Open Access
Add to BibSonomy
Abstract
A passive dual-comb laser can generate two optical frequency combs with different repetition frequencies. These repetition differences have high relative stability and mutual coherence through passive common-mode noise suppression without complex tight phase locking from a single-laser cavity. The comb-based frequency distribution requires the dual-comb laser to have a high repetition frequency difference. This paper presents a high repetition frequency difference bidirectional dual-comb fiber laser based on an all-polarization-maintaining cavity configuration and a semiconductor saturable absorption mirror with single polarization output. The proposed comb laser has a standard deviation of 69 Hz and an Allan deviation of 1.17 × 10−7 at τ = 1 s under different repetition frequencies of 12.815 MHz. Moreover, a transmission experiment has been conducted. Owing to the passive common-mode noise rejection capability of dual-comb laser, after passing an 84 km fiber link, the frequency stability of the repetition frequency difference signal is improved by two orders of magnitude than the repetition frequency signal at the receiver side.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
A passive dual-comb laser that can generate two optical frequency combs with repetition rate difference ($\varDelta f_{rep}$) from a single-laser cavity has attracted attention because of its high relative stability and mutual coherence through passive common-mode noise suppression without complex tight phase locking [1–7]. This benefit has prompted several applications, such as dual-comb spectroscopy measurements [3,8,9], dual-comb metrology [10] and dual-comb spectroscopic ellipsometry [11]. Moreover, it has great potential to be used in comb-based time-frequency distribution [12–15].
In recent years, passive dual-comb lasers have been implemented on different material platforms. The dual-comb lasers for different materials have different properties. For example, solid-state dual-comb lasers based on spatial multiplexing have a high output power [16], microcavity dual-comb seed sources based on dispersion modulation have a high fundamental repetition frequency [17,18], and fiber-based passive dual-comb seed sources have a high stability [19]. The easy construction of a fiber-based passive dual-comb seed source with low output noise and good stability attracts more researchers’ interest. People have developed various methods to implement a fiber-based passive dual-comb laser, such as bidirectional [4–7], dual-wavelength [20–23], polarization-multiplexed [1,2] and cavity-multiplexed [19] mode-locking. The first passive dual-comb laser is based on bidirectional mode-locking [4,5]. The bidirectional mode-locking uses the inconsistency of the effective refractive index in the cavity of the bi-directionally propagating mode-locking pulses to achieve a slight repetitive frequency difference. The generation of bi-directionally propagating mode-locking pulses is caused by the difference in absorption efficiency between the two sides of the natural saturable absorber (mainly carbon nanotubes) [5–7]. It has the advantage of good consistency of the output pulse spectrum. However, $\varDelta f_{rep}$ cannot be controlled or adjusted, and the output pulse power also cannot be altered. By using two saturable absorbers with same characteristics can avoid this problem [6,7]. Dual-wavelength mode-locking is based on the slight difference in the fiber’s refractive index for different wavelengths to obtain two pulse trains with a small $\varDelta f_{rep}$ [20,23]. Compared to bidirectional mode-locking, dual-wavelength mode-locking has the advantages of higher output pulse energy, simple structure, and easy-to-realize dual-comb output. However, the $\varDelta f_{rep}$ still cannot be tuned because of the fixed wavelength difference. Moreover, the passive dual-comb seed source need to achieve all polarization-maintaining (PM) structures, which is helpful in suppressing environmental fluctuations [24]. The polarization multiplexing method adopts all PM structures and solves the aforementioned problems [1,19]. However, it suffers from polarization crosstalk because the polarization extinction ratio is not high enough. For frequency distribution based on a passive dual-comb laser, a considerable $\varDelta f_{rep}$, tunable, all PM structures without polarization crosstalk are required. The enormous $\varDelta f_{rep}$ is used to carry radio frequency (RF) signal. The tunability of $\varDelta f_{rep}$ is used to compensate for residual phase jitter during frequency transfer. All PM structures without polarization crosstalk are used to improve the stability of the light source. For frequency distribution based on a passive dual-comb laser, the bidirectional mode-locking and dual-wavelength mode-locking is hard to provide high repetition frequency differences and tunability of $\varDelta f_{rep}$ based on the same mode-locking element. Although the bi-directional mode-locked structure [6] can achieve a tunable repetition frequency difference and high-frequency stability using two saturated absorbers, the slight repetition frequency difference is still unsuitable for frequency distribution. The polarization multiplexing structure can achieve a high $\varDelta f_{rep}$ and all-PM structure, but is accompanied by polarization crosstalk problems.
