Open Access
Add to BibSonomy
Abstract
Tri-comb and multi-comb techniques could enable many advanced measurement applications beyond the reach of traditional dual-comb schemes. However, the sophisticated and bulky control systems of the conventional schemes based on three comb lasers render them impractical for many potential applications. Like their dual-comb counterparts, tri-comb and multi-comb lasers are being investigated as attractive alternatives. In contrast to previous dual-comb lasers using only one multiplexing dimension of optical pulses, this work simultaneously leverages multiplexing methods in three physical dimensions, i.e. wavelength, polarization, and direction, to generate triple to quadruple asynchronous pulse trains in a bidirectional mode-locked fiber laser. Because of the unique cavity structure studied here, both wavelength-multiplexed and polarization-multiplexed dual-comb generation from a completely shared-cavity and wavelength/polarization-multiplexed multi-comb generation from a bidirectional partially shared-cavity are achieved. Good relative stability among the generated combs of the fiber laser is demonstrated, as well as proof-of-concept dual-comb spectroscopy measurements, which validates the mutual coherence between the combs. The analysis of the experimental results further reveals interesting performance comparisons between combs from different multiplexing schemes, thanks to the special laser design used here that allows a side-by-side dual-comb demonstrations from different combinations of outputs from the same laser. Our investigation could facilitate multi-comb generation based on one light source for field-deployable multi-comb applications.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Optical frequency combs (OFCs) with a wide spectrum of equally-spaced and mutually coherent spectral lines can serve as a very precise tool in diverse applications [1–3]. In particular, dual-comb techniques which hold promise to dramatically increase acquisition speed, sensitivity, and resolution have drawn much more attention in recent years [4]. With two slightly different frequency repetition rates, temporal asynchronous optical sampling (ASOPS) is well-established by employing them. Spectral information such as absorption could be retrieved from the Fourier transform of ASOPS interferograms. Recently, to alleviate the complexity of stabilized dual-laser-comb sources with sophisticated and bulk control systems [5], several multiplexing methods in the dimensions of wavelength [6–10], polarization [11–13], direction [14–20], and pulse-shape [21] are exploited to simultaneously generate two asynchronous pulse trains by one mode-locked fiber laser. Some of the multiplexed dual-comb lasers had been applied to dual-comb applications as simple and attractive light sources [6–8,13,22–27].
While dual-comb technique shows good performance in OFC-based applications, there exist several bottlenecks such as “dead-bands” in frequency measurements [28], limited temporal sampling window [29], non-ambiguous range limitation [30], hard to applied to multidimensional coherent spectroscopy [31] and etc. To fully leverage the advantages of frequency combs, tri-comb technique consisting of three combs with slightly different mode spacings has become an attractive research topic. The introduced third comb in tri-comb scheme could add additional temporal/spectral information and further realize gap-less frequency measurement, enable fast acquisition in nonlinear coherent spectroscopy, or increase ambiguity range in distance measurement for improving the capability of dual-comb schemes. It could be further conceived that quad-comb or multi-comb techniques may enhance the performance of multi-comb applications in the future.
Yet, the challenge of developing low-complexity, well mutually coherent multi-comb light sources for precise metrology applications remains huge. While tri-comb generation from three independent mode-locking lasers have been proposed with better performances, the independent random cavity drifts between such lasers could destroy the coherence between their output comb lines, and phase-locked control systems are still needed [5,32]. Recently, tri-comb generation based on multi-wavelength lasing [33,34] and dual-ring structure [35] from just one light source have been proposed. However, the mutual coherence between their output comb lines is not investigated, and their limited spectral bandwidths render them impractical for many multi-comb applications. More recently, by changing light propagation characteristics in two physical dimensions of wavelength and polarization, tri/quad-comb operations with good stability have been experimentally demonstrated [36]. Based on this concept, different laser cavity configurations and more multiplexing dimensions for multi-comb generation in a mode-locked fiber laser as well as their output stability and mutual coherence could be further explored.
