of comb spectroscopy, the use of two mutually coherent combs with slightly different repetition rates, namely dual-comb spectroscopy (DCS), has shown great potential for fast and high resolution measurements without the need for complex and expensive instruments.^11,12 DCS has been well demonstrated with mode-locked lasers in the near-infrared (NIR), but the MIR is more interesting as molecules generally have stronger absorption features, which is advantageous for many applications such as trace gas detection¹³ or isotope ratio measurements.¹⁴ DCS with QCLs is then highly interesting as it provides a compact, low footprint, and high-resolution spectrometer.^4–6 

In DCS, comb stabilization is not strictly necessary thanks to the availability of computational phase correction of free-running lasers.¹⁵ Nevertheless, stabilization of the combs allows accurate frequency referencing and arguably more flexibility, e.g., smaller repetition rates. Moreover, to properly establish QCLs as a source of choice for MIR comb applications such as optical frequency synthesis,^16–18 demonstrating high spectral purity and coherent control can be considered as important as increasing their bandwidth and detecting their offset frequency.¹⁹ 

For QCLs, actuation on the drive-current is the most straightforward way to phase-lock a comb line,^20–22 while the other degree of freedom, namely the repetition rate, is locked by electrically injecting a radio-frequency (RF) signal close to the round-trip frequency.²³ These two handles allow the coherent control of QCL combs and can be used together.¹⁸ However, as for distributed feedback (DFB) QCLs,^24,25 we expect the intrinsic frequency noise of the QCL comb and the stabilization by drive current to involve the same physical process, i.e., current to temperature to refractive index change. In that case, the time scale of the stabilization will always be close to the cutoff of the noise process, thus limiting the performance of the lock. A solution adopted for other types of lasers is to employ another actuator bound by time scales much faster than the noise source such as opto-optical modulation.²⁶ 

Light illumination at another wavelength also enables control of QCLs and can act as an actuator. The technique has been used on DFB-QCLs emitting a single wavelength for applications such as fast switching,²⁷ gain enhancement,²⁸ stabilization,²⁹ and frequency modulation.³⁰ More recently, a QCL comb emitting in the THz range was locked via the intensity modulation of a white light-emitting diode, although with a relatively low bandwidth of 800 Hz.³¹ We also note that the illumination of resonant light enabled the mutual lock between two MIR QCL combs via injection locking.³² However, this only allows mutual locking at the same optical frequency, whereas modulation by off-resonant light offers more possibilities.

Indeed, light illumination at a different wavelength can influence various parameters with different strengths, for example, to allow pure frequency modulation of a DFB-QCL.³³ Moreover, multiple locking schemes could be possible for combs, such as the locking of the repetition rate via current actuation^34,35 combined with the locking of the comb line frequency with NIR light. Finally, the NIR is supported by mature technologies, allowing a wide range of possibilities. Among others, the high modulation bandwidths reaching a few tens of GHz could enable the injection locking of the QCL comb repetition frequency. In light of the above, there is a compelling interest in investigating the potential of NIR light illumination for the coherent control of MIR QCL combs.

In this work, we characterize the influence of NIR light illuminating the front facet of a MIR QCL comb emitting in the 8 μm range. We measure its transfer function at the comb frequencies and compare it to the more conventional electrical actuation. We demonstrate that the limits of electrical actuation for phase-locks can be bypassed using intensity modulated NIR light by tightly locking a QCL comb to a DFB-QCL. Finally, we show that the repetition rate of the QCL can also be injection-locked by intensity modulation of the NIR light.

The experimental setup considered here is presented in Fig. 1 and pivots around a QCL comb. The laser is controlled in current and temperature with a custom-made driver that sets the operation point of the laser to 1200 mA (1.45 times the lasing threshold) and 0 °C. A frequency comb centered around 1305 cm⁻¹ is emitted, with ∼80 lines, a total power of 126 mW, and a repetition frequency of 11.057 GHz. In QCL combs, the comb modes beating together in the Fabry–Perot cavity lead to a measurable voltage oscillating at the repetition frequency.³⁶ Therefore, two wire bonds connect the top of the QCL waveguide near the front and back facets of the laser to RF waveguides on a printed circuit board to efficiently inject and extract the repetition rate independently of the drive current.