In this paper, we developed an all-PM bidirectional dual-comb fiber laser based on a single semiconductor saturable absorption mirror (SESAM) with a single polarization output. The two frequency combs are generated from the same cavity with an standard deviation of 69 Hz and an Allan deviation of $1.17 \times 10^{-7}$ at $\tau =1 s$ under repetition frequency difference of 12.815 MHz because of technical common-mode noise suppression with the same SESAM. Large $\varDelta f_{rep}$ can be achieved by setting the length difference of the non-common part of the fiber. And fine adjustment of $\varDelta f_{rep}$ can be achieved by adjusting the fiber length of the bidirectional branches through changing the piezoelectric ceramic transducer (PZT) voltage while the laser is running. We measured the Allan deviation of $\varDelta f_{rep}$ to show its relative stability. To evaluate the common mode noise rejection and demonstrate the superiority of the dual combs in frequency transfer, we transferred the $f_{rep}$ and $\varDelta f_{rep}$ signal through an 84 km fiber link with a dispersion compensating fiber module and measured the Allan deviations at the receiver side. Both experiments had no servo control of $f_{rep}$ and $\varDelta f_{rep}$.
2. Experimental setup
The experimental setup of the all-PM bidirectional fiber laser has a completely symmetrical structure, which is illustrated in Fig. 1. The gain medium on the clockwise (CW) and counter-clockwise (CCW) branch is a 0.5 m long PM erbium-doped fiber (PM-EDF, Liekki, Er80-4/125/HD-PMF, -22 $ps/nm\cdot km$ at 1550nm), which is pumped independently through two 976 nm laser diodes (LD). The gain medium for the counter clockwise (CW) and counter clockwise (CCW) branches are not require the same length. But the same length can help to improve signal-to-noise ratio of the repetition frequency difference signal at detection part. The other PMF has a dispersion parameter at 1550nm is 32 $ps/nm\cdot km$ at 1550nm. The circulators ensure that the CW and CCW lights do not interfere with each other when amplified and after SESAM (SAM-1550-27-2ps). Both fast and slow axes of light from the polarization beam splitters (PBSs, extinction ratio of 23 dB) input part are aligned to the slow axis of the input fiber. The output of PBS is connected to the SESAM, which the BATOP company produces. The SESAM’s modulation depth, saturation fluence, and relaxation time constant are 16$\%$, 70 uJ/cm, and 2 ps, respectively. All the circulator have 50 dB isolation from port 2 to port 1 and port 3 to port 2, operating wavelength range from 1530nm to 1570nm, and slow axis working. The bandpass filter (BPF) eliminates polarization crosstalk between CW and CCW light due to an insufficient PBS polarization extinction ratio. The bandpass width of both filters is 14 nm. The center wavelength of BPF1 is 1570 nm, and the center wavelength of BPF2 is 1530 nm which are all in the circulator operating wavelength range. The 40 nm spacing ensures the complete elimination of polarization crosstalk. All the non-common paths are placed closely to share the mechanical vibration. Additionally, the laser outputs (comb1 and comb2) pass through the same 30:70 coupler. The 30$\%$ of propagating power as output light via this coupler and measured using an optical spectrum analyzer (Yokogawa, AQ6370D) and RF spectrum analyzer (RIGOL, DSA815) via a fast photodetector (Menlo Systems, FPD-130). All optical devices in the cavity except the PBS are slow-axis work devices to achieve single polarization output. In this setup, since both PMF and PM-EDF have anomalous dispersion at 1550 nm, the net cavity dispersion is also anomalous. All the experiments in this study are conducted in a free-running operation, as described in the following sections.
