Open Access
Add to BibSonomy
Abstract
Dual comb spectroscopy (DCS) is a broadband technique offering high resolution and fast data acquisition. Current state-of-the-art designs are based on a pair of fiber or solid-state lasers, which allow broadband spectroscopy but require a complicated stabilization setup. Semiconductor lasers are tunable, cost-effective, and easily integrable while limited by a narrow bandwidth. This motivates a hybrid design combining the advantages of both systems. However, establishing sufficiently long mutual coherence time remains challenging. This work describes a hybrid dual-comb spectrometer comprising a broadband fiber laser (FC) and an actively mode-locked semiconductor laser (MLL) with a narrow but tunable spectrum. A high mutual coherence time of around 100 seconds has been achieved by injection locking the MLL to a continuous laser (CW), which is locked on a single line of the FC. We have also devised a method to directly stabilize the entire spectrum of FC to a high finesse cavity. This results in a long term stability of 5 × 10−12 at 1 second and 5 × 10−14 at 350 seconds. Additionally, we have addressed the effect of cavity dispersion on the locking quality, which is important for broadband comb lasers.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
The invention of broadband coherent frequency combs (FC) [1–3] has enabled new schemes for broadband spectroscopy [4,5] at a wide range of wavelengths. The availability of highly stable FC has enabled a related, highly versatile spectroscopy scheme known as dual-comb spectroscopy (DCS) [6–8]. DCS offers significant advantages over other broadband spectroscopy methods, mainly in terms of high-frequency resolution, fast data acquisition, and mechanical stability due to the absence of any moving part [9]. DCS involves two frequency combs with slightly different repetition rates. One laser interrogates a sample such that the complex spectral response (amplitude and phase) of the sample gets mapped onto that laser spectrum, which is consequently sampled by the second laser, generating beats in the RF domain at multiples of the difference between the repetition rates. The sample properties are detectable on the RF spectrum. Signal-to-noise ratio (SNR), defined as the ratio between the signal peak-to-peak strength to the background noise, increases with the data measurement time as $\tau ^{1/2}$ so that long data acquisition times are desirable when the signal to be measured is weak. However, during the long measurements, the lasers need to remain coherent; hence, long mutual coherence is imperative.
DCS was studied with many laser platforms. Erbium-doped fiber laser systems and semiconductor laser sources are dominant in the NIR wavelength range. Micro resonators based systems offer integrated platforms and may be dominant in the future. However, currently, they lack cavity-length and wavelength tunability. The extension of DCS to the mid-IR range was demonstrated with quantum cascade laser sources [10]. Other solutions include silicon nanophotonics waveguide [11], optical parametric oscillators (OPO) [12], and intra-pulse difference frequency generators [13], which extend DCS systems to arbitrary wavelengths while preserving the coherent properties of the parent combs. Systems with various degrees of mutual coherence ranging from two free runnings [14–17] to phase-locked combs (with and without locking to an external reference) [10,18], having different spectral resolutions, have been demonstrated. DCS systems based on an all-fiber platform were also demonstrated where OFCs generated from a single fiber laser so that the common noise or the drifts are cancelled [19,20]. Different DCS schemes have been used to perform numerous spectroscopic experiments studying many materials [21–26], thereby establishing the technique as a major tool for broadband spectroscopy.
Fiber-based erbium doped laser sources or Ti:Sa mode-locked lasers require an octave-wide spectrum that enables the well-known f-2f stabilization scheme of the carrier-envelope offset [27–29]. The repetition rate is stabilized by locking the laser cavity length either to an optical reference or a stable radio-frequency (RF) source [30]. A stable CW laser can synchronize both lasers separately to attain mutual coherences between two combs. With this approach, mutual coherences up to 1s have been attained [31]. Further enhancement in the mutual coherence time has been achieved using various numerical means [14,31]. Another scheme in which two CW lasers were used to measure the relative fluctuations of the repetition rate and carrier-envelope offset (CEO) of the two DCS lasers, with the result used to feed forward to actuators like an acoustic optic modulator and cavity length was demonstrated with mutual coherence times of up to 2000 seconds [32,33].
An interesting DCS structure where a single semiconductor mode-locked integrated external-cavity surface-emitting laser (MIXSEL) generates two combs at slightly different repetition rates was demonstrated by Keller and co-workers [34]. These two combs are naturally highly coherent, which avoids all locking electronics. Nevertheless, the laser cavity and the pump laser must be stabilized to an absolute reference, such as an optical cavity or some atomic transition, to ensure long-term stability. The advantages of semiconductor lasers include their availability at a wide range of wavelengths and the potential for chip-scale integration [35].
Hybrid designs of DCS combine the various advantages of two different laser systems. Hybrid DCS configurations have been realized by several groups [35,36]. However, in most reported solutions, it is challenging to establish high mutual coherences when the two lasers are very different.
