Open Access
Add to BibSonomy
Abstract
We demonstrate efficient single- and multi-wavelength lasers at 2 $\mu$m exploiting Brillouin scattering in a SM1950 fiber. Using a SM1950 fiber as the Brillouin gain medium, higher output Stokes power and slope efficiency are achieved for a threshold pump power that is three to four times lower than the Brillouin lasing threshold in a longer length SMF with similar or higher feedback factors. We realize single and multi-Stokes Brillouin lasers with low threshold pump powers of $\sim$ 130 mW and $\sim$ 385 mW, respectively, using a 100 m SM1950 fiber ring and a Fabry-Perot resonator. For a fixed SM1950 cavity length, as the feedback factor is varied from 90$\%$ to 50$\%$, the output Stokes power and slope efficiency increased four times with only a small penalty on lasing threshold. For multi-Stokes Brillouin lasing, we observe 14 lines, including four-wave mixing components, at a maximum pump power of 822 mW. To the best of our knowledge, this is the first detailed study of Brillouin lasing at 2 $\mu$m that studies the effect of different cavity parameters such as length, feedback factor, and resonator geometry on Brillouin lasing.
© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
The wavelength region around 2 $\mu$m is of great importance as it has remarkable properties like falling in atmospheric transparency window and being ’Eye safe’. These two unique properties combined with the presence of spectroscopic signature of molecules like water, carbon dioxide and ammonia makes this wavelength region suitable for atmospheric sensing. Further, the large gain bandwidth (1800 nm-2200 nm) of Thulium doped fiber amplifiers (TDFA) around 2 $\mu$m comes as an added advantage [1,2]. All these properties make the wavelength region around 2 $\mu$m highly suitable for applications like Doppler LIDAR, Optical communication [3,4] and medical procedures [5,6]. Exploiting the 2 $\mu$m wavelength regime for the aforementioned applications requires a variety of pulsed and continuous wave (CW) sources. Narrow linewidth, tunable single- and multi-wavelength CW lasers are examples of such sources, which are required for optical communications and sensing.
Brillouin scattering, which arises due to the interaction of light with acoustic modes of a medium, has been exploited in optical fibers [7–13], photonic chip platforms [14–16], and high-Q resonators [17–19] to generate single- and multi-wavelength [20–23] narrow linewidth lasers around 1.55 $\mu$m for applications in coherent optical communications, tunable radio frequency synthesis [24–27] and generation of gigahertz repetition rate phase-locked pulses [28–31]. However, there have been very few demonstrations of Brillouin lasers around 2 $\mu$m. Recently, single wavelength Brillouin lasing was demonstrated in a 1.5 m long suspended core chalcogenide (As$_{38}$Se$_{62}$) fiber with a record low threshold pump power $P_{th} \sim$ 52 mW [32]. However, the low threshold in this demonstration comes at the expense of small slope efficiency and low output Stokes power $<$ 100 $\mu$W. While large output Stokes power and slope efficiency has been achieved for a single wavelength Brillouin laser using a 14 m long single mode fiber (SMF), it comes at the expense of large threshold pump power $\sim$ 1 W [33]. Multi-Stokes Brillouin lasing, where 5 Stokes lines were generated with a pump power of 3.2 W, has also been demonstrated using a 450 m long SMF-28 fiber as the Brillouin gain medium [34].
Here, we present efficient single- and multi-wavelength Brillouin lasing at 2004 nm using a Nufern SM1950 fiber, which is specifically designed for operation at 2000 nm. We exploit ring and Fabry-Perot resonator configurations, to realize single- and multi-wavelength Brillouin lasers respectively. Only the back scattered Stokes signal is fed back in the ring configuration and it is realized using 50 m and 100 m long SM9150 fibers. For each ring length, we study single-wavelength Brillouin lasing using 50$\%$ and 90$\%$ feedback fractions (FF). Using a feedback factor of 50$\%$ in a 100 m long ring, we achieve high slope efficiency ($SE \sim 17\%$) and maximum output Stokes power (${P_{s}^{max}}_{out}$ $\sim$ 90 mW), which are four times the SE $\sim$ 4$\%$ and ${P_{s}^{max}}_{out}$ $\sim$ 22 mW for FF$=90\%$. This large increase in slope efficiency comes at the cost of only 56 $\%$ increase in threshold pump power ($P^{50\%}_{th} \sim$ 206 mW, $P^{90\%}_{th} \sim$ 132 mW). For the single wavelength Brillouin laser, we achieve a maximum slope efficiency of 23$\%$ when 50$\%$ feedback is used with a 50 m long ring.
