Open Access
Add to BibSonomy
Abstract
We investigated the stability and mutual coherence of a Raman microcomb in a silica microrod resonator by monitoring the output power and longitudinal mode spacings. The results indicate that we can obtain a stable Raman comb formation without the need for four-wave mixing processes. The use of a Raman comb will open the possibility of simplifying the setup because it will relax the phase matching condition usually required for microresonator frequency comb generation. Although there are some restrictions in regard to using a Raman comb for applications due to the coexistence of the comb components in different mode families, a proof-of-concept demonstration shows that it is sufficiently stable and robust for applications such as optical communications.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Although various optical nonlinearities [1] have been studied since the invention of the laser, moving the technologies to the practical stage remains challenging. Among various optical nonlinearities, stimulated Raman scattering (SRS) is one of the phenomena actively applied in practical systems and equipment such as telecommunications and sensing devices. In particular, SRS in silica has been shown to provide broad amplification in optical fibers, enabling Raman amplifiers [2] to be used for long-haul optical communications. Although the spontaneous Raman process induces noise, which sometimes significantly degrades the signal [3], the SRS process is usually stable and robust.
A small resonator with a high-quality factor ($Q$) supports efficient optical nonlinearities because it makes it possible to employ a large electrical field, even with a small input [4,5]. It has recently been shown that various optical nonlinear effects such as cascaded four-wave-mixing (FWM) in whispering-gallery-mode (WGM) microresonators and microrings enable frequency comb generation [6–12], known as microcombs, in a wide variety of material platforms [13]. The stability of microcombs has been intensively studied to establish the framework for mode-locking in Kerr microresonators [14–16]. The hyper-parametric oscillation based on a strict phase-matching condition inherently exhibits an excellent phase-coherence and thus has attracted great interest [17–19]. Soliton comb generation also features stable and low-noise output [20], which provides an ideal platform for many applications. However, it generally requires sophisticated control of a pump laser to generate and stabilize soliton combs [21–23]. Ultimately, it makes the system complex. Therefore, developing the idea of exploiting SRS in silica for microcomb generation is straightforward because it will relax the phase-matching condition but still support broad bandwidth gain.
This motivation has already driven several studies. Several research groups have reported on Raman lasing [24–27] and the generation of a microcomb with SRS (i.e., a Raman comb) in crystalline material [28,29] and amorphous material [30–32]. Researchers have tried to obtain a phase-locked state since it is the quietest, and have successfully realized a phase-locked Raman comb with the help of cross-phase-modulation (XPM) between SRS-generated and FWM-generated combs. This is known as a Stokes soliton [33]. This work revealed that the mode spacings (i.e., repetition rates) are locked to each other thanks to the Kerr effect, but studies on stable Raman comb generation, where no FWM is involved, are of interest in terms of simplicity. Although a study has investigated the stability of a Raman comb in a crystalline WGM microresonator [28], the stability and spectral purity of a broad-bandwidth Raman comb have still not been fully explored. The SRS process appears straightforward but involves a more complex phenomenon, such as the interaction between two cascaded SRS processes [30,34] and competition between the FWM and SRS processes [35–37]. With this in mind, we investigate the power stability and mutual coherence between the longitudinal modes of a Raman comb generated in a silica rod microresonator. By collecting that information, we move a step nearer to understanding and controlling the stability of a Raman comb, which is essential if we want to use it for practical applications.
The paper is organized as follows. In Section 2, we investigate the long-term power stability of the output power of a Raman comb. Section 3 discusses the longitudinal mode spacing and origin of Raman combs. Then we describe an optical transmission experiment in Section 4.