This paper describes a new hybrid DCS system comprising a broadband fiber laser (FC) whose spectrum covers 1500-1600 nm and an injection-locked semiconductor active mode-locked laser (MLL) whose spectrum is narrow but tunable from 1480-1570 nm. We devised a new locking scheme based on a CW laser that is locked to one comb line of the FC while also injection-locking the MLL, simplifying the stabilization system. The dynamical response of the semiconductor laser enables efficient injection locking, which is key to the long 100 seconds mutual coherence time we have achieved without any numerical phase correction. The narrowband MLL spectrum allows for high optical power per comb line and its tunability enables scanning its central frequency over the entire FC broadband spectrum without compromising the mutual coherence [37]. The external cavity bulk MLL configuration also offers tunability of the repetition rate compared to the chip scale design, which is required for certain applications [38,39].
Absolute stability was achieved by directly stabilizing a comb on a high-finesse cavity operating in the transmission mode. Locking in the transmission mode does not require all the comb lines to be resonant with the cavity mode, as in the case of detection in reflection, which lifts a significant restriction on the cavity length. The frequency fluctuation of the MLL was measured by transmitting its output through the high finesse cavity while it was locked to the FC. The measurement served to feed the feedback loop that corrected the frequency of the FC. The linewidth of each MLL comb line was evaluated by mixing it with another cavity-stabilized CW laser (with a linewidth of less than 100 Hz). The heterodyne beat showed a reduction of the linewidth of the MLL mode from 880 kHz, in the free-running case, to 17 kHz when the system was fully locked. The long-term stability of the system was evaluated from the Allan deviation of the beat signal yielding stability of $5 \times 10^{-12}$ at 1 second and $5 \times 10^{-14}$ at 350 seconds. Time domain characterization of the MLL pulses (whose repetition rate was 250 MHz) yielded a jitter of 0.13 ps.
The system we devised was used to measure the absorption spectrum of rubidium atoms with a high SNR owing to the long 100 seconds mutual coherence time of the system. Since the system operates in the 1550 nm regime, the two combs had to be amplified, and the frequency doubled to 780 nm. This, in principle, can be avoided with two 780 nm combs, further simplifying the DCS system. High absolute long-term stability and the long mutual coherence of the system make it suitable for spectroscopy of a wide range of materials that exhibit weak transitions.
2. Experimental set-up
Figure 1 describes a general schematic of the hybrid dual-comb spectroscopy apparatus. A detailed description of the setup is presented in Fig. S1 in the Supplement 1. A commercial fiber laser FC (Menlo systems, FC1500-250-ULN, covering the spectral range of 1500-1600 nm, with a repetition rate, $f_{rep}$ of 250 MHz, is one of the lasers. The second is a semiconductor mode-locked laser, MLL (gain chip, SAF 1126 from Thorlabs), whose structure is shown in the orange-shaded part of Fig. 1. A phase-locked oscillator (PLO) referenced on an RF signal derived from the FC repetition rate generates the drive signal to the MLL thereby determining its repetition rate. The laser employs a piezo-mounted mirror in the cat-eye configuration and an intracavity interference filter. By varying the intra-cavity interference filter, the center wavelength can be tuned from 1480 nm to 1570 nm, maintaining an instantaneous bandwidth of 25 GHz. The MLL repetition rate $\Omega$ is offset from the FC by $\delta f_{rep}$ of 4.5 kHz. The MLL is injection-locked by a CW external cavity semiconductor laser. That CW laser is mixed with the FC to form a beat with one of the FC comb lines. This heterodyne beat which is an RF signal contains information about the frequency fluctuation of the FC and the CW laser. This signal is mixed with the local oscillator and detected by a phase detector. The filtered, mixed-signal has a derivative profile that locks the CW laser by applying a fast-feedback to an acoustic-optic modulator, AOM2, and slow feedback to the piezo-mounted mirror of the CW laser cavity.
Fig. 1. Schematics of the hybrid set-up for dual-comb spectroscopy. (a) A commercial FC is used to stabilize a CW laser which injection locks the MLL. This transfers the fluctuations of the FC to the carrier envelope offset (CEO) of the MLL. A phase-locked oscillator (PLO) referenced on an RF signal derived from the FC repetition rate generates the drive signal to the current of the MLL thereby determining its repetition rate. The FC is stabilized to a high finesse cavity which provides long term stability. AOM: Acoustic-optic modulator, BT: Bias-Tee, PM: Phase modulator, HFC: high finesse cavity (b) A detailed schematic of the MLL is shown in the orange shaded area. BS: Non-polarizing beam splitter, IF: Interference filter, PM: Piezo mounted mirror. (c) Both FC and MLL are amplified and frequency doubled by a periodically poled lithium niobate crystal (PPLN). The frequency doubled FC interrogates the rubidium cell and is combined with the second harmonic of the MLL to generate the RF beats.