Here, we experimentally demonstrate the tri-comb and quad-comb generation in a bidirectional mode-locked fiber laser. The laser has different configurations in the two counter-propagating directions, so that the mechanisms of wavelength-multiplexing and polarization-multiplexing can be respectively realized. By combining the direction-multiplexing in the laser cavity, triple and quadruple asynchronous pulse trains are generated and analyzed. Moreover, the relative stability and mutual coherence between the combs of quad-comb are investigated.
2. Experimental setup
Figure 1 shows the experimental setup and photo of a bidirectional mode-locked fiber laser with two counter-propagating branches. The main laser cavity is composed of two 980/1550 nm wavelength division multiplexers (WDMs), 0.8-m erbium-doped fiber (EDF, Er110) bidirectionally pumped by two 980 nm laser diodes (LDs, LD1 and LD2 in this case), a 2 × 2 optical coupler (OC) with 50% output, and a length of single-mode fiber (SMF). Polarization controllers (PCs, PC1 and PC2) and homemade single-wall carbon nanotube (SWNT) mode-lockers as saturable absorbers (SAs) are placed in both of the branches. Two variable attenuators (VAs, VA1 and VA2) are also inserted to balance of gain and loss in each branch. Besides, two circulators are used to couple the branches into the main laser cavity. In the absence of an in-line optical isolator in the main cavity, pulses can propagate under a directions-multiplexed mechanism with clockwise (CW) and counter-clockwise (CCW) operations. Moreover, in the CW branch, the introduced in-line polarizer (ILP) with 60-cm polarization-maintained fiber (PMF) (the model birefringence is 4.0 × 10−4) pigtails can function as an intracavity Loyt filter. Similar to previous reports [8,10,23], wavelength-multiplexed mode-locking can be achieved by separating two peaks of the gain profile modulated by the filter. In the CCW branch, a piece of 50-cm long PMF is inserted with some limited but considerable birefringence, which plays a critical role to enable polarization-multiplexed mode-locking [11]. The total lengths in the two directions are ∼5.14 m and ∼5.13 m, and the net group velocity dispersion (GVD) are estimated to be −0.0594 ps2 and −0.0593 ps2, respectively. All of the fiber paths in the laser cavity are placed closely on an aluminum plate inside an aluminum enclosure (35 × 25 × 7 cm) with a cover, as shown in Fig. 1(b), so that they could experience almost the same external fluctuations. The CW direction output is divided into two wavelengths (λ1 and λ2) by a coarse wavelength division multiplexer (CWDM) as well as the CCW output is divided into two polarization (Pol1 and Pol2) by a polarization beam splitter (PBS). The CW/CCW laser outputs are separately monitored by an optical spectrum analyzer (OSA, Agilent, 6375B), an oscilloscope (OSC, Tektronix, MSO72004), and a radio frequency (RF) spectrum analyzer (Siglent, SSA1015X) combined with a 150-MHz bandwidth photodetector (PD).
Fig. 1. (a) The experimental setup of the multidimensional-multiplexed multi-comb fiber laser, and (b) photograph of the laser in an aluminum enclosure.
3. Results and discussions
3.1 Dual-comb mode-locking operations
Due to the laser’s different configurations in two branches, the wavelength-multiplexed mode-locking and polarization-multiplexed mode-locking could be enabled in the CW and CCW outputs, respectively. To avoid the uneven gain distribution caused by the difference in pump strength from the two 980 nm LDs, the pump drive conditions and pump power values are set almost equal. Thus, the total pump power is recorded in our experiment. By fine-adjusting the pump powers, PCs, and attenuators, three types of dual-comb operations can be achieved: the first one (i.e. dual-comb I) is only wavelength-multiplexed mode-locking operation in the CW output; the second one (i.e. dual-comb II) is only polarization-multiplexed mode-locking operation in the CCW output; the third one (i.e. dual-comb III) is only direction-multiplexed mode-locking output-single wavelength mode-locking in both directions.