3. Experiment result and discussion
3.1 Dual-comb seed source
Figures 2(a) and (b) show the optical spectra of the two outputs of mode-locked fiber laser. In the CCW output, the center wavelength, full-width at half-maximum (FWHM) bandwidth of the spectrum, and output power are 1562 nm, 4.88 nm, and approximately 9 mW, respectively. In the CW output, the center wavelength, FWHM bandwidth, and output power are 1532 nm, 5 nm, and approximately 14 mW, respectively. Both CW and CCW outputs are ground state soliton with Kelley’s sidebands. The PBS uses a coupling fiber slow-axis alignment (fast axis to slow axis, slow axis to slow axis), so the dual-comb mode locking oscillation is only along the slow axis. For the day-to-day operations, the dual-comb mode-locking operation with almost the same optical spectra was always obtained after the pump was turned on. The dual-comb mode-locking operation could be maintained for more than three months. Thanks to the all-PM configuration and single SESAM structure, we achieved high long-term stability and excellent repeatability.
Figures 2(c) and (d) show the RF spectra of CCW and CW pulse at a resolution bandwidth (RBW) of 300 Hz. The fundamental $f_{rep}$ for the CCW comb was 17.333 MHz and 30.145 MHz for CW comb corresponding to a cavity length of approximately 11.5 m and 6.6 m, respectively. The $\varDelta f_{rep}$ was 12.815 MHz. The CCW and CW pulse has a signal-noise ratio (SNR) at a resolution bandwidth (RBW) of 300 Hz is more than 50 dB. Figures 2(e) and (f) show the temporal variation in the CCW and CW pulse repetition rates. The time domain waveform is clean as a typical mode-locked pulse.
Figures 2(g) and (h) show the observed autocorrelation trace for the CCW and CW output. A background-free SHG-type autocorrelator (APE pulse check NX) was used for the measurement. A pedestal-free, almost symmetric autocorrelation trace was observed. This is an instrumental measurement imperfection. For CCW output, the pulse width was 1.062 ps under the assumption of a $sech^2$ pulse. The transform-limited pulse width estimated from the spectral width of 4.88 nm was 525 fs. About the CW output, the pulse width was 885 fs under the assumption of a $sech^2$ pulse. The transform-limited pulse width estimated from the spectral width of 5 nm was 493 fs. The sizeable temporal broadening was caused by the chromatic dispersion of the output couplers and optical isolator. The slight variation in the background noise level was due to the low SNR of this measurement’s low peak power of the broadened output pulses.
To evaluate the relative stability in the RF domain, we measured $f_{rep}$ for the two frequency combs simultaneously using two frequency counters (Keysight, 53230A) with a reference of a microwave signal generator (R$\&$S, SMC100A). Figure 3(a) shows the temporal variation in $f_{rep}$ for the two frequency combs (upper) and $\varDelta f_{rep}$ (lower) in the free-running operation. The following equation can calculate the cavity length and repetition frequency of a free-running mode-locked laser: $f_{rep}=\frac {c}{n_g\times l}$, where $l$ is the cavity length, $n_g$ is the group refractive index. This equation shows that the higher the repetition frequency, the shorter the cavity length. At the same cavity length perturbation, the higher repetition frequency of pulse gets the greater jitter of repetition frequency. In Figs. 3(b) and (c), a change of $\sim$600 Hz was observed in $f_{{rep}_{CW}}$ and $\sim$350 Hz in $f_{{rep}_{CCW}}$ due to environmental perturbation. The trends of $f_{{rep}_{CW}}$ and $f_{{rep}_{CCW}}$ are consistent. The relative stability was obtained for $\varDelta f_{rep}$ with a standard deviation of 69 Hz and $\varDelta f_{rep}$ of 12.815 MHz without servo control, i.e., owing to the single SESAM and passive common-mode noise cancellation. Figure 3(e) shows the Allan deviation of $\varDelta f_{rep}$. It was measured using a frequency counter (Kesight 53230A). The measured instability starts at $1.2\times 10^{-7}$ at $\tau = 1 s$ and continuously drops to below $1\times 10^{-10}$ at $10^4$s including its uncertainty. The downward trend of the curve coincides with $\frac {1}{\tau }$ and shows that when the white noise dominates the measurements, the standard deviation decreases by ten as the integration time is 100-fold increased. So, the main noise source is white frequency noise. This laser structure can suppress the random walk and flicker frequency noise often caused by environmental disturbance.