The MLL was phase modulated at 12 kHz by an electro-optic modulator and transmitted through the cavity, HFC, at the output of which it was demodulated by a lock-in amplifier. The high finesse cavity (HFC) is a commercial cavity from Stable Laser Systems. Its finesse is 350,000, and the free spectral range is 6 GHz. The cavity is made of a low thermal expansion material and is temperature stabilized and placed inside a vacuum chamber with a pressure of $4 \times 10^{-9}$ bars. The frequency fluctuations of the cavity resonance frequency are of the order of $10^{-14}$ Hz up to 100 seconds (measured at 1550 nm), which are negligible compared to the kHz range frequency fluctuations we have measured. The error signal feeds the feedback control of the FC CEO through AOM1 and provides slow feedback on the length of the FC. The fully stabilized MLL emits pulses with a duration of 20 ps.
The dual-comb interferometer was used to measure the Doppler broadened spectrum of the rubidium atoms at 313 K. Both the FC and MLL were tuned to 1560 nm and were amplified by an erbium-doped fiber amplifier. The amplified signals were frequency doubled by a temperature stabilized periodically poled lithium niobate crystals (PPLN) with an efficiency of $25 {\% }$ to generate a second harmonic at 780 nm. The frequency-doubled FC was focussed through the 75 cm glass cell with rubidium atoms held at 313 K. After interacting with the gas cell in a single-pass configuration, the frequency-doubled FC was combined with the frequency-doubled MLL and detected by a photo-detector, PD, FPD610-FC-VIS. The detected signal was filtered, amplified, and digitized. A fast Fourier transform was computed, and the amplitude of the spectrum was retrieved.
3. Results
The MLL is injection-locked by a tunable CW laser which controls the carrier-envelope offset (CEO) of the MLL. The CW laser is stabilized on a single tooth of the FC. This allows the CEO of the MLL to follow the frequency fluctuation of the FC that eliminates the need to stabilize the CEO using the conventional f-2f scheme [27–29] which requires an octave wide spectrum. An advantage of locking the CW laser to the FC is that the MLL central frequency can be tuned with a step of 125 MHz, which is half of the repetition rate of the FC. The tuning can be finer yet by introducing an additional acousto-optic modulator (AOM) in the setup. For the pulsed-mode operation, the gain chip of the MLL is directly modulated by an RF signal which is derived from the phase-locked oscillator (PLO). The RF frequency defines the repetition rate of the MLL. The PLO is referenced, in turn, on an RF signal extracted from the FC’s repetition rate. This allows the MLL to continuously follow the timing and phase fluctuations of the FC in real time, yielding the long coherence times between the two combs. The DC bias controls the bandwidth of the MLL spectrum. The maximum spectral width of the MLL obtained with various settings of DC bias is 25 GHz. We tuned the DC bias such that the laser spectrum optimally overlaps the rubidium spectrum.
Conventionally, mutual coherences between the DCS laser sources are attained by optical injection locking or by optical referencing two combs to a cavity-stabilized CW laser. However, some of the laser sources, fiber lasers, for example, cannot be injection-locked efficiently due to their dynamic response. Also, the optical reference scheme requires a highly coherent CW laser since the linewidth of that laser determines the mutual coherence. The system we present overcomes this restriction as the mutual coherence depends only on how well the CW laser is locked on one of the FC comb lines and follows the time and phase fluctuations. This is explained in detail in the Supplement 1.
3.1 Stabilization and characterization of the hybrid DCS
To attain absolute stability, the MLL was phase modulated at 12 kHz and transmitted through the cavity at the output, of which it was demodulated by a lock-in amplifier. Around the cavity resonance, the phase of the laser lines changes by $\pi$ yielding a phase difference between the resonant mode and its modulated components forming a dispersive error signal with a zero-crossing as shown in Fig. 2(a). Since the MLL is stabilized on the FC, it carries the same noise as the FC. The error signal generated by probing the MLL through the cavity is then compensated by applying feedback to the FC to reduce the noise.
Fig. 2. Stabilization and characterization of the DCS system The MLL is locked on the FC and passes through the high finesse cavity. (a) Measured cavity transmission (blue), an error signal (yellow), and a locked cavity transmission signal (red) of the MLL. (b) Calculated slope of the error signal as a function of modulation frequency $\Omega$ and modulation depth $\beta$. A red star signifies the experimentally used parameters. (c) Measured heterodyne beat between the MLL and a cavity-stabilized CW laser, characterizing the MLL stability. The linewidth of the MLL, which represents the short-term frequency noise, reduced from 880 kHz in the free-running case (shown in the inset) to 17 kHz for the fully locked system. (d) The Allan deviation showing long term stability of $5 \times 10^{-12}$ at 1 second and $5 \times 10^{-14}$ at 350 seconds. (e) Timing jitter of the MLL, measured in terms of the dependence on the harmonic number of the noise index, which is the ratio of the integrated noise skirt to the peak power of the corresponding harmonic. (f) The power spectrum of the 48th harmonic under locked and unlocked conditions.