For dual-comb I, a dual-wavelength multiplexed mode-locking in the CW output can be achieved when increasing the pump power to ∼185 mW, adjusting the VA1’s loss to 1.5 dB and the VA2’s loss to its maximum of ∼56 dB, and tuning PC1 properly. The laser output power is 2.2 mW. As shown in Fig. 2(a), two center wavelengths located at 1555.2 nm (λ1) and 1565.6 nm (λ2) could be observed. They have similar shapes and their 3 dB bandwidths are 2.9 nm and 2.7 nm, respectively. Due to the inserted in-line polarizer with 60 cm-long PMF pigtails (its modal birefringence ∼ 4.0 × 10−4) in the CW branch, the free spectral range (FSR) between the introduced comb filtering curve can be calculated as ∼10.0 nm [21,37], which roughly matches the spectral separation between the two center wavelengths. As shown in Fig. 2(b), the frequency repetition rates are measured around 41.281 MHz, consistent with light propagation length in the CW direction, and the difference between the two repetition rates is 1037 Hz. The two asynchronous pulse trains are shown in Fig. 2(c), and their respective time intervals correspond to their frequency repetition rates.
Fig. 2. Three types of dual-comb operations and their output characteristics. (a) The optical spectrum, (b) RF spectrum, and (c) pulse trains of dual-comb I; (d) the optical spectrum, (e) RF spectrum, and (f) pulse trains of dual-comb II; (g) the optical spectra, (h) RF spectra, and (i) pulse trains of dual-comb III.
Similarly, when increasing the pump power to 195 mW, adjusting the tunable VA1’s loss to its maximum of ∼56 dB and the VA2’s loss to 1.5 dB instead, and tuning PC2 properly, a polarization-multiplexed mode-locking (dual-comb II, pol1 and pol2) state in the CCW output can be observed, as shown in Figs. 2(d-f). The center wavelength of the optical spectrum is 1559.6 nm with a 3 dB bandwidth of 3.1 nm. The measured output power of the laser is 2.3 mW. The measured results show that the frequency repetition rates of the two asynchronous pulse trains are around 41.286 MHz, which corresponds to light propagation length in the CCW direction. The difference between the two repetition rates is ∼503 Hz. Such a polarization-multiplexed mode-locking state can not be observed when the PMF is absent in the CCW branch. On the other hand, by further tuning VA1’s loss to 5.3 dB and VA2’s loss to 6.2 dB, the pulse in the CW direction output trends to mode-locking first. Subsequently, by slightly adjusting the PC2, the other mode-locked pulse could also be observed in the CCW output. The optical spectra, RF spectra, and pulse trains of the direction-multiplexed mode-locking (dual-comb III) are measured and shown in Figs. 2(g-i). Their center wavelengths are 1556.0 nm and 1559.5 nm, and the 3 dB bandwidths are ∼3.7 nm and ∼2.9 nm, respectively. With the output powers of 2.3 mW and 2.8 mW, respectively, the CW pulse at 1556.0 nm has a repetition rate of ∼41.280910 MHz, and the CCW pulse at 1559.5 nm of that is ∼41.286227 MHz. The difference between the two repetition rates is ∼5317 Hz. Since the output repetition rates are highly dependent on the fiber lengths in the CW and CCW directions, their repetition rate difference could be slightly tuned by carefully tailoring the lengths of SMF between the two directions.
3.2 Tri-comb mode-locking operations
Based on the dual-comb operations shown above, a combination of more multiplexed schemes of pulses in more physical dimensions could be extended and become an alternative for tri-comb generation. The exploration for tri-comb schemes can be achieved in the two cases: the first one (i.e. tri-comb I) is two combs based on wavelength-multiplexing in CW direction and the third comb based on single pulse mode-locking in CCW direction; the second one (i.e. tri-comb II) is two combs based on polarization-multiplexing in CCW direction and the third comb based on single pulse mode-locking in CW direction.
For the generation of tri-comb I, when further increasing the pump power to 265 mW, adjusting VA2’s loss from its maximum to 6.6 dB, and carefully tuning the two PCs based on the generation of the dual-comb I, the optical spectra, RF spectra, and pulse trains of the CW and CCW outputs simultaneously show the stable generation of the tri-comb (see Figs. 3(a)-(c)). The output powers of the two directions are 3.5 mW and 3.8 mW, respectively. The center wavelengths of wavelength-multiplexed mode-locking in CW output are 1550.8 nm and 1560.9 nm with 3 dB bandwidths of 2.5 nm and 3.0 nm, respectively, and that of single pulse mode-locking in CCW output is 1555.3 nm with 3 dB bandwidth of 3.1 nm. Their frequency repetition rates are 41.285990 MHz, 41.280786 MHz, and 41.279675 MHz, respectively. The output triple asynchronous pulse trains correspond to their frequency repetition rates.