A custom-made dichroic mirror produced by ion beam sputtering is placed in the optical comb path to direct NIR light from a continuous wave (CW) laser at 1.55 μm (Optilab, DFB-1550-EAM-12-K) to the front facet of the QCL via the collimation lens (Thorlabs, C037TME-F). The NIR laser has an output power of around 1 mW and can be modulated up to 12 GHz using an integrated electro-absorption modulator (EAM). The beam is aligned into the QCL so as to maximize the frequency response (see Sec. III). The amount of light effectively reaching the front facet is 55% of the emitted power of the NIR laser, and these losses are mainly due to the transmission of the QCL collimation lens at 1.55 μm. The polarization of the NIR light was fixed; however, it did not seem to change the experimental results.

After passing through the dichroic mirror, the comb is mixed on a 50/50 beam splitter with CW MIR light generated by a DFB-QCL (Alpes Laser). The latter is driven at a current of 191 mA and a temperature of 0 °C to emit at a frequency f_cw = 1309.79 cm⁻¹, which is within the spectral range of the frequency comb. A typical optical spectrum of the comb and the DFB recorded with a Fourier transform infrared spectrometer (Bristol 771A-MIR) is presented in Fig. 2. The beating f_b between the comb and the DFB-QCL is recorded on a fast photodetector (VIGO, PV-4TE-10.6).

In Sec. III, we will start by studying the frequency response of the QCL comb when NIR light illuminates its front facet.

We start with the static response before moving on to the frequency dependent response.

First, we slowly vary the NIR power reaching the QCL from 0 to 0.6 mW and measure on an RF spectrum and phase noise analyzer (Rohde & Schwarz, FSWP26) the frequency shift of a comb line f_n via its beating with the DFB-QCL and of the repetition rate f_r, measured directly via the independent channel for RF extraction on the QCL comb. For comparison, we also measure the frequency shifts when the drive current of the QCL comb is varied over 1 mA. These results are presented in Figs. 3(a) and 3(b), where the shift in f_r is scaled by the mode number n = 3550 for better comparability with f_n.

For small variations (1 mA) of the QCL drive currents, the frequencies shift linearly with a superimposed sinusoidal modulation on f_r due to back-reflections.³⁷ The fitted functions to the experimental data (dashed lines in Fig. 3) using a linear model supplemented by a sine wave give an average slope of −210 MHz/mA and −85 kHz/mA for f_n and f_r, respectively, although the slope for f_r is dependent on the drive current (position within the modulation) due to the back reflections. The response to low power NIR light suggests a quadratic trend. Moreover, the shift ratio between f_n and nf_r depends on the alignment of the NIR light on the active region of the QCL comb. The main alignment method used in this article (alignment 1, described in Sec. III B) is to maximize the dynamic response of f_n at modulation frequencies of 100 kHz. Another method would be to maximize the static shift of f_n (alignment 2). In the latter case, f_r shows a sinusoidal modulation that is nearly nonexistent for alignment 1 and varies far less than for alignment 1. For alignment 1, the slopes interpolated at zero power are −315 MHz/mW and −570 kHz/mW for f_n and f_r, respectively.

Figure 4 shows the resulting phase θ_i and amplitude responses Δf_i of the frequencies (f_n, nf_r, and f₀) to modulation of the electrical drive current, ΔI = 200 μA, and the NIR power, ΔP = 50 μW, where Δ represents the peak amplitude of the modulation. Note that Δf_r is scaled by n for better comparison with Δf_n. In addition, the contributions of various components of the characterization scheme (i.e., the FDs and the laser driver) were measured and deducted in order to obtain the laser response as faithfully as possible. Moreover, the responses were measured with two different settings for the ranges [1 Hz, 100 Hz] and [100 Hz, 10 MHz], leading to negligible mismatches at 100 Hz.