Moreover, owing to the all-PM configuration, the mode-locking operation can be maintained even if perturbations are caused by vibration or touching the fibers.
3.2 Transfer repetition frequency difference through an 84km laboratory optical fiber link
For fiber-based frequency transfer, the factor that affects the stability of the final transmitted signal is the phase noise superimposed on the final signal due to the time delay jitter caused mainly by the fiber temperature variations and possibly by some varying mechanical tensions [25]. The transmission delay variations in optical fiber can be expressed as:
The $f$ denotes the center frequency of the received spectrum of the photodetector (PD). The $n$ indicates the number of combs received on PD within the full width at half maximum spectrum. The $f_r$ and $\varDelta f_r$ are the repetition frequency and repetition frequency variance of the optical frequency comb, respectively. The $r_i$ represents the proportion of jitter contribution of the current two adjacent comb beat frequencies in the final composite beat frequency. Assuming that the contribution of every two adjacent combs to the final synthetic frequency variance is the same, then we simplify the Eq. (2) as:
Equationally when the output pulse trains of two optical frequency comb with the same central wavelength with coherence pass through the same fiber at the same time, the time delay jitter due to the fiber being subjected to external temperature variations can be considered as common-mode noise. A common mode noise suppression mechanism can eliminate this part of common mode noise. At the same time, due to the coherence of the output pulse train of the two optical frequency combs, the repetition frequency variance of the output pulses of the two optical frequency combs contains a part of the common mode component, which can be eliminated through optical mixing detection.Therefore, the final repetition frequency difference signal can get better frequency stability after fiber optic transmission than independently transmitted repetition frequency signal.
Fig. 1. The dual-comb seed source architecture. LD: Laser diode, CIR: circulator (port 1 to port 2, port 2 to port 3), EDF: erbium-doped fiber, WDM: wavelength division multiplexer, OC: optic coupler (split beam ratio of 50:50), ISO: isolator, SESAM: semiconductor saturable absorber mirror, OBPF: optical bandpass filters (The center wavelength of OBPF1 is 1530 nm and the bandwidth is 15 nm. The center wavelength of OBPF2 is 1570 nm and the bandwidth is 15 nm).
Fig. 2. (a) Optical spectra of counter-clockwise (CCW) pulse, (b) Optical spectra of clockwise (CW) pulse, (c) RF spectra of CCW pulse, (d) RF spectra of CW pulse, (e) Temporal variation in the repetition rates of CCW pulse, (d) Temporal variation in the repetition rates of CW pulse, (g) Autocorrelation curve of CCW pulse, (h) Autocorrelation curve of CW pulse.
Fig. 3. (a) The repetition rate drift over 24 hours of dual-comb source output frequencies. (b) The repetition rate drifts over 24 hours of CW pulses. (b) The repetition rate drifts over 24 hours of CCW pulses. (b) Frequency drift over 24 hours of repetition rate difference. (e) Allan variance of dual-comb source output frequencies.
To confirm our conjecture, an 84 km laboratory fiber optic link was built. The schematic of dual-comb source output stability test after 84km fiber link is shown in Fig. 4. The outputs of comb1 and comb2 were spectrally amplified by an erbium-doped fiber amplifier (EDFA) and a highly nonlinear fiber and then filtered by a bandpass filter with a center frequency of 1570 nm. A 50:50 1*2 coupler is used for the input to the fiber link. After the fiber optic link transmission, a dispersion-compensating fiber module with 80 km of standard single-mode fiber dispersion is used for dispersion compensation and amplified by EDFA to compensate for the link attenuation. After being filtered by a bandpass filter with a center frequency of 1570 nm, the incoming light power is controlled by an optical attenuator at -4 dBm into the photodetector (PD), and the signal from the photodetector is filtered by a low-noise amplifier and a bandpass filter with a center frequency of 13 MHz to obtain a heavy frequency difference signal. The obtained heavy $\varDelta f_{rep}$ signal is mixed with the 12.815 MHz signals generated by the microwave source and then input to the frequency counter for Allan variance measurement. The measurement result is shown in Fig. 5.