Fig. 3. Output characteristics of the two kinds of tri-comb operations. (a) The optical spectra, (b) RF spectra, and (c) pulse trains of tri-comb I; (d) the optical spectra, (e) RF spectra, and (f) pulse trains of tri-comb II.
On the other hand, by further adjusting the loss of VA1 from its maximum to 8.3 dB and slightly adjusting PC1 based on the generation of dual-comb II, another tri-comb operation (tri-comb II) can be achieved where a shorter wavelength at 1555.4 nm is mode-locking in CW direction and polarization-multiplexed dual-comb is still existing in CCW direction (see Figs. 3(d)-(f)). The measured output powers of the two directions are 3.4 mW and 3.6 mW, respectively. It is noted that the spectral filter effect of the Lyot filter can be clearly observed and the longer wavelength could be mode-locking at the center wavelength of 1565.3 nm instead by further adjusting the PC1. The triple pulse trains have repetition rates of 41.280942 MHz, 41.286039 MHz, and 41.286425 MHz, respectively. Therefore, by properly designing the laser cavity combined with different multiplexed mechanisms, e.g., direction, wavelength, and polarization in this case, dual/tri-comb with low-complexity can be enabled with one mode-locked light source.
3.3 Quad-comb mode-locking operation
As discussed in the generation of dual/tri-comb operations above, quad-comb operation could be achieved by simultaneously generating two pairs of wavelength-multiplexed combs and polarization-multiplexed combs in the bidirectional mode-locked fiber laser. This can be obtained by further increasing the pump power of 288 mW and tuning the PC1 based on the generation of tri-comb II. As shown in Fig. 4(a), at the output powers of 3.7 mW and 3.8 mW in the two directions, respectively, the center wavelengths of wavelength-multiplexed mode-locking are 1553.1 nm and 1563.3 nm, and that of polarization-multiplexed mode-locking is 1557.6 nm. Their 3 dB bandwidths are 2.7 nm, 3.3 nm, and 3.0 nm, respectively. The frequency repetition rates and their difference of wavelength-multiplexed mode-locking are around 41.281 MHz and 1029 Hz, and that of polarization-multiplexed mode-locking are around 41.287 MHz and 607 Hz (see Fig. 4(b)). The repetition rate difference between the multiplexed combs can be altered by carefully tailoring the fiber lengths in the two directions. As further shown in Fig. 4(c), quadruple asynchronous pulse trains with distinct time intervals can be observed, which may be required in many multi-comb applications. It is noted that dual/tri/quad-comb operations can be reversed and mode-locking again when the pump power is tuned in the opposite direction combining with finely adjusting the intracavity variable attenuators and the polarization controllers.
Fig. 4. Quad-comb generation and its output characteristics. (a) The optical spectra, (b) RF spectra, and (c) pulse trains of the quad-comb; monitored variations in the frequency repetition rates and their difference in (d) f1 and f2, (e) f3 and f4, and (f) f1 and f4.