Focusing first on the electrical actuation in Figs. 4(a) and 4(c), we observe that the amplitude response Δf_n decreases steadily with the modulation frequency, setting the 3-dB modulation bandwidth to 30 kHz before decreasing sharply after about 200 kHz. The phase response remains flat up to 10 kHz with a 90° modulation bandwidth at 420 kHz, which is coherent with previous tight-locking results.²⁰ Moreover, the response of f_n closely mimics that of DFB-QCLs.^25,40 f_r follows a similar behavior as f_n with a 3-dB and 90° modulation bandwidth of 80 and 840 kHz, respectively. The dashed line in Fig. 4(c) is the phase response of f_n with the laser driver and has a 90° modulation bandwidth of 280 kHz. The difference between Δf_n and nΔf_r gives the response f₀, which has a flatter response in amplitude with a 3-dB modulation bandwidth of 160 kHz. The uncertainty in the measurements of Δf_n and nΔf_r, in particular the slope of the FDs, which depend on the input RF power, induces a large absolute uncertainty on Δf₀. As for the phase, its response is also flatter, reaching −70 near 1 MHz, after which the measurement is no longer accurate due to the lack of sensitivity. The (quasi-) fix point^38,39 increases with modulation frequency from mode number 1850 at 1 Hz to mode number 2200 at 100 kHz.

Although the transfer function of a MIR QCL frequency comb has already been reported in Ref. 35, our measurements highlight a 90° modulation bandwidth, one order of magnitude above what was previously shown. This is in agreement with the response of DFB-QCLs^25,40,41 and other QCL combs, measured directly⁴² or demonstrated in a phase-lock loop.^20,22 This discrepancy with the measured modulation bandwidth could be attributed to the frequency response of the bias-tee used in Ref. 35. Furthermore, we observed in Fig. 3 that modulations of f_r due to back reflections locally change the slope, such that the ratio between Δf₀ and Δf_n and the fix points are expected to be modulated as well.

We now turn to the optical actuation shown in Figs. 4(b) and 4(d). For this measurement, the NIR laser was aligned on the QCL to maximize the dynamic response of f_n at a 100 kHz modulation. We observe a nearly flat phase response for f_r up to 1 MHz, with a small resonance near 33 Hz and the start of a roll-off near 1 MHz. At the resonance near 33 Hz, the amplitude response decreases by a factor 2 and then remains nearly flat apart from the onset of the roll-off near 1 MHz. The 33-Hz resonance also marks a change of regime for f_n due to the crossing of nΔf_r with Δf₀, the latter having a similar response as f_r, although a smaller relative change in amplitude response and opposite phase response. Therefore, for modulation frequencies lower (higher) than 33 Hz, Δf₀ is smaller (larger) than nΔf_r, such that the response of f_n flips sign from 180° to 0° from 1 Hz to 1 kHz. The respective (quasi-) fixed points are at mode numbers 3250 and 3950. An associated dip in the amplitude response of f_n is also visible. Above 1 kHz, the response is flat up to about 50 kHz, where the response increases in phase and magnitude before showing a signature of a roll-off near 1 MHz.

The mechanism causing frequency modulation due to the drive current change is identical to DFB-QCLs, a change of the refractive index.²⁵ In the case of a NIR injection, the strong inter-band absorption in the InGaAs quantum wells (the absorption coefficient α = 6000 cm⁻¹ at 1550 nm) that are part of the active region of the QCL is responsible for the modulation of the refractive index through the generation of carriers in the vicinity of the NIR injection point. In addition, we believe that the response below 30 Hz is dominated by thermal processes (heating of the QCL), as the sign of the responses is equal to drive current modulation and as the optimization of the maximum static shift of f_n causes modulation of f_r as with drive current changes.

From the perspective of locking the QCL comb, the actuation via the NIR power is advantageous as it offers a higher bandwidth than the drive current actuation for all comb frequencies, even when the driver response has been accounted for. It is especially well suited for the stabilization of f₀ if it can be measured. The stabilization of f_n will require a countermeasure against the sign reversal as detailed in Sec. IV. As for f_r, the increased actuation bandwidth is not as interesting given that it can be tightly locked by actuation on the drive current.³⁵ 