Figure 5(a) shows the output spectrum of the PD with only the $f_{rep}$ signal of two pulses on it, because the system uses a spectrum expansion to overlap the spectra of CW and CCW pulses, and the output $\varDelta f_{rep}$ signal is feeble. The received spectrum after amplification is shown in Fig. 5(b). The CW and CCW pulse repetition rate signals, as well as the frequency components such as the $\varDelta f_{rep}$ signal and $f_{rep}$ signals, can be seen from it. Due to the nonlinear cross-tuning distortion of the amplifier, both $4\left ( f_{rep_{CCW}}-\varDelta f_{rep} \right )$ and $5\left ( f_{rep_{CCW}}-\varDelta f_{rep} \right )$ are detected. Figures 5(c) and (d) show the frequency bias and Allan variance of each output frequency component of the dual-comb seed source obtained from actual tests. Due to the fiber’s thermal expansion and thermoelectric effects [26], the change of external temperature causes a change in fiber length and dispersion. The $f_{rep_{CW}}$ represented in red, and the $f_{rep_{CCW}}$ represented in blue, are the results of independent measurements. Each independent measurement is performed by disconnecting the corresponding spread-spectrum light input at the coupler. At the same time, due to the inconsistency between the two measurements, the temperature change between the two measurements is different. So, the final obtained frequency variance after crossing the fiber is not consistent. The repetition frequency difference signal represented by black in the figure is measured when $f_{rep_{CW}}$ and $f_{rep_{CCW}}$ are input simultaneously after the expanded spectrum light enters the fiber. At this time, the time delay jitter caused by the fiber link is the same for both, and the frequency variance of both is correlated, which can be eliminated by the passive common mode noise suppression mechanism. Thus, the repetition frequency difference signal has good frequency stability after the fiber optic link. The measured instability of $\varDelta f_{rep}$ starts at $2.03\times 10^{-9}$ at second and continuously drops to below $1\times 2.7^{-11}$ at $10^4$ s, including its uncertainty. Compared to CW pulses and CCW pulses, the $\varDelta f_{rep}$ signal has more than two orders of magnitude improvement in second stability and one order of magnitude improvement in kilo-second stability. The frequency transfer advantage of the $\varDelta f_{rep}$ may be more pronounced when compensation measures are applied to compensate for the $f_{rep}$ jitter of the link and the light source.
Fig. 4. Schematic of dual-comb source output stability test after 84km fiber link. EDFA: Erbium-doped fiber amplifier, HNLF: Highly nonlinear fiber. OBPF: Optical bandpass filters (The center wavelength of OBPF3 is 1570 nm, and the bandwidth is 15 nm. The center wavelength of OBPF4 is 1570 nm, and the bandwidth is 14 nm). DCM: Dispersion compensated fiber module. EBPF: Electrical bandpass filters. Amp: Low-noise electric amplifier.
Fig. 5. The measurement results of the dual-comb source output stability test after 84 km fiber link. (a) RF spectra of PD output frequencies, (b) RF spectra of low noise electric amplifier output frequencies, (c) The measurement of frequency bias for dual-comb output frequencies over an 84 km fiber link, (d) The measurement of Allan variance results for dual-optical comb output frequencies over an 84 km fiber link.