2. Long-term power stability measurement of Raman comb
2.1 Silica rod microresonator fabrication and resonator characterization
First, we fabricated a silica rod microresonator with CO$_2$-laser -machining, where we shaped a fused silica rod to support the WGM by performing ablation and reflow simultaneously [38]. A microscopic image of the fabricated device is shown in Fig. 1(a), where the major diameter of the WGM resonator is 1.4 mm, corresponding to a free spectral range (FSR) of 46.6 GHz, and the minor diameter is about 130$\,\mathrm {\mu }\textrm {m}$, corresponding to an effective mode area of about 75$\,\mathrm {\mu }\textrm {m}^{2}$ for the fundamental mode at a wavelength of 1480 nm. The resonant spectrum is measured with a tapered fiber setup where the transmission spectrum is shown in Fig. 1(b). Figure 1(c) is the magnified spectrum of one of the resonances with a $Q$ of 1.85$\times$10$^{8}$ at 1481.67 nm, which is close to the pump wavelength we used in the experiments. The resonance exhibits mode splitting due to clockwise and counter-clockwise mode coupling [39,40].
Fig. 1. (a) Microscopic photograph of a fabricated silica rod microresonator. (b) Transmission spectrum of the silica rod microresonator obtained by using a tapered fiber setup. (c) Magnified view of one of the resonances, yielding a quality factor of 1.85$\times$10$^{8}$.
2.2 Raman comb generation
Next, we generated a Raman comb using a standard tapered fiber experimental setup. A continuous-wave (CW) laser at 1480 nm was amplified to 145 mW with an S-band thulium-doped fiber amplifier (TDFA), and then the light was injected into a silica rod microresonator via a tapered fiber to generate the Raman comb. The generated comb was measured using an optical spectrum analyzer at a wavelength resolution of 20 pm. We chose a pump wavelength of 1480 nm so that the output Raman comb was located at around 1600 nm, where we could use an L-band optical amplifier and several optical components. To discuss various aspects of the Raman comb quantitatively and qualitatively, we performed a similar experiment using a modulation instability (MI) comb, which is as easy to generate as a Raman comb for reference. To generate an MI comb, we pumped the same cavity at 1546 nm after amplifying the CW laser to 76 mW with a C-band erbium-doped fiber amplifier (EDFA).
2.3 Long-term power stability of the Raman comb
Figures 2(a) and 2(b) show the spectra of the generated Raman comb. We obtained a broad comb spectrum ranging from 1575–1610 nm thanks to the broad bandwidth Raman gain of silica. It should be noted that the generated comb consisted of different mode families with different FSRs, which was possible because of the relaxed phase-matching condition of the SRS process. In addition, a detailed view of the Raman gain spectrum reveals several peaks, often modeled with 13-different vibrational modes in fused silica [41]. We labeled two of the prominent peaks as peak-1 and peak-2, as defined in our previous study [30].
Fig. 2. (a) Measured spectrum of the pump and generated Raman comb. The orange line is the Raman gain in silica taken from Ref [41]. (b) A magnified view of (a). (c) A heatmap showing the spectra recorded for 60 min. (d) The recorded power variations with time of pump (R(P)) and three longitudinal modes of the generated Raman comb ((R(A), R(B), and R(C)). The wavelengths for R(P), R(A), R(B), and R(C) are 1480 nm, 1584.19 nm, 1590.56 nm, and 1598.06 nm, respectively. The data are recorded every two seconds.
Next, we continuously monitored and recorded the spectrum every 30 seconds for 60 minutes. The result is shown with a colormap in Fig. 2(c). To observe the power fluctuations more carefully, we plot the power of the longitudinal modes R(A), R(B), and R(C) as a function of time in Fig. 2(d). Longitudinal modes R(A) and R(B) are part of peak-1, whereas mode R(C) is located at the center of peak-2. R(P) corresponds to the transmitted pump line at 1480 nm for reference. Although longitudinal modes R(A) and R(B) (peak-1) are unstable, we observe high power stability at mode R(C) (peak-2). Even though the system is free-running (i.e., we apply no feedback to the cavity or the pump laser), the difference between the maximum and minimum power of mode R(C) was only 1.9 dB during the measurement. Although peak-2 of the generated Raman comb is relatively stable, we believe there is a need for further detailed studies based on the comparison between different states of combs to understand it more quantitively.