We now seek to implement a mutual lock between one comb line f_n of the QCL comb and a DFB-QCL as a proof-of-principle demonstration. The electrical part of the setup is adapted according to the orange path in Fig. 1. The phase fluctuations between the two lasers are obtained by mixing the signal f_b after division by 15 with a synthesized reference frequency locked to the maser. This error signal is injected into two proportional integral differential (PID) controllers (Vescent, D2-125). The output of one PID controller is fed back to the driver of the QCL comb to modulate the electrical current. The output of the second PID controller is fed back, after high-pass filtering with a 2^nd-order custom-designed filter with a cutoff at 1 kHz, to the EAM to modulate the intensity of the NIR CW laser. We also monitor the beat note with the RF spectrum and phase noise analyzer. In this way, slow (⁠$<100$ kHz) corrections of f_n, which cannot be handled by the NIR light due to the sign reversal, are performed by the drive current, while the NIR light extends the available bandwidth and cancels added noise from the drive current, i.e., the servo bump.

Figures 5(a) and 5(b), respectively, show the results of the stabilization of f_b in terms of phase noise and the RF power spectrum. When only electrical actuation is considered, we observe two bumps in the phase noise power spectral density (PSD). The first is due to the limit of the integrator at about 100 kHz, while the second near 300 kHz is the servo bump, which nearly coincides with the 90° modulation bandwidth of the combined driver and laser [see dashed blue line in Fig. 4(c)]. The white phase noise from 1 Hz to about 100 Hz is due to the reference oscillator, which, due to the division by 15, has its contribution increased by 23 dB. The resulting RF spectrum shows a Gaussian shape topped with a coherent peak.

The addition of the optical actuation reduces the phase noise PSD to a value in the order of −80 dBc/Hz, below the β-line,⁴³ for all Fourier frequencies. As a result, the integrated phase noise between 1 Hz and 10 MHz is decreased from 2.16 rad to 200 mrad [see inset in Fig. 5(a)]. The electrical servo bump is eliminated, while a new servo bump appears at 2 MHz. This fast bandwidth allows us to employ a lower division ratio of 4: the residual phase noise from 1 Hz to 3 kHz is set by the reference oscillator. At higher frequencies, we believe that the mismatch between the reference voltages of the two different servo controllers added noise to the system. Moreover, the bumps near 3 kHz coincide with the cutoff frequency of the high-pass filter. Furthermore, optimization of the electronic components could improve the lock and decrease the integrated phase noise further, including the use of a single dual-output servo controller. We also believe the stabilization bandwidth could be increased by shortening all the cables, fibers, and free-space paths. In terms of spectrum [Fig. 5(b)], the power in the coherent peak improves by 20 dB. The height of the pedestal is decreased by 15 dB, such that the difference between the coherent peak and the top of the pedestal is 50 dB at a resolution bandwidth (RBW) of 100 Hz, or about 25 dB more than in Ref. 20 at a 500 Hz RBW. The inset shows a zoom over the peak at a 1 Hz RBW with a signal-to-noise ratio (SNR) of 70 dB.

In parallel, the repetition frequency of the comb is stabilized by RF injection locking using a resonant RF signal with 15 dBm of power delivered by a signal generator (Rohde & Schwarz, SMF100A) referenced to a maser. This RF signal is sent to the QCL via the dedicated channel for RF injection. Therefore, both degrees of freedom are tightly locked simultaneously, with low residual phase noise. The electrical injection of the repetition rate is the usual approach to its stabilization. However, the previous results suggest that the repetition rate could also be injection-locked by modulating the NIR light.

We thus modulated the EAM of the NIR laser near the repetition frequency of 11.06 GHz while monitoring the generated voltage modulation of the QCL via the dedicated RF extraction port on an RF spectrum analyzer. At low NIR power and close to resonance (1 MHz offset), the modulation frequency was picked up by the QCL, which thus acted as a NIR detector [see Fig. 6(a)]. By slightly increasing the average NIR power with an amplifier to 1.5 mW at the QCL and the RF power on the EAM to 17 dBm (estimated modulation depth close to 100%), we were able to injection-lock the repetition frequency to the synthesizer and obtain the resolution-limited signal shown in Fig. 6(b) at 50 Hz RBW. We obtained a lock range of a few kHz when scanning the modulation frequency across the free running repetition frequency [see Fig. 6(c)]. The phase noise PSD was reduced up to a Fourier frequency of about 3 kHz compared to the free-running case [Fig. 6(d)]. We expect that larger locking ranges could be achieved when using more NIR power, which will be one of the studies we present in another dedicated article.