The ability to maintain good stability and mutual coherence among the combs of the generated quad-comb in such a free-running laser is critical for many potential multi-comb applications. To evaluate the relative stability among the combs in the RF domain, a two-channel frequency counter (Agilent, 53132A) is used for the measurement. The frequency counter’s gate time is set to 0.1s. Due to the limitation of the channels that can be measured, only two combs of the quad-comb can be monitored simultaneously. Since the generation of quad-comb is from two pairs of wavelength-multiplexed combs and polarization-multiplexed combs, the stability of the quad-comb is needed to be measured in the three cases: wavelength-multiplexed combs (λ1 and λ2, corresponding to the repetition rates of f1 and f2), polarization-multiplexed combs (pol1 and pol2, corresponding to the repetition rates of f3 and f4), and the two combs based on one comb of wavelength-multiplexed combs with one comb of polarization-multiplexed combs (for example, λ1 and pol2, corresponding to the repetition rates of f1 and f4). Figures 4(d)-(f) show the temporal variation in frequency repetition rate (frep) and repetition rate difference (Δfrep) under the three cases. The frequency drifts are ∼26 Hz, 30 Hz and 32 Hz, respectively, in frep due to the environmental perturbation like temperature changes. The repetition rates exhibit the same trends and identical amounts under 30 min in each case. Noted that the differences in the drift directions of frep between the three cases are due to those measurements being sensitive to environmental perturbation under different moments. Yet, the stability of Δfrep in each case remain stable and their standard deviations are 77 mHz, 81 mHz, and 93 mHz, respectively, while their repetition rates are varied by around 30 Hz. This is a significant advantage for multi-comb applications, where the long-term stability of Δfrep should be maintained constant during the measurement of multi-heterodyne beat signals.
To evaluate the mutual coherence, the asynchronous coherent sampling and the temporal interferograms based on the above three types of two combs are performed and detected. A typical ASOPS experimental setup is shown in Fig. 5. Two asynchronous pulse trains are selected from the quad-comb light source by exploiting CWDM/PBS filters, and further amplified and nonlinearly spectral broadened with overlapped spectra by erbium-doped fiber amplifiers (EDFAs). To avoid spectrum aliasing, two dense wavelength-division multiplexers (DWDMs) with filtered 1.6-nm bandwidth spectra are used in each arm. To investigate the capability to coherent averaging and measure fine spectral features, the light in one arm is transmitted through two cascaded fiber Bragg gratings (FBGs, FBG1 and FBG2) with the reflection center wavelengths of 1552.2 nm and 1552.9 nm as test samples. Their 3 dB bandwidths are about 0.2 nm and their peak spectral reflectivity are ∼94%. When the two asynchronous pulses are re-combined at a 2 × 2 OC, the ASOPS interferograms are generated at a balanced photodetector (BPD, Thorlabs, PDB420).
The detected ASOPS interferograms between two asynchronous pulses are shown in Fig. 6(a), which is directly detected by an A/D card when the power before the BPD is ∼9 µW. The inset in Fig. 6(a) shows the expanded view of the central burst. The interferograms have a period of 0.19 ms, consistent with the repetition rate difference of 5121 Hz. It had been suggested that linear phase correction [8,23,38] could be applied to correct for residual phase excursions in many conventional near-IR dual-comb systems. The Fourier transform of the interferograms is averaged with 550 curves with or without phase correction [8,23], respectively, in the frequency domain, which can be seen in Fig. 6(b). Compared to the averaged curve without phase correction, after phase correction, the signal-to-noise ratio is improved and reliable spectroscopic results could be obtained. Figure 6(c) shows the 5 times and 3126 times averaged results after phase correction, respectively. The two averaged spectral results match very well with each other. After averaging 3126 curves, corresponding to the data acquisition time of ∼0.61 s, the measured two transmitted dips of FBG1 and FBG2 with the center wavelength of 1552.2 nm and 1552.9 nm can be clearly resolved. As shown in the inset of Fig. 6(c), good agreement is also found between the normalized averaged agreement and that measured by an optical spectrum analyzer around 1552.9 nm. Figures 7(a) and 7(b) show similar spectral features by using the other two kinds of combs (λ1-λ2 combs and Pol1-Pol2 combs). Noted that the slight shape differences in their measured spectra are due to the differences in the nonlinear broadened spectra and the filtered spectra after EDFAs.
Fig. 6. (a) ASOPS interferograms. The inset shows the expanded view around the central burst. (b) Fourier transformed spectra with and without phase correction averaged with 550-time curves. (c) Fourier transformed spectra with different numbers of averaged curves with phase correction. Inset: the comparison of the measurement of FBG2 using the dual-comb spectroscopy with that using OSA around 1552.9 nm.
Fig. 7. The Fourier transformed spectra with 5 and 3126 curves based on the ASOPS interferograms between (a) λ1 and λ2 combs and (b) Pol1 and Pol2 combs, respectively; (c) the log-log plots of spectral SNR vs. the number of averaged curves in the three cases.