Figure 3(a) shows the recorded spectra of the generated MI comb using the same cavity, where the pump power was about 76 mW. Figure 3(b) shows the power stability of three different modes of the MI comb, where we observed a power fluctuation exceeding 10 dB for several comb modes. Even in the most stable longitudinal mode, the maximum and minimum power difference during the measurement was 5.1 dB. The results show that a Raman comb features power stability comparable to that of an MI comb, which is operated in the thermal self-locking regime [42]. However, we cannot reach a concrete conclusion as to why peak-2 is more stable than peak-1 from the results alone. The phenomenon can be partly explained as follows. Based on previous studies [30,34], the generation of peak-2 is explained by the simultaneous excitation provided directly by the pump and by the cascaded excitation of the generated peak-1 component. Since peak-2 is complementarily fed from two components, that is, one directly from the pump and the other from the Raman components of peak-1, the peak-2 component can exhibit higher power stability. On the other hand, the energy of peak-1 is exploited when cascaded excitation occurs, so the stability of peak-1 is lower than that of peak-2. Although we will need further investigation to reach a concrete conclusion, our experimental result shows that the generated Raman comb at peak-2 is stable, allowing us to use it for further applications.
Fig. 3. (a) Observed spectrum of an MI comb (upper panel) and a heatmap showing the spectra recorded for 60 min (lower panel). (c) The recorded light power of the pump (M(P) and longitudinal modes M(A), M(B), and M(C), where the MI comb wavelengths are 1544.29 nm, 1544.67 nm, and 1547.66 nm, respectively. The wavelength positions are indicated in (a). The data are acquired every two seconds.
3. Longitudinal mode spacing measurement
If an FWM process is involved in the formation of the peak-2 component, the mode spacing between longitudinal modes should be equidistant due to the strict phase-matching condition that is required for this process to occur. To investigate the origin of Raman combs, we developed a precise measurement technique to determine the longitudinal mode spacing of the Raman comb. The experimental setup is shown in Fig. 4(a). Since the silica rod microresonator used in this experiment has an FSR of $\sim$ 46.6 GHz, it is a challenge to directly measure the beat signal of the generated Raman comb. Therefore, we modulated the output comb at 7.7 GHz using an intensity modulator to create sidebands in each comb line to downconvert the comb beat frequency [43]. The down-converted longitudinal mode spacing of the Raman comb (i.e., the beat signals between the third-order sidebands of $\pm$23.1 GHz shifted from the native comb modes), which is around 0.3–0.5 GHz, is then detected using a photodetector. In addition, we inserted a 2-nm wide bandpass filter (BPF) to extract four or five longitudinal modes to closely examine the mode-spacings across the entire wavelength of the Raman comb. By scanning the center wavelength of the BPF, we obtained the wavelength-dependent mode-spacing of the Raman combs.
Fig. 4. (a) Experimental setup used for the precise longitudinal mode spacing measurement of the generated Raman comb. The frequency of the signal generator (SG) is 7.7 GHz. The power of the pump light is 145 mW at a wavelength of 1480 nm. The resolution of the ESA is 300 Hz. PC: Polarization controller, BPF: Band-pass filter, IM: Intensity modulator, PD: Photodiode, ESA: Electrical spectrum analyzer, OSA: Optical spectrum analyzer. (b) Spectra after the BPF. Different colors of the spectra correspond to different center wavelengths of the BPF. The background light below -40 dBm is caused by the amplified spontaneous emission from the L-band EDFA. (c) Magnified view of spectrum in (b). We observe longitudinal modes from two different mode families. (d) Recorded RF spectrum of (b). The color corresponds to that of the optical spectrum shown in (b). The multi-peaks around 387.5 MHz and 392.5 MHz originate from two different mode families as seen in (c). (e) The extracted comb mode spacings from (d). Three mode families with different dispersion profiles can be identified.