4. Conclusion
In conclusion, we developed a bidirectional dual-comb fiber laser based on an all-polarization-maintaining cavity configuration and a SESAM, which realize a tunable, robust, and simple structure with large $\varDelta f_{rep}$. Two OBPFs are used to solve polarization crosstalk and realize bidirectional isolation. Owing to the common-mode noise cancellation origination from the bidirectional laser cavity and the same saturable absorber,we achieve a standard deviation is 69 Hz and an Allan deviation of $1.17 \times 10^{-7}$ at $\tau =1 s$ for $\varDelta f_{rep}$ in 12.815 MHz without active stabilization. Therefore, the two independent pumps can be replaced by one pump through the 980 nm beam splitter to improve common-mode noise cancellation further. Furthermore, the all-PM-based configuration is robust against practical environmental perturbations.
Moreover, such a passive common-mode noise suppression capability can be outstanding in the time-frequency transmission to reduce the common-mode phase jitter brought by the fiber link. We measured the stability of three output pulse frequencies of the dual-comb source. Without additional residual phase jitter compensation, the $\varDelta f_{rep}$ signal exhibits the best frequency transmission stability in the output frequency of the dual optical comb seed source and has an order of magnitude improvement in frequency transfer stability in measurement. Furthermore, the developed dual-comb laser structure by adjusting repetition frequency difference have potential to be used in various platforms beyond frequency transfer, such as dual-comb spectroscopy, dual-comb metrology or synchronization between ultra-short pulse trains with different colors for various nonlinear optical measurements.
Funding
fundamental research funds of BUPT (2022RC08-500422353, 2022RC08-500422355); National Natural Science Foundation of China (61427813, 61531003, 61701040).
Disclosures
The authors declare that there are no conflicts of interest related to this article.
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
References
1. Y. Nakajima, Y. Hata, and K. Minoshima, “All-polarization-maintaining, polarization-multiplexed, dual-comb fiber laser with a nonlinear amplifying loop mirror,” Opt. Express 27(10), 14648–14656 (2019). [CrossRef]
2. X. Zhao, T. Li, Y. Liu, Q. Li, and Z. Zheng, “Polarization-multiplexed, dual-comb all-fiber mode-locked laser,” Photonics Res. 6(9), 853–857 (2018). [CrossRef]
3. X. Zhao, G. Hu, B. Zhao, C. Li, Y. Pan, Y. Liu, T. Yasui, and Z. Zheng, “Picometer-resolution dual-comb spectroscopy with a free-running fiber laser,” Opt. Express 24(19), 21833–21845 (2016). [CrossRef]
4. K. Kieu and M. Mansuripur, “All-fiber bidirectional passively mode-locked ring laser,” Opt. Lett. 33(1), 64–66 (2008). [CrossRef]
5. 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), 231104 (2016). [CrossRef]
6. Y. Nakajima, Y. Hata, and K. Minoshima, “High-coherence ultra-broadband bidirectional dual-comb fiber laser,” Opt. Express 27(5), 5931–5944 (2019). [CrossRef]
7. S. Saito, M. Yamanaka, Y. Sakakibara, E. Omoda, H. Kataura, and N. Nishizawa, “All-polarization-maintaining er-doped dual comb fiber laser using single-wall carbon nanotubes,” Opt. Express 27(13), 17868–17875 (2019). [CrossRef]
8. Z. Chen, M. Yan, T. W. Hänsch, and N. Picqué, “A phase-stable dual-comb interferometer,” Nat. Commun. 9(1), 3035 (2018). [CrossRef]