In order to demonstrate multi-wavelength Brillouin lasing, we exploit Fabry-Perot resonator geometry, where both the pump and Stokes signals are fed back into a 100 m long SM1950 fiber using circulators and couplers. Using the FP resonator, we generate 8 Stokes lines with an input power of 822 mW. In our demonstration, four-wave mixing between the pump and Stokes components gives rise to idlers at the anti-Stokes wavelength. Low threshold, high slope efficiency and high Stokes output power in SM1950 fiber based single- and multi-wavelength Brillouin lasers enables efficient CW and pulsed sources, which can be achieved via phase locking of Stokes components of multi-Stokes Brillouin laser [28–31], at 2000 nm for applications such as optical communications and CO$_2$ sensing at 2004 nm.
2. Brillouin laser
Figure 1(a) shows the experimental setup for realizing a Brillouin laser using a ring resonator configuration. A 2004 nm laser (Eblana) with $\sim$ 3 MHz linewidth and 2.5 mW output power is first amplified using a low-power Thulium doped fiber amplifier (TDFA) to increase the input pump power up to $\sim$ 100 mW. A second stage TDFA is then used to increase the pump power to $\sim$ 1 Watt. The amplified pump is launched into SM1950 fiber using port 2 of circulator (C1). Backscattered Stokes is collected at port 3 of C1 and is fedback using one port of the optical coupler (OC-1). Optical couplers with splitting ratios of 90/10 and 50/50 are used for achieving feedback fractions (FF) of 90$\%$ and 50$\%$, respectively. The remaining 10$\%$ or 50$\%$ output of OC-1 is then further split using OC-2 (90/10 splitter) to measure the output Stokes signal using a Yokogawa AQ 6375B optical spectrum analyser (OSA) at 10$\%$ port and a power meter at 90$\%$ port. Fiber lengths of 50 m and 100 m are used as the Brillouin gain medium, where the 100 m long fiber is obtained by concatenating two same 50 m long spools.
Fig. 1. (a) The experimental setup used for generation of Brillouin laser, OC-1: optical coupler(50-50 or 90-10), OC-2: 90-10 Splitter, TDFA: Thulium doped fiber amplifier, OSA: Optical spectrum analyzer, PM: Power meter, FUT: Fiber under test. Mode field profile of SMF-28e (b) and SM1950 (c) fibers obtained using COMSOL.
Figures 1(b) and (c) show the mode profiles, which are simulated using COMSOL, for SMF-28 and SM1950 fibers, respectively, at 2 $\mu$m. We estimate mode field diameters (MFDs) of 14 $\mu m$ and 8 $\mu m$ for SMF-28 and SM1950, respectively. This implies that the effective mode area ($A_{eff}$) of SM1950 fiber is three times smaller than SMF-28 at 2 $\mu$m.
Figures 2(a)-(d) show the optical spectra for four different combinations of fiber length and feedback fraction, which are shown in respective figs., at different input pump powers. From the measured optical spectra in Fig. 2, we obtain a Brillouin spacing of 8.004 GHz for SM1950 fiber at a pump wavelength of 2 $\mu$m. From Figs. 2 (a)-(d), it is evident that, irrespective of the ring length, 50$\%$ feedback fraction results in higher output Stokes power compared to 90$\%$ feedback. For an input pump power of $\sim$ 700 mW, we achieve a maximum Stokes output power of $\sim$ 10 dBm for both the 50 m and 100 m long fiber rings when 50$\%$ feedback fraction is used (Figs. 2 (a), (c)). It is important to note that the OSA spectra are recorded using only 10$\%$ of the measurable Stokes output power, remaining 90$\%$ is measured using a power meter, which is then used to plot Fig. 3. For Brillouin lasing using 90$\%$ feedback fraction, the maximum Stokes output power for 100 m and 50 m long fiber rings is nearly the same (see Figs. 2 (b), (d)).
Fig. 2. Brillouin laser optical spectra for different combinations of fiber-length and feedback factor: (a) 100 meter with 50% feedback, (b) 100 meter with 90% feedback, (c) 50 meter with 50% feedback and (d) 50 meter with 90% feedback.