The spectrum transmitted from the BPF is shown in Fig. 4(b). Different colors correspond to different center wavelengths of the BPF. A magnified view of the spectrum around 1596 nm is shown in Fig. 4(c). The measured down-converted beat signals are shown in Fig. 4(d), where the color corresponds to that of Fig. 4(b). First, the beat note spectra show a peak at specific frequencies, indicating that each longitudinal mode exhibits frequency-variant coherence. The 3-dB linewidth of the peaks ranges from $\sim$100 kHz to 3 MHz. Next, we also note that the peaks are located at different frequencies, which reveals that the longitudinal mode spacings are non-equidistant. The beat frequency decreases at a longer wavelength, and this feature agrees with the fact that a silica microrod resonator has an anomalous dispersion in this wavelength region [30,44]. Since the longitudinal mode spacings are not equidistant, we conclude that no FWM is involved in Raman comb generation. Additional evidence for the fact that only SRS is involved in this process is shown in Fig. 4(c), where combs in different mode families are generated simultaneously. Here, we find three different groups in the RF beat signals. The group around the wavelength of 1587 nm corresponds to peak-1, which is unstable, and the fitted dispersion is 5.8 ps/km/nm. The group around the wavelength of 1594 nm corresponds to peak-2, which is stable, and the dispersion is 69.8 ps/km/nm. The pump and two Raman modes exhibit different dispersion profiles, which indicate that these modes belong to different mode families [32]. These results suggest that a stable Raman comb is obtained without an FWM process. After all, the phase matching condition is relaxed, which may allow us to obtain a broad bandwidth comb in a simple configuration, which is attractive for applications.
4. Potential application of Raman laser and comb
One of the potential applications of such a stable Raman comb is a multi-wavelength light source for optical communications [45,46]. To explore the possibility, we performed back-to-back optical transmission experiments using Raman signals in silica microcavities with a broad bandwidth Raman gain (Fig. 5(a)). The platforms we used for this demonstration were silica toroid and silica rod microresonators. We chose a silica microtoroid with a major diameter of 60$\,\mathrm {\mu }\textrm {m}$ that has much fewer transverse modes (i.e., mode families) than microrods, and thus enables single-mode lasing. We pumped the microtoroid under different conditions and obtained single-mode Raman lasing at different wavelengths corresponding to peak-1 and peak-2 as shown in Fig. 5(b). These lines were amplified with an L-band EDFA and then modulated with a 10-GHz intensity modulator to encode a non-return-to-zero (NRZ) signal.
Fig. 5. (a) Experimental setup for an optical transmission experiment at 10 Gbps. PPG: Pulse pattern generator. PWM: Power meter. VOA: Variable optical attenuator. (b) Spectra of observed SRS lasing and comb. From top to bottom: The pump and SRS lasing spectra at peak-1 and peak-2 gain peaks in a silica toroid. The pump and Raman comb spectra in a silica rod resonator. (c) Eye pattern diagrams measured by a sampling oscilloscope. The color corresponds to that in (b). (d) Back-to-back BER measurement results as a function of the received optical power. The gray symbols indicate a CW reference using a pump laser (linewidth<100 kHz).
We then modulated the output from the microtoroid at 10 Gbps and recorded the eye patterns (Fig. 5(c)). We also measured the bit-error rate as a function of the received power (Fig. 5(d)). We obtained clear eye-openings in peak-1 and peak-2, but a detailed comparison of the BERs of peak-1 and peak-2 shows a clear difference as regards performance. The BER of peak-2 is the same as that of the reference, but peak-1 is worse because of instability. Although our demonstration is a preliminary experiment, we have shown the possibility of using stable peak-2 for applications.