The relationship between the spectral signal-to-noise ratio (SNR), i.e. the standard deviation of the spectral curve normalized by its corresponding averaged magnitude [4], and the averaged curves in each case are given in Fig. 7(c). By exploiting the wavelength- multiplexed combs (corresponding to λ1 and λ2 combs), the SNR improves from 28.3 to 414.5 when the number of averaged curves increases from 5 to 3126, similar to the levels of the SNR with the same averaged numbers by using polarization multiplexed combs (corresponding to Pol1 and Pol2 combs). When averaged the same numbers of curves from 5 to 3126 by using the third kind of combs (corresponding to λ1 and Pol2 combs), the SNR varies from 23.6 to 238.2. One can see that three curves follow similar trends and saturation is not yet reached in the number of averaging. The figure of merits (FoM’s) of these three cases, i.e. the product of the SNR per unit acquisition time and the number of resolved spectral elements [38], are ∼1.32*106 (λ1 and λ2 combs), 1.20*106 (Pol1 and Pol2 combs), and 1.28*106 Hz1/2 (λ1 and Pοl2 combs) based on the SNR values at an acquisition time of 1s, respectively. These results are in line with the theoretical prediction in many conventional near-IR dual-comb systems [4]. This illustrates the stability in Δf as well as the mutual coherence between the combs within the averaging time window. While their FoM’s are comparable, the SNR curve begins to show early signs of saturation for the λ1 and Pοl2 combs at the same amount of acquisition time when compared to the other cases. This could have further implications to applications targeting higher achieved SNR.
It is noted that the unique laser structure studied here, which is a combination of completely shared-cavity and partially shared-cavity, allows us to make a relatively easy comparison of their performance from the very same laser platform. To our knowledge, there had been no such report of similar studies. This could reveal additional factors that affect the dual-comb performance of this kind of lasers, and would be helpful for future studies on similar lasers and the prediction and evaluation of their performance. Also, it is noted that the absorption spectra of FBGs measured in this demonstration are relatively broad, studies on molecular gases with narrower absorption spectral features would be expected in our future investigations, similar to previous demonstrations [8,10,23], to further validate the potential of the proposed dual-comb laser. Such multi-comb lasers could help to overcome the complexity for the multi-comb schemes and potentially be applied to multi-comb applications with simultaneously detecting multiple interferograms.
4. Conclusions
We experimentally investigate the tri-comb and quad-comb generation in a bidirectional mode-locked Er-doped fiber laser. The multi-comb mode-locking is enabled by simultaneously exploiting three multiplexed methods of wavelength-multiplexing, polarization-multiplexing, and direction-multiplexing. Triple and quadruple asynchronous pulse trains are generated and have been demonstrated with good stability and mutual coherence. The dual-comb spectroscopy results further demonstrate the quality in relative stability and mutual coherence of the generated quad-comb. Such lasers could be further investigated for the multi-comb generation from one laser source as well as for low-complexity and practical multi-comb applications.
Funding
Natural Science Foundation of Shanxi Province (20210302124027, 20210302124169); National Natural Science Foundation of China (52273252, 62105232, 62127814).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper may be available from the corresponding author upon reasonable request.