The error signal fed the feedback control of the FC CEO through AOM1 and provided slow feedback on the length of the FC. The free spectral range of the cavity is 6 GHz, which means that every 24th mode of the MLL passes through the cavity and contributes to the error signal. Fig. 2(b) shows the simulation result where the slope of the error signal is calculated from the eqn. (2) and plotted as a function of the modulation frequency and depth. A red star in the figure represents the values used in the experiment. Stabilization using the transmission mode was previously demonstrated for CW lasers [40] while for a pulsed laser, a single line was used to lock the repetition rate of the entire comb [41]. The present system has contributions of multiple comb lines stabilizing the entire comb spectrum with a high signal-to-noise ratio (SNR). Section 3 of the supplementary presents a detailed calculation of the characteristics of the generated error signal.
To quantify the quality of the locking scheme, we performed a heterodyne measurement of the MLL with a second CW laser, which was locked to the high finesse cavity and had a linewidth below 100 Hz. This yielded short-term frequency noise. For the free-running MLL, the linewidth of the heterodyne beat was around 880 kHz, while under a stabilized condition, the linewidth reduced to 17 kHz, as shown in Fig. 2(c). The heterodyne beat frequency between the MLL and the CW laser was recorded over 500 seconds using a frequency counter, FXE65, to calculate the Allan deviation (AD) [42], as shown in Fig. 2(d). The stability was found to be $5 \times 10^{-12}$ at 1 second and $5 \times 10^{-14}$ at 350 seconds.
The stability of the MLL was also characterized in the time domain by measuring its timing jitter using the Van der Linde technique [43]. Timing jitter of a pulse train constantly broadens the spectrum of harmonics of the repetition rate. Each harmonic contains a signal and a noise skirt which results from both amplitude and phase fluctuations. The amplitude noise grows as $n$, and the harmonic number and the phase noise contribution grow as $n^2$. Therefore, a high harmonic must be observed to extract the phase noise contribution. The timing jitter ($\Delta t$) of a pulse train is given by $\Delta t/T =\frac {1}{2\pi n} [(\frac {P_B}{P_A})\frac {\Delta f_J}{\Delta f_{res} }]^{1/2}$ where, $P_A$ and $P_B$ are the spectral powers in the main peak and the noise skirt, $\Delta f_J$ is the width of the noise skirt, $\delta f_{res}$ is the resolution bandwidth and $T$ is the periodicity of the pulse train. The noise index for each harmonic is defined as the ratio between the integrated power of the noise bands and the peak power of the corresponding harmonic. Figure 2(e) shows the noise index as a function of the harmonic number. Figure 2(f) shows the power spectrum of the 48th harmonic (recorded with a resolution bandwidth of 1 Hz) of an unlocked and a locked MLL. The calculated timing jitter of the locked MLL (whose repetition rate was 250 MHz) was 0.13 ps which is more than a ten-fold improvement over the unlocked case.
3.2 Effect of the cavity dispersion on stabilization
Direct interrogation of a broadband comb through a high finesse cavity shifts the spectral position of the far modes of the laser from its equidistant position due to the cavity dispersion [30]. This shift results in the broadening of the error signal reducing its slope when the contributions from all the modes are combined. Stabilization in transmission mode is more sensitive to cavity dispersion as the carrier and modulated signal are spectrally very close to each other.
To study this effect, we consider a frequency comb field with a repetition rate, $\omega _{rep}$ and carrier-envelope offset, $\omega _{ceo}$. The electric field can be written as,
where, the carrier frequency, $\omega _l = l \omega _{rep} + \omega _{ceo}$. FM modulating a comb at a frequency $\Omega$ with a modulation depth, $\beta$, yields an error signalTo study the impact of dispersion on the error signal, we have added a mode-dependent shift, $\Delta _l$, to the cavity resonance frequency $\omega _{cav,l}$. The cavity transmission function $T_l(\omega )$ for the $l^{th}$ comb line is written as,
Depending on the level of dispersion, a linear shift of the resonance position as a function of the mode number relative to the central line is added to the calculation. The error signal for different strengths of dispersion is shown in Fig. 3(a), where $\Delta$ represents the mode shift from an equidistant position of the far modes; the error signal’s slope decreases with the dispersion level. The error signal width dependence on the dispersion level is presented in Fig. 3(b). The dispersion effect on a broadband signal is detailed in section 3 of the Supplement 1.
Fig. 3. Cavity dispersion effect on the error signal in a broadband comb laser. (a) The cavity dispersion induces a cavity mode shift ($\Delta$) from the equidistant position. The error signal is calculated for different $\Delta$ for the edge modes and shows the broadening of the error signal width with increased dispersion strength. $\kappa$ represents the 20 kHz cavity linewidth. (b) Calculated error signal width as a function of the cavity resonance shift ($\Delta$) of the edge comb modes.