Next, we performed the same experiment with the peak-2 line of a Raman comb in a silica microrod. We expected to find the same tendency as we obtained with the peak-2 SRS lasing in a toroid; however, it turned out that there was significant degradation in the eye pattern and in the BER measurement. The result is not intuitive because the output power of the Raman comb is stable as with peak-2. We attribute the reason to the multi-mode lasing behavior of Raman combs, which involves different mode families, as shown in Fig. 4(d). This feature causes unwanted interference and beating [47], which could degrade the coherence. Nevertheless, our result suggests that the Raman lasing from peak-2 is more stable and coherent, indicating the potential for various applications.
5. Conclusion
We studied the power stability and mutual coherence of a Raman comb generated in a silica microrod. First, we acquired information on the power of the broad bandwidth Raman comb and observed a better long-term power stability for peak-2. During a one-hour measurement, we monitored the power and found that the fluctuation was > 10 dB and 1.9 dB for peak-1 and peak-2, respectively. The power fluctuation of peak-2 was less than that of one of the MI comb lines (5.1 dB). So, we conclude that the Raman comb in peak-2 is more stable, although peak-1 is unstable because it complementarily provides energy to peak-2. By performing a precise longitudinal mode-spacing measurement, we confirmed that no FWM process is involved during the generation of the Raman comb.
As a proof-of-principle experiment, we performed preliminary demonstrations on optical communication and obtained positive and negative results. We achieved an error-free BER of 10$^{-9}$ in a 10 Gbps speed intensity modulation and with direct detection (IM-DD) using peak-2 Raman lasing in a microtoroid. This is a positive result because it indicates that peak-2 is sufficiently stable for applications. In addition, we found it challenging to use a Raman comb when it contains different mode families, which may degrade the phase and intensity noise of the Raman combs. Although we need further study to elucidate the mechanism behind Raman comb generation with broadband silica gain, we believe that this study paves the way for understanding the stability and coherence of the Raman comb, which is essential for practical applications.
Funding
Japan Society for the Promotion of Science (JP19H00873, JP22K14625); Ministry of Education, Culture, Sports, Science and Technology (JPMXS0118067246).
Acknowledgments
This work was supported by JSPS KAKENHI and MEXT Quantum Leap Flagship Program (MEXT Q-LEAP). We thank H. Kumazaki and S. Kogure for technical assistance.
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.
References
1. P. A. Franken, A. E. Hill, C. W. Peters, and G. Weinreich, “Generation of optical harmonics,” Phys. Rev. Lett. 7(4), 118–119 (1961). [CrossRef]
2. M. Islam, “Raman amplifiers for telecommunications,” IEEE J. Sel. Top. Quantum Electron. 8(3), 548–559 (2002). [CrossRef]