Fig. 3. Output Stokes power as a function of input pump power for different cavity configurations: (a) 100 m ring resonator with 50% (black) and 90% (red) feedback and (b) 50 m ring resonator with 50% (black) and 90% (red) feedback.
In order to calculate the Brillouin lasing threshold and slope efficiency, we plot total output Stokes power vs input pump power for 100 m and 50 m long fiber ring resonators in Figs. 3 (a) and (b) respectively. For the 100 m long fiber ring resonator, reducing the feedback factor from 90$\%$ to 50$\%$ increases the maximum Stokes output power ${P_{s}^{max}}_{out}$ and slope efficiency to four times at the expense of only 56$\%$ increase in threshold pump power (see Fig. 3 (a)). Similar increase in slope efficiency and ${P_{s}^{max}}_{out}$ is observed for 50 m long fiber ring when the feedback factor is varied from 90$\%$ to 50$\%$. From Figs. 3 (a) and (b), we note that, irrespective of the feedback factor, the lasing threshold is lower for ring resonators designed using longer fiber length. The lower threshold for longer length fiber ring can be understood using Eq. 1 for the threshold gain exponent $G^{th}_B$ of a single-pass configuration, which is given as:
where $g_B$ is the Brillouin gain coefficient, $P_{th}$ is the threshold pump power, $L_{eff}$ is the effective fiber length, and $A_{eff}$ is the effective mode area of the fiber. From Eq. 1, it is evident that for a fixed $A_{eff}$, higher pump power is needed to excite Brillouin scattering in short length fibers. In the case of a Brillouin laser, the threshold pump power further scales with the Finesse of the cavity $F$ as $\frac {1}{F^2}$ [9], which reduces $P_{th}$ for Brillouin laser below the value obtained using Eq. 1.While the threshold is lower for a higher feedback factor, it comes at the expense of lower output Stokes power and slope efficiency. Therefore, there is a trade-off between low threshold and higher output power and a choice can be made based on the application of interest. In our demonstration, the output Stokes power and slope efficiency for a 100 m long ring resonator with 50$\%$ feedback are four times higher than that for 90$\%$ feedback and comes at the expense of only a 56$\%$ increase in $P_{th}$ (see Fig. 3 (a)). We calculate the lasing threshold for our cavity configuration using the condition that the round-trip loss of the cavity is compensated exactly by the gain [9]. The calculated threshold for each feedback and cavity length combination is given in Table 1 along with the measured threshold. From Table 1 we note that the calculated thresholds are within 10% of the observed value.
Table 1. Comparison of theoretical and observed threshold for various cavity configurations
3. Brillouin multi-Stokes
In order to realize a multi-Stokes Brillouin laser at 2 $\mu$m, we exploit a Fabry-Perot resonator configuration. Figure 4 shows the experimental set up to realize multi-Stokes Brillouin lasing where pump feedback is achieved by connecting port 3 and 1 of circulator C2. Back scattered Stokes and pump signals at port 3 of circulator C1 are fedback to a 100 m long SM 1950 fiber, which acts as the Brillouin gain medium, through a high power TDFA using OC-1 (50/50 coupler). The 99$\%$ port of a 99/1 coupler (OC-2), connected at the output of a high-power TDFA, is used as the input at port1 of C1. The 1$\%$ port of OC-2 is connected to another 90/10 coupler (OC-3) to measure the optical spectrum (10%) and the input pump power (90%).
Fig. 4. The experimental setup used for generation of Brillouin combs. A 2 $\mu$m laser amplified using a low power TDFA acts as the input to a high power TDFA through OC-1: 50/50 coupler. OC-2: 99/1 splitter, OC-3: 90-10 splitter.
Figure 5(a) shows the measured optical spectra for multi-Stokes Brillouin lasing at different input powers. As the input pump power is increased from 385 mW to 822 mW, the number of Stokes components increased to 8. Four-wave mixing between the co-propagating pump and Stokes components lead to the appearance of lines at the anti-Stokes frequencies, resulting in a total of 14 observed lines. A peak of fixed height that appears in all the traces at 2005.25 nm corresponds to a laser side mode.
Fig. 5. (a)Optical spectra of cascaded SBS as the function of TDFA