The present experiment used the relatively narrow band, 25 GHz, MLL, which is stabilized on the FC to generate the error signal, stabilizing the FC. This helps to avoid the detrimental effect of cavity dispersion.
3.3 Dual comb spectroscopy with the rubidium atoms
The mutual coherence of the system we constructed was characterized by measuring the rubidium Doppler spectrum at 313 K with different integration times. Both the FC and MLL tuned to 1560 nm and were amplified before frequency doubling to 780 nm. The frequency-doubled FC was focused on the rubidium cell and combined with the frequency-doubled MLL. The beat between them reveals the Doppler profile of the rubidium atoms, as shown in Fig. 4(a). In Fig. 4(a), the beat spectrum (blue) and the red curve represent the averaged rubidium spectrum extracted from 200 sets of 0.5 s (for a total of 100 seconds) time trace data. The pedestals in Fig. 4(a) are due to the sidebands originating from the two stabilization units. Each stabilization unit comprises two servo loops to compensate for the fast and slow fluctuations. Various transition peaks of rubidium isotopes are isolated and shown in Fig. 4(b). Figure 4(c) represents the 100 seconds averaged rubidium spectrum, extracted after the background was subtracted from Fig. 4(a). This is represented by blue points. We fit four Gaussian functions to the data shown in the red line. The model used is given by $f(x)=-a_1 e^{-(x-b_1 )^2/c_1^2} -a_2 e^{-(x-b_2 )^2/c_2^2} -a_3 e^{-(x-b_3 )^2/c_3^2} -a_4 e^{-(x-b_4 )^2/c_4^2}+d$, where, $a_1$, $a_2$, $a_3$ and $a_4$ are the amplitude strength, $b_1$, $b_2$, $b_3$ and $b_4$ are the central frequencies of the peaks and are the fixed parameters given by the transition frequencies of the rubidium atoms [44,45]. $c_1$, $c_2$, $c_3$ and $c_4$ are the width of the peaks. Their initial values are the known Doppler broadened widths of the various transitions. These values are consequently optimized to get the best fit. $d_1$ represents the offset of the fit.
Fig. 4. Dual-comb spectroscopy of rubidium atom. (a) DCS spectrum containing rubidium spectrum is shown (blue lines) for an averaged data integration time of 100s. The Doppler broadened spectrum of rubidium atoms is extracted from the beats (red). b) Energy level diagram of $^{87}\text {Rb}$ and $^{85}\text {Rb}$ isotopes. (c) Rubidium spectrum for an averaged integration time 100 seconds (blue points) after the background was subtracted and fitted by four Gaussians (red). A Doppler broadened spectral width of 535 MHz (FWHM) at 313 K is extracted. (d) The SNR as a function of different data integration times. The inset represents the rubidium spectrum from 500 ms data trace. The coherence of the system is deduced from the slope of 0.51 indicating the expected square root behavior of the SNR on the measurement time.
Due to the technical limitations of the data acquisition system, we measure 200 sets of 500 ms long-time traces of the interferogram. This was converted into a Fourier signal, and the averaging was performed in the Fourier domain. A Doppler width of 535 MHz (FWHM) is extracted from the absorption spectra of $^{87}\text {Rb}$ and $^{85}\text {Rb}$ after averaging for 100 seconds, as described in Fig. 4(c). The calculated SNR for different integration times is shown in Fig. 4(d). The slope of 0.51 confirms the square root dependence of the SNR on the integration time, demonstrating the coherence between the two laser systems.
The figure of merit ($F$) is defined as the product of the SNR and the number of effective comb lines ($M$) [8]. In our case, $F= 10^3$ for an $SNR= 10$ and $M=100$. The figure of merit can be increased by increasing the optical bandwidth. One method would be to replace the gain chip of the external cavity semiconductor laser with a two-section device where one (short) section acts as a saturable absorber under reverse bias. This is standard in monolithically mode-locked lasers [46]. The saturable absorber shortens the pulse significantly, and correspondingly, the bandwidth increases. A second scheme adds a dispersion compensation element within the pulsed laser cavity [47,48]. Another way to improve F is to increase the SNR. One way is to heat the Rb vapor, which increases the vapor pressure and the beam diameter through the vapor cell. The SNR can be further improved by optimizing the power of the optical beams in each arm of the DCS setup.
The primary source of noise in our overall system is the low optical power of the semiconductor laser. The total output power from the semiconductor laser is 5 mW. Most of this power is transferred to the high finesses cavity to attain a strong error signal for the cavity lock. The obtained optical power of the frequency-doubled light is around 5 mW at 780 nm. The optical bandwidth of this laser is around 25 GHz, meaning the power is distributed to 100 spectral lines. The optical power reaching the detector is less than 250 nW per comb mode. Due to all these constraints, our experiment greatly benefits from the narrowband detection as the power per mode decreases with the increase in optical span.