3. S. J. Carter and P. D. Drummond, “Squeezed quantum solitons and Raman noise,” Phys. Rev. Lett. 67(27), 3757–3760 (1991). [CrossRef]
4. T. J. Kippenberg, S. M. Spillane, and K. J. Vahala, “Kerr-Nonlinearity Optical Parametric Oscillation in an Ultrahigh- Q Toroid Microcavity,” Phys. Rev. Lett. 93(8), 083904 (2004). [CrossRef]
5. X. Ji, F. A. S. Barbosa, S. P. Roberts, A. Dutt, J. Cardenas, Y. Okawachi, A. Bryant, A. L. Gaeta, and M. Lipson, “Ultra-low-loss on-chip resonators with sub-milliwatt parametric oscillation threshold,” Optica 4(6), 619 (2017). [CrossRef]
6. P. Del’Haye, A. Schliesser, O. Arcizet, T. Wilken, R. Holzwarth, and T. J. Kippenberg, “Optical frequency comb generation from a monolithic microresonator,” Nature 450(7173), 1214–1217 (2007). [CrossRef]
7. T. Herr, K. Hartinger, J. Riemensberger, C. Y. Wang, E. Gavartin, R. Holzwarth, M. L. Gorodetsky, and T. J. Kippenberg, “Universal formation dynamics and noise of Kerr-frequency combs in microresonators,” Nat. Photonics 6(7), 480–487 (2012). [CrossRef]
8. E. Obrzud, S. Lecomte, and T. Herr, “Temporal solitons in microresonators driven by optical pulses,” Nat. Photonics 11(9), 600–607 (2017). [CrossRef]
9. T. J. Kippenberg, A. L. Gaeta, M. Lipson, and M. L. Gorodetsky, “Dissipative kerr solitons in optical microresonators,” Science 361(6402), eaan8083 (2018). [CrossRef]
10. T. Tanabe, S. Fujii, and R. Suzuki, “Review on microresonator frequency combs,” Jpn. J. Appl. Phys. 58(SJ), SJ0801 (2019). [CrossRef]
11. M. Zhang, B. Buscaino, C. Wang, A. Shams-Ansari, C. Reimer, R. Zhu, J. M. Kahn, and M. Lončar, “Broadband electro-optic frequency comb generation in a lithium niobate microring resonator,” Nature 568(7752), 373–377 (2019). [CrossRef]
12. Y. Sun, J. Wu, M. Tan, X. Xu, Y. Li, R. Morandotti, A. Mitchell, and D. J. Moss, “Applications of optical microcombs,” Adv. Opt. Photonics 15(1), 86–175 (2023). [CrossRef]
13. A. Kovach, D. Chen, J. He, H. Choi, A. H. Dogan, M. Ghasemkhani, H. Taheri, and A. M. Armani, “Emerging material systems for integrated optical Kerr frequency combs,” Adv. Opt. Photonics 12(1), 135–222 (2020). [CrossRef]
14. A. B. Matsko, A. A. Savchenkov, D. Strekalov, V. S. Ilchenko, and L. Maleki, “Optical hyperparametric oscillations in a whispering-gallery-mode resonator: Threshold and phase diffusion,” Phys. Rev. A 71(3), 033804 (2005). [CrossRef]
15. J. Pfeifle, A. Coillet, R. Henriet, K. Saleh, P. Schindler, C. Weimann, W. Freude, I. V. Balakireva, L. Larger, C. Koos, and Y. K. Chembo, “Optimally coherent kerr combs generated with crystalline whispering gallery mode resonators for ultrahigh capacity fiber communications,” Phys. Rev. Lett. 114(9), 093902 (2015). [CrossRef]
16. H. Taheri, A. A. Eftekhar, K. Wiesenfeld, and A. Adibi, “Anatomy of phase locking in hyperparametric oscillations based on Kerr nonlinearity,” IEEE Photonics J. 9(3), 1–11 (2017). [CrossRef]
17. Y. Okawachi, M. Yu, K. Luke, D. O. Carvalho, S. Ramelow, A. Farsi, M. Lipson, and A. L. Gaeta, “Dual-pumped degenerate Kerr oscillator in a silicon nitride microresonator,” Opt. Lett. 40(22), 5267–5270 (2015). [CrossRef]