9. Y. Qin, B. Cromey, O. Batjargal, and K. Kieu, “All-fiber single-cavity dual-comb for coherent anti-stokes raman scattering spectroscopy based on spectral focusing,” Opt. Lett. 46(1), 146–149 (2021). [CrossRef]
10. H. Wright, J. Sun, D. McKendrick, N. Weston, and D. T. Reid, “Two-photon dual-comb lidar,” Opt. Express 29(23), 37037–37047 (2021). [CrossRef]
11. T. Minamikawa, Y.-D. Hsieh, K. Shibuya, E. Hase, Y. Kaneoka, S. Okubo, H. Inaba, Y. Mizutani, H. Yamamoto, T. Iwata, and T. Yasui, “Dual-comb spectroscopic ellipsometry,” Nat. Commun. 8(1), 610–618 (2017). [CrossRef]
12. J. Kim, J. A. Cox, J. Chen, and F. X. Kärtner, “Drift-free femtosecond timing synchronization of remote optical and microwave sources,” Nat. Photonics 2(12), 733–736 (2008). [CrossRef]
13. B. Ning, S. Zhang, D. Hou, J. Wu, Z. Li, and J. Zhao, “High-precision distribution of highly stable optical pulse trains with 8.8× 10- 19 instability,” Sci. Rep. 4(1), 5109 (2014). [CrossRef]
14. S. Zhang and J. Zhao, “Frequency comb-based multiple-access ultrastable frequency dissemination with 7× 10-17 instability,” Opt. Lett. 40(1), 37–40 (2015). [CrossRef]
15. H. J. Kang, J. Yang, B. J. Chun, H. Jang, B. S. Kim, Y.-J. Kim, and S.-W. Kim, “Free-space transfer of comb-rooted optical frequencies over an 18 km open-air link,” Nat. Commun. 10(1), 4438 (2019). [CrossRef]
16. J. Pupeikis, B. Willenberg, F. Bruno, M. Hettich, A. Nussbaum-Lapping, M. Golling, C. P. Bauer, S. L. Camenzind, A. Benayad, P. Camy, B. Audoin, C. R. Phillips, and U. Keller, “Picosecond ultrasonics with a free-running dual-comb laser,” Opt. Express 29(22), 35735–35754 (2021). [CrossRef]
17. G. Villares, J. Wolf, D. Kazakov, M. J. Süess, A. Hugi, M. Beck, and J. Faist, “On-chip dual-comb based on quantum cascade laser frequency combs,” Appl. Phys. Lett. 107(25), 251104 (2015). [CrossRef]
18. Y. Xu, M. Erkintalo, Y. Lin, S. Coen, H. Ma, and S. G. Murdoch, “Dual-microcomb generation in a synchronously driven waveguide ring resonator,” Opt. Lett. 46(23), 6002–6005 (2021). [CrossRef]
19. Y. Nakajima, Y. Kusumi, and K. Minoshima, “Mechanical sharing dual-comb fiber laser based on an all-polarization-maintaining cavity configuration,” Opt. Lett. 46(21), 5401–5404 (2021). [CrossRef]
20. A.-P. Luo, Z.-C. Luo, and W.-C. Xu, “Switchable dual-wavelength passively mode-locked fiber ring laser using sesam and cascaded fiber bragg gratings,” Laser Phys. 21(2), 395–398 (2011). [CrossRef]
21. L. Yun, X. Liu, and D. Mao, “Observation of dual-wavelength dissipative solitons in a figure-eight erbium-doped fiber laser,” Opt. Express 20(19), 20992–20997 (2012). [CrossRef]
22. Z. Yan, X. Li, Y. Tang, P. P. Shum, X. Yu, Y. Zhang, and Q. J. Wang, “Tunable and switchable dual-wavelength tm-doped mode-locked fiber laser by nonlinear polarization evolution,” Opt. Express 23(4), 4369–4376 (2015). [CrossRef]
23. G. Hu, Y. Pan, X. Zhao, S. Yin, M. Zhang, and Z. Zheng, “Asynchronous and synchronous dual-wavelength pulse generation in a passively mode-locked fiber laser with a mode-locker,” Opt. Lett. 42(23), 4942–4945 (2017). [CrossRef]
24. L. C. Sinclair, I. Coddington, W. C. Swann, G. B. Rieker, A. Hati, K. Iwakuni, and N. R. Newbury, “Operation of an optically coherent frequency comb outside the metrology lab,” Opt. Express 22(6), 6996–7006 (2014). [CrossRef]
25. Ł. Śliwczyński, P. Krehlik, and M. Lipiński, “Optical fibers in time and frequency transfer,” Meas. Sci. Technol. 21(7), 075302 (2010). [CrossRef]
26. L. G. Cohen and J. W. Fleming, “Effect of temperature on transmission in lightguides,” The Bell Syst. Tech. J. 58(4), 945–951 (1979). [CrossRef]