Mutual coherence is independent of the absolute stability of the FC. However, long data acquisition times demand that the long-term FC frequency fluctuations be much lower than the sample absorption width so as not to degrade the SNR. This limitation is severe for Doppler-free spectroscopy. The direct locking of a pulsed laser to a high finesse cavity, which we have implemented, simplifies the stabilization setup and ensures high long-term absolute stability. Since the error signal is generated in the transmission mode, the restriction that all comb laser lines have to be resonant with the cavity mode (which is the case in reflection mode) is eliminated. The repetition rate of the comb is tuned such that some lines at the spectrum edges are resonant with the cavity mode and contribute to the error signal. This led to the stabilization of the entire comb spectrum.
4. Conclusions
In conclusion, we have constructed a hybrid dual-comb spectrometer with a broadband fiber comb laser and an injection-locked MLL. Different locking schemes established a mutual coherence time of 100 seconds between the two. The maximum measured mutual coherence time is set by the limitations of the electronic digitizer, whose storage capacity is insufficient for measurements longer than 100 seconds. We have demonstrated a method to directly reference the DCS set up to a high finesse cavity reaching stability of $5 \times 10^{-12}$ at 1 second and $5 \times 10^{-14}$ at 350 seconds, which is good enough for DCS applications. However, the absolute stability can be further improved by increasing the bandwidth of the cavity lock. Moreover, we have addressed the impact of cavity dispersion on stabilizing broadband sources. We have shown that the dispersion broadens the error signal when the contribution of far comb lines is combined, reducing the stabilization quality. However, generating several error signals from different comb spectral regions can mitigate the effect of cavity dispersion as this limits the number of modes contributing to a single error signal and reduces the impact of the broadband spectrum.
The spectrum of the MLL can be broadened by using a gain chip containing a saturable absorber or by introducing a dispersion compensation element within the external cavity. Two such semiconductor lasers can be used in a DCS setup and injection-locked with a single CW laser, simplifying the stabilization setup as the lasers will be mutually phase coherent without any active stabilization. However, the CW laser must be stabilized to attain absolute long-term stability. This can be done, for example, by the conventional Pound-Drever-Hall locking scheme [49].
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
Supplemental document
See Supplement 1 for supporting content.
References
1. T. Udem, J. Reichert, R. Holzwarth, and T. W. Hänsch, “Absolute optical frequency measurement of the cesium $\mathit {d}_{1}$ line with a mode-locked laser,” Phys. Rev. Lett. 82(18), 3568–3571 (1999). [CrossRef]
2. S. A. Diddams, T. Udem, J. C. Bergquist, E. A. Curtis, R. E. Drullinger, L. Hollberg, W. M. Itano, W. D. Lee, C. W. Oates, K. R. Vogel, and D. J. Wineland, “An optical clock based on a single trapped 199Hg+ ion,” Science 293(5531), 825–828 (2001). [CrossRef]
3. T. Udem, R. Holzwarth, and T. W. Hänsch, “Optical frequency metrology,” Nature 416(6877), 233–237 (2002). [CrossRef]
4. S. A. Diddams, L. Hollberg, and V. Mbele, “Molecular fingerprinting with the resolved modes of a femtosecond laser frequency comb,” Nature 445(7128), 627–630 (2007). [CrossRef]
5. N. Picqué and T. W. Hänsch, “Frequency comb spectroscopy,” Nat. Photonics 13(3), 146–157 (2019). [CrossRef]
6. F. Keilmann, C. Gohle, and R. Holzwarth, “Time-domain mid-infrared frequency-comb spectrometer,” Opt. Lett. 29(13), 1542–1544 (2004). [CrossRef]
7. A. Schliesser, M. Brehm, F. Keilmann, and D. W. van der Weide, “Frequency-comb infrared spectrometer for rapid, remote chemical sensing,” Opt. Express 13(22), 9029–9038 (2005). [CrossRef]