18. S. Fujii, S. Tanaka, M. Fuchida, H. Amano, Y. Hayama, R. Suzuki, Y. Kakinuma, and T. Tanabe, “Octave-wide phase-matched four-wave mixing in dispersion-engineered crystalline microresonators,” Opt. Lett. 44(12), 3146–3149 (2019). [CrossRef]
19. X. Lu, G. Moille, A. Singh, Q. Li, D. A. Westly, A. Rao, S.-P. Yu, T. C. Briles, S. B. Papp, and K. Srinivasan, “Milliwatt-threshold visible–telecom optical parametric oscillation using silicon nanophotonics,” Optica 6(12), 1535–1541 (2019). [CrossRef]
20. T. Herr, V. Brasch, J. D. Jost, C. Y. Wang, N. M. Kondratiev, M. L. Gorodetsky, and T. J. Kippenberg, “Temporal solitons in optical microresonators,” Nat. Photonics 8(2), 145–152 (2014). [CrossRef]
21. J. R. Stone, T. C. Briles, T. E. Drake, D. T. Spencer, D. R. Carlson, S. A. Diddams, and S. B. Papp, “Thermal and Nonlinear Dissipative-Soliton Dynamics in Kerr-Microresonator Frequency Combs,” Phys. Rev. Lett. 121(6), 063902 (2018). [CrossRef]
22. H. Guo, M. Karpov, E. Lucas, A. Kordts, M. H. Pfeiffer, V. Brasch, G. Lihachev, V. E. Lobanov, M. L. Gorodetsky, and T. J. Kippenberg, “Universal dynamics and deterministic switching of dissipative Kerr solitons in optical microresonators,” Nat. Phys. 13(1), 94–102 (2017). [CrossRef]
23. S. Fujii, K. Wada, R. Sugano, H. Kumazaki, S. Kogure, Y. K. Kato, and T. Tanabe, “Versatile tuning of Kerr soliton microcombs in crystalline microresonators,” Commun. Phys. 6(1), 1 (2023). [CrossRef]
24. T. J. Kippenberg, S. M. Spillane, D. K. Armani, and K. J. Vahala, “Ultralow-threshold microcavity Raman laser on a microelectronic chip,” Opt. Lett. 29(11), 1224–1226 (2004). [CrossRef]
25. B.-B. Li, Y.-F. Xiao, M.-Y. Yan, W. R. Clements, and Q. Gong, “Low-threshold raman laser from an on-chip, high-Q, polymer-coated microcavity,” Opt. Lett. 38(11), 1802–1804 (2013). [CrossRef]
26. F. Vanier, M. Rochette, N. Godbout, and Y.-A. Peter, “Raman lasing in As2S3 high-Q whispering gallery mode resonators,” Opt. Lett. 38(23), 4966–4969 (2013). [CrossRef]
27. Y. Ooka, Y. Yang, J. Ward, and S. Nic Chormaic, “Raman lasing in a hollow, bottle-like microresonator,” Appl. Phys. Express 8(9), 092001 (2015). [CrossRef]
28. W. Liang, V. S. Ilchenko, A. A. Savchenkov, A. B. Matsko, D. Seidel, and L. Maleki, “Passively mode-locked raman laser,” Phys. Rev. Lett. 105(14), 143903 (2010). [CrossRef]
29. G. Lin and Y. K. Chembo, “Phase-locking transition in raman combs generated with whispering gallery mode resonators,” Opt. Lett. 41(16), 3718–3721 (2016). [CrossRef]
30. R. Suzuki, A. Kubota, A. Hori, S. Fujii, and T. Tanabe, “Broadband gain induced Raman comb formation in a silica microresonator,” J. Opt. Soc. Am. B 35(4), 933 (2018). [CrossRef]
31. Y. Yang, S. Zhao, Y. Shen, L. Meng, T. Chen, Z. Huang, L. Zhang, and K. Wang, “Transition from kerr comb to raman soliton comb in micro-rod resonator for broadband comb applications,” IEEE J. Quantum Electron. 57(6), 1–6 (2021). [CrossRef]
32. T. Kato, A. Hori, R. Suzuki, S. Fujii, T. Kobatake, and T. Tanabe, “Transverse mode interaction via stimulated Raman scattering comb in a silica microcavity,” Opt. Express 25(2), 857–866 (2017). [CrossRef]