References
1. T. Udem, R. Holzwarth, and T. Hänsch, “Optical frequency metrology,” Nature 416(6877), 233–237 (2002). [CrossRef]
2. S. T. Cundiff and J. Ye, “Colloquium: femtosecond optical frequency combs,” Rev. Mod. Phys. 75(1), 325–342 (2003). [CrossRef]
3. T. W. Hänsch, “Nobel Lecture: Passion for precision,” Rev. Mod. Phys. 78(4), 1297–1309 (2006). [CrossRef]
4. I. Coddington, N. R. Newbury, and W. C. Swann, “Dual-comb spectroscopy,” Optica 3(4), 414–426 (2016). [CrossRef]
5. J. Yang, X. Zhao, L. Zhang, and Z. Zheng, “Single-cavity dual-comb fiber lasers and their applications,” Front. Phys. 10, 1070284 (2023). [CrossRef]
6. X. Zhao, Z. Zheng, L. Liu, Y. Liu, Y. Jiang, X. Yang, and J. Zhu, “Switchable, dual-wavelength passively modelocked ultrafast fiber laser based on a single-wall carbon nanotube modelocker and intracavity loss tuning,” Opt. Express 19(2), 1168–1173 (2011). [CrossRef]
7. 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]
8. J. Chen, X. Zhao, Z. Yao, T. Li, Q. Li, S. Xie, J. Liu, and Z. Zheng, “Dual-comb spectroscopy of methane based on a free-running Erbium-doped fiber laser,” Opt. Express 27(8), 11406–11412 (2019). [CrossRef]
9. Y. Zhu, F. Xiang, L. Jin, S. Y. Set, and S. Yamashita, “All-fiber dual-wavelength mode-locked laser using a bend-induced-birefringence Lyot-filter as gain-tilt equalizer,” IEEE Photonics J. 11(6), 1–7 (2019). [CrossRef]
10. J. Chen, K. Nitta, X. Zhao, T. Mizuno, T. Minamikawa, F. Hindle, Z. Zheng, and T. Yasui, “Adaptive-sampling near-Doppler-limited terahertz dual-comb spectroscopy with a free-running single-cavity fiber laser,” Adv. Photonics 2(3), 036004 (2020). [CrossRef]
11. 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]
12. 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]
13. L. A. Sterczewski, A. Przewloka, W. Kaszub, and J. Sotor, “Computational Doppler-limited dual-comb spectroscopy with a free-running all-fiber laser,” APL Photonics 4(11), 116102 (2019). [CrossRef]
14. K. Kieu and M. Mansuripur, “All-fiber bidirectional passively modelocked ring laser,” Opt. Lett. 33(1), 64–66 (2008). [CrossRef]
15. C. Ouyang, P. Shum, K. Wu, J. H. Wong, H. Q. Lam, and S. Aitya, “Bidirectional passively mode-locked soliton fiber laser with a four-port circulator,” Opt. Lett. 36(11), 2089–2091 (2011). [CrossRef]
16. X. Zhao, Z. Zheng, Y. Liu, G. Hu, J. Liu, and Z. Zheng, “Dual-wavelength, bidirectional single-wall carbon nanotube mode-locked fiber laser,” IEEE Photonics Technol. Lett. 26(17), 1722–1725 (2014). [CrossRef]
17. H. Jiang, Y. Wang, S. Y. Set, and S. Yamashita, “Bidirectional Mode-locked Soliton Fiber Laser in 2µm Using CNT Saturable Absorber,” in Advanced Solid State Lasers Conference, OSA Technical Digest Series (Optical Society of America, 2017), paper JM5A.21.
18. Y. Nakajima, Y. Hata, and K. Minoshima, “High-coherence ultrabroadband bidirectional dual-comb fiber laser,” Opt. Express 27(5), 5931–5944 (2019). [CrossRef]
19. 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]
20. B. Li, J. Xing, D. Kwon, Y. Xie, N. Prakash, J. Kim, and S.-W. Huang, “Bidirectional mode-locked all-normal dispersion fiber laser,” Optica 7(8), 961–964 (2020). [CrossRef]
21. Y. Liu, X. Zhao, G. Hu, C. Li, B. Zhao, and Z. Zheng, “Unidirectional, dual-comb lasing under multiple pulse formation mechanisms in a passively mode-locked fiber ring laser,” Opt. Express 24(19), 21392–21398 (2016). [CrossRef]
22. S. Mehravar, R. A. Norwood, N. Peyghambarian, and K. Kieu, “Real-time dual-comb spectroscopy with a freerunning bidirectionally mode-locked fiber laser,” Appl. Phys. Lett. 108(23), 231104 (2016). [CrossRef]