8. I. Coddington, N. Newbury, and W. Swann, “Dual-comb spectroscopy,” Optica 3(4), 414–426 (2016). [CrossRef]
9. N. R. Newbury, I. Coddington, and W. Swann, “Sensitivity of coherent dual-comb spectroscopy,” Opt. Express 18(8), 7929–7945 (2010). [CrossRef]
10. A. H. G. Villares, S. Blaser, and J. Faist, “Dual-comb spectroscopy based on quantum-cascade-laser frequency combs,” Nat. Commun. 5(1), 5192 (2014). [CrossRef]
11. N. Nader, A. Kowligy, J. Chiles, E. J. Stanton, H. Timmers, A. J. Lind, F. C. Cruz, D. M. B. Lesko, K. A. Briggman, S. W. Nam, S. A. Diddams, and R. P. Mirin, “Infrared frequency comb generation and spectroscopy with suspended silicon nanophotonic waveguides,” Optica 6(10), 1269–1276 (2019). [CrossRef]
12. A. V. Muraviev, V. O. Smolski, Z. E. Loparo, and K. L. Vodopyanov, “Massively parallel sensing of trace molecules and their isotopologues with broadband subharmonic mid-infrared frequency combs,” Nat. Photonics 12(4), 209–214 (2018). [CrossRef]
13. J. Zhang, K. Fritsch, Q. Wang, F. Krausz, K. F. Mak, and O. Pronin, “Intra-pulse difference-frequency generation of mid-infrared (2.7-20 μm) by random quasi-phase-matching,” Opt. Lett. 44(12), 2986–2989 (2019). [CrossRef]
14. D. Burghoff, Y. Yang, and Q. Hu, “Computational multiheterodyne spectroscopy,” Sci. Adv. 2(11), e1601227 (2016). [CrossRef]
15. A. Dutt, C. Joshi, X. Ji, J. Cardenas, Y. Okawachi, K. Luke, A. L. Gaeta, and M. Lipson, “On-chip dual-comb source for spectroscopy,” Sci. Adv. 4(3), e1701858 (2018). [CrossRef]
16. N. B. Hébert, J. Genest, J.-D. Deschênes, H. Bergeron, G. Y. Chen, C. Khurmi, and D. G. Lancaster, “Self-corrected chip-based dual-comb spectrometer,” Opt. Express 25(7), 8168–8179 (2017). [CrossRef]
17. L. A. Sterczewski, J. Westberg, and G. Wysocki, “Computational coherent averaging for free-running dual-comb spectroscopy,” Opt. Express 27(17), 23875–23893 (2019). [CrossRef]
18. I. Coddington, W. C. Swann, and N. R. Newbury, “Coherent multiheterodyne spectroscopy using stabilized optical frequency combs,” Phys. Rev. Lett. 100(1), 013902 (2008). [CrossRef]
19. S. Mehravar, R. A. Norwood, N. Peyghambarian, and K. Kieu, “Real-time dual-comb spectroscopy with a free-running bidirectionally mode-locked fiber laser,” Appl. Phys. Lett. 108(23), 1 (2016). [CrossRef]
20. R. Liao, Y. Song, W. Liu, H. Shi, L. Chai, and M. Hu, “Dual-comb spectroscopy with a single free-running thulium-doped fiber laser,” Opt. Express 26(8), 11046–11054 (2018). [CrossRef]
21. T. J. Kippenberg, R. Holzwarth, and S. A. Diddams, “Microresonator-based optical frequency combs,” Science 332(6029), 555–559 (2011). [CrossRef]
22. D. A. Long, A. J. Fleisher, K. O. Douglass, S. E. Maxwell, K. Bielska, J. T. Hodges, and D. F. Plusquellic, “Multiheterodyne spectroscopy with optical frequency combs generated from a continuous-wave laser,” Opt. Lett. 39(9), 2688–2690 (2014). [CrossRef]
23. P. Martín-Mateos, B. Jerez, and P. Acedo, “Dual electro-optic optical frequency combs for multiheterodyne molecular dispersion spectroscopy,” Opt. Express 23(16), 21149–21158 (2015). [CrossRef]
24. V. Durán, S. Tainta, and V. Torres-Company, “Ultrafast electrooptic dual-comb interferometry,” Opt. Express 23(23), 30557–30569 (2015). [CrossRef]
25. G. Millot, S. Pitois, M. Yan, T. Hovhannisyan, A. Bendahmane, T. W. Hänsch, and N. Picque, “Frequency-agile dual-comb spectroscopy,” Nat. Photonics 10(1), 27–30 (2016). [CrossRef]
26. Y. Wang, M. G. Soskind, W. Wang, and G. Wysocki, “High-resolution multi-heterodyne spectroscopy based on fabry-perot quantum cascade lasers,” Appl. Phys. Lett. 104(3), 031114 (2014). [CrossRef]
27. H. Telle, G. Steinmeyer, A. Dunlop, J. Stenger, D. Sutter, and U. Keller, “Carrier-envelope offset phase control: A novel concept for absolute optical frequency measurement and ultrashort pulse generation,” Appl. Phys. B: Lasers Opt. 69(4), 327–332 (1999). [CrossRef]
28. F. Helbing, G. Steinmeyer, J. Stenger, H. Telle, and U. Keller, “Carrier–envelope-offset dynamics and stabilization of femtosecond pulses,” Appl. Phys. B: Lasers Opt. 74(S1), s35–s42 (2002). [CrossRef]