In this article, we used a low power NIR CW light illuminating the front facet of a MIR QCL frequency comb as an optical actuator for the phase stabilization of a comb line and as a means to achieve coherent injection locking of the repetition rate. First, by characterizing the response of the QCL, we showed that intensity modulation of the NIR light offers a higher modulation bandwidth compared to conventional drive current modulation. Then, we implemented a stabilization scheme exploiting the NIR light to extend the locking-bandwidth from 300 kHz to over 2 MHz, which resulted in an increase of the SNR by 35 dB and an integrated phase noise as low as 200 mrad. Finally, we showed that the QCL can act as a detector of NIR light modulated at a frequency of 11 GHz and that it can be injection-locked in such a way.

We believe that the tighter mutual stabilization enabled by the high bandwidth of the NIR light could lead to higher sensitivities through coherent averaging in DCS,^22,44 which is currently one of the main applications of QCL combs. In this regard, a comprehensive comparison with the performance of computational coherent averaging¹⁵ is necessary. The high bandwidth could also allow the locking of enhancement cavities for further improvement of sensitivity.⁴⁵ Moreover, high spectral purity in the MIR is relevant for a variety of applications such as quantum control of molecules,⁴⁶ tests of fundamental physics^47,48 and, generally the study of molecules via high-resolution spectroscopy.^5,49,50 Therefore, we expect our results to facilitate the application of QCL frequency combs in the MIR.

As a further outlook, we anticipate that other wavelengths³³ could be more suitable for orthogonal control without sign reversal of the comb properties such as the offset and repetition frequencies, while perhaps they could also be used to dynamically tune laser parameters such as dispersion, gain, or nonlinearity. Faster modulations from 10 MHz to a few GHz could be investigated as a way to achieve (pure) frequency modulation of the comb. To keep the compactness of the device and its low footprint, light could be delivered by fiber or directly generated and modulated on the same chip if low power is sufficient. Then, full optical control of the QCL comb merely driven by a battery could be envisaged. Optical control could also be investigated for interband cascade lasers.⁵¹ Moreover, the recent work on free-space communications using QCL combs⁴² inspires the adaptation of injection locking of the QCL by NIR light for direct conversion of NIR telecommunication streams to MIR signals. We believe that increasing the injected optical power could increase the locking range of the repetition rate to a sufficient level for this application. Further work including theoretical and numerical investigations of the laser dynamics^52,53 is necessary to understand the full potential of controlling QCLs via optical means.

We acknowledge Stéphane Schilt for his support in the early stage of the investigation. We acknowledge Alpes Laser for providing the DFB-QCL used in this work. We acknowledge funding from the Schweizerischer Nationalfonds zur Förderung der Wissenschaftlichen Forschung (Grant No. 40B2-1_176584).

The authors have no conflicts to disclose.

Kenichi N. Komagata: Conceptualization (lead); Formal analysis (lead); Investigation (lead); Methodology (lead); Validation (equal); Visualization (lead); Writing – original draft (lead). Alexandre Parriaux: Conceptualization (supporting); Formal analysis (supporting); Investigation (equal); Methodology (equal); Validation (equal); Visualization (equal); Writing – original draft (supporting); Writing – review & editing (lead). Mathieu Bertrand: Formal analysis (equal); Validation (equal); Writing – review & editing (equal). Johannes Hillbrand: Resources (equal); Writing – review & editing (supporting). Mattias Beck: Resources (equal); Writing – review & editing (supporting). Valentin J. Wittwer: Funding acquisition (equal); Resources (equal); Supervision (equal); Validation (supporting); Writing – review & editing (equal). Jérôme Faist: Funding acquisition (equal); Resources (equal); Supervision (supporting); Writing – review & editing (supporting). Thomas Südmeyer: Funding acquisition (equal); Supervision (equal); Writing – review & editing (equal).

The data that support the findings of this study are openly available in EUDAT B2SHARE at http://doi.org/10.23728/b2share.4c30e6bcadd3443d8d49e00200cbd7b5.⁵⁴