33. Q.-F. Yang, X. Yi, K. Y. Yang, and K. Vahala, “Stokes solitons in optical microcavities,” Nat. Phys. 13(1), 53–57 (2017). [CrossRef]
34. S. Kasumie, F. Lei, J. M. Ward, X. Jiang, L. Yang, and S. Nic Chormaic, “Raman laser switching induced by cascaded light scattering,” Laser Photonics Rev. 13(10), 1900138 (2019). [CrossRef]
35. S. Fujii, T. Kato, R. Suzuki, A. Hori, and T. Tanabe, “Transition between Kerr comb and stimulated Raman comb in a silica whispering gallery mode microcavity,” J. Opt. Soc. Am. B 35(1), 100–106 (2018). [CrossRef]
36. Y. Okawachi, M. Yu, V. Venkataraman, P. M. Latawiec, A. G. Griffith, M. Lipson, M. Lončar, and A. L. Gaeta, “Competition between raman and kerr effects in microresonator comb generation,” Opt. Lett. 42(14), 2786–2789 (2017). [CrossRef]
37. M. Yu, Y. Okawachi, R. Cheng, C. Wang, M. Zhang, A. L. Gaeta, and M. Lončar, “Raman lasing and soliton mode-locking in lithium niobate microresonators,” Light: Sci. Appl. 9(1), 9 (2020). [CrossRef]
38. S. B. Papp, P. Del’Haye, and S. A. Diddams, “Mechanical control of a microrod-resonator optical frequency comb,” Phys. Rev. X 3(3), 031003 (2013). [CrossRef]
39. M. L. Gorodetsky, A. D. Pryamikov, and V. S. Ilchenko, “Rayleigh scattering in high-Q microspheres,” J. Opt. Soc. Am. B 17(6), 1051 (2000). [CrossRef]
40. S. Fujii, A. Hori, T. Kato, R. Suzuki, Y. Okabe, W. Yoshiki, A.-C. Jinnai, and T. Tanabe, “Effect on Kerr comb generation in a clockwise and counter-clockwise mode coupled microcavity,” Opt. Express 25(23), 28969–28982 (2017). [CrossRef]
41. D. Hollenbeck and C. D. Cantrell, “Multiple-vibrational-mode model for fiber-optic raman gain spectrum and response function,” J. Opt. Soc. Am. B 19(12), 2886–2892 (2002). [CrossRef]
42. T. Carmon, L. Yang, and K. J. Vahala, “Dynamical thermal behavior and thermal self-stability of microcavities,” Opt. Express 12(20), 4742–4750 (2004). [CrossRef]
43. P. Del’Haye, S. B. Papp, and S. A. Diddams, “Hybrid electro-optically modulated microcombs,” Phys. Rev. Lett. 109(26), 263901 (2012). [CrossRef]
44. S. Fujii and T. Tanabe, “Dispersion engineering and measurement of whispering gallery mode microresonator for Kerr frequency comb generation,” Nanophotonics 9(5), 1087–1104 (2020). [CrossRef]
45. P. Marin-Palomo, J. N. Kemal, M. Karpov, A. Kordts, J. Pfeifle, M. H. P. Pfeiffer, P. Trocha, S. Wolf, V. Brasch, M. H. Anderson, R. Rosenberger, K. Vijayan, W. Freude, T. J. Kippenberg, and C. Koos, “Microresonator-based solitons for massively parallel coherent optical communications,” Nature 546(7657), 274–279 (2017). [CrossRef]
46. S. Fujii, S. Tanaka, T. Ohtsuka, S. Kogure, K. Wada, H. Kumazaki, S. Tasaka, Y. Hashimoto, Y. Kobayashi, T. Araki, K. Furusawa, N. Sekine, S. Kawanishi, and T. Tanabe, “Dissipative Kerr soliton microcombs for FEC-free optical communications over 100 channels,” Opt. Express 30(2), 1351–1364 (2022). [CrossRef]
47. S. Babin, D. Churkin, A. Fotiadi, S. Kablukov, O. Medvedkov, and E. Podivilov, “Relative intensity noise in cascaded-Raman fiber lasers,” IEEE Photonics Technol. Lett. 17(12), 2553–2555 (2005). [CrossRef]