29. D. J. Jones, S. A. Diddams, J. K. Ranka, A. Stentz, R. S. Windeler, J. L. Hall, and S. T. Cundiff, “Carrier-envelope phase control of femtosecond mode-locked lasers and direct optical frequency synthesis,” Science 288(5466), 635–639 (2000). [CrossRef]
30. R. J. Jones and J.-C. Diels, “Stabilization of femtosecond lasers for optical frequency metrology and direct optical to radio frequency synthesis,” Phys. Rev. Lett. 86(15), 3288–3291 (2001). [CrossRef]
31. A. M. Zolot, F. R. Giorgetta, E. Baumann, J. W. Nicholson, W. C. Swann, I. Coddington, and N. R. Newbury, “Direct-comb molecular spectroscopy with accurate, resolved comb teeth over 43 thz,” Opt. Lett. 37(4), 638–640 (2012). [CrossRef]
32. T. W. H. Zaijun Chen, M. Yan, and N. Picqué, “A phase-stable dual-comb interferometer,” Nat. Commun. 9(1), 3035 (2018). [CrossRef]
33. Z. Chen, T. W. Hänsch, and N. Picqué, “Mid-infrared feed-forward dual-comb spectroscopy,” Proc. Natl. Acad. Sci. 116(9), 3454–3459 (2019). [CrossRef]
34. S. M. Link, D. J. H. C. Maas, D. Waldburger, and U. Keller, “Dual-comb spectroscopy of water vapor with a free-running semiconductor disk laser,” Science 356(6343), 1164–1168 (2017). [CrossRef]
35. K. Van Gasse, Z. Chen, E. Vicentini, J. Huh, S. Poelman, Z. Wang, G. Roelkens, T. W. Hänsch, B. Kuyken, and N. Picqué, “An on-chip iii-v-semiconductor-on-silicon laser frequency comb for gas-phase molecular spectroscopy in real-time,” (2020).
36. L. Consolino, M. Nafa, M. D. Regis, F. Cappelli, K. Garrasi, F. P. Mezzapesa, L. Li, A. G. Davies, E. H. Linfield, M. S. Vitiello, S. Bartalini, and P. D. Natale, “Quantum cascade laser based hybrid dual comb spectrometer,” Commun. Phys. 3(1), 69 (2020). [CrossRef]
37. A. Prehn, R. Glöckner, G. Rempe, and M. Zeppenfeld, “Fast, precise, and widely tunable frequency control of an optical parametric oscillator referenced to a frequency comb,” Rev. Sci. Instrum. 88(3), 033101 (2017). [CrossRef]
38. N. B. Hébert, S. Boudreau, J. Genest, and J.-D. Deschênes, “Coherent dual-comb interferometry with quasi-integer-ratio repetition rates,” Opt. Express 22(23), 29152–29160 (2014). [CrossRef]
39. S. Ghosh and G. Eisenstein, “Fast high-resolution measurement of an arbitrary optical pulse using dual-comb spectroscopy,” Phys. Rev. Appl. 14(1), 014061 (2020). [CrossRef]
40. D. Hils and J. L. Hall, “Response of a fabry–perot cavity to phase modulated light,” Rev. Sci. Instrum. 58(8), 1406–1412 (1987). [CrossRef]
41. E. Krüger, “Frequency stabilization and control of a mode-locked dye laser,” Rev. Sci. Instrum. 66(10), 4806–4812 (1995). [CrossRef]
42. D. Allan, “Statistics of atomic frequency standards,” Proc. IEEE 54(2), 221–230 (1966). [CrossRef]
43. D. Von der Linde, “Characterization of the noise in continuously operating mode-locked lasers,” Appl. Phys. B 39(4), 201–217 (1986). [CrossRef]
44. D. Steck, “Rubidium 87 d line data,” https://steck.us/alkalidata/ (2003).
45. D. Steck, “Rubidium 85 d line data,” https://steck.us/alkalidata/ (2003).
46. M. Radziunas, A. G. Vladimirov, E. A. Viktorov, G. Fiol, H. Schmeckebier, and D. Bimberg, “Pulse broadening in quantum-dot mode-locked semiconductor lasers: Simulation, analysis, and experiments,” IEEE J. Quantum Electron. 47(7), 935–943 (2011). [CrossRef]
47. Y. Liu and J. G. Zhang, “Design of low-timing-jitter, stable picosecond optical-pulse source using an uncooled gain-switched fabry–perot semiconductor laser with external continuous-wave light injection,” Microw. Opt. Technol. Lett. 53(9), 2100–2105 (2011). [CrossRef]
48. S. Kono, H. Watanabe, R. Koda, N. Fuutagawa, and H. Narui, “140-fs duration and 60-w peak power blue-violet optical pulses generated by a dispersion-compensated gainn mode-locked semiconductor laser diode using a nonlinear pulse compressor,” Opt. Express 23(25), 31766–31771 (2015). [CrossRef]
49. E. D. Black, “An introduction to pound–drever–hall laser frequency stabilization,” Am. J. Phys. 69(1), 79–87 (2001). [CrossRef]