23. 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]
24. J. Guo, Y. Ding, X. Xiao, L. Kong, and C. Yang, “Multiplexed static FBG strain sensors by dual-comb spectroscopy with a free running fiber laser,” Opt. Express 26(13), 16147–16154 (2018). [CrossRef]
25. B. Willenberg, J. Pupeikis, L. M. Kruger, F. Koch, C. R. Phillips, and U. Keller, “Femtosecond dual-comb Yb:CaF2 laser from a single free-running polarization-multiplexed cavity for optical sampling applications,” Opt. Express 28(20), 30275–30288 (2020). [CrossRef]
26. T. Mizuno, Y. Nakajima, Y. Hata, T. Tsuda, A. Asahara, T. Kato, T. Minamikawa, T. Yasui, and K. Minoshima, “Computationally image-corrected dual-comb microscopy with a free-running single-cavity dual-comb fiber laser,” Opt. Express 29(4), 5018–5032 (2021). [CrossRef]
27. S. L. Camenzind, J. F. Fricke, J. Kellner, B. Willenberg, J. Pupeikis, C. R. Phillips, and U. Keller, “Dynamic and precise long-distance ranging using a free-running dual-comb laser,” Opt. Express 30(21), 37245–37260 (2022). [CrossRef]
28. X. Zhao, C. Li, T. Li, G. Hu, R. Li, M. Bai, T. Yasui, and Z. Zheng, “Dead-band-free, high-resolution microwave frequency measurement using a free-running triple-comb fiber laser,” IEEE J. Select. Topics Quantum Electron. 24(3), 1–8 (2018). [CrossRef]
29. J. Yang, J. Liu, T. Li, J. Hu, J. Wang, Y. Wu, S. Xie, X. Zhao, and Z. Zheng, “Dynamic spectroscopic characterization for fast spectral variations based on dual asynchronous undersampling with triple optical frequency combs,” Opt. Laser Eng. 156, 107077 (2022). [CrossRef]
30. X. Zhao, X. Qu, F. Zhang, Y. Zhao, and G. Tang, “Absolute distance measurement by multi-heterodyne interferometry using an electro-optic triple comb,” Opt. Lett. 43(4), 807–810 (2018). [CrossRef]
31. B. Lomsadze, B. C. Smith, and S. T. Cundiff, “Tri-comb spectroscopy,” Nat. Photonics 12(11), 676–680 (2018). [CrossRef]
32. R. Liao, H. Tian, W. Liu, R. Li, Y. Song, and M. Hu, “Dual-comb generation from a single laser source: principles and spectroscopic applications towards mid-IR-A review,” JPhys Photonics 2(4), 042006 (2020). [CrossRef]
33. Z.-C. Luo, A.-P. Luo, W.-C. Xu, H.-S. Yin, J.-R. Liu, Q. Ye, and Z.-J. Fang, “Tunable multiwavelength passively mode-locked fiber ring laser using intracavity birefringence-induced comb filter,” IEEE Photonics J. 2(4), 571–577 (2010). [CrossRef]
34. X. Liu, D. Han, Z. Sun, C. Zeng, H. Lu, D. Mao, Y. Cui, and F. Wang, “Versatile multi-wavelength ultrafast fiber laser mode-locked by carbon nanotubes,” Sci. Rep. 3(1), 2718 (2013). [CrossRef]
35. R. Yang, H. Sun, H. Lv, J. Xu, J. Wu, P. Hu, H. Fu, H. Yang, and J. Tan, “A multidimensional multiplexing mode-locked laser based on a dual-ring integrative structure for tri-comb generation,” Appl. Sci. 10(22), 8260 (2020). [CrossRef]
36. T. Li, X. Zhao, J. Chen, Q. Li, S. Xie, and Z. Zheng, “Tri-comb and quad-comb generation based on a multi-dimensional multiplexed mode-locked laser,” J. Lightwave Technol. 37(20), 5178–5184 (2019). [CrossRef]
37. Y. S. Fedotov, S. M. Kobtsev, R. N. Arif, A. G. Rozhin, C. Mou, and S. K. Turitsyn, “Spectrum-, pulsewidth-, and wavelength-switchable all-fiber mode-locked Yb laser with fiber based birefringent filter,” Opt. Express 20(16), 17797–17805 (2012). [CrossRef]
38. N. R. Newbury, I. Coddington, and W. Swann, “Sensitivity of coherent dual-comb spectroscopy,” Opt. Express 18(8), 7929–7945 (2010). [CrossRef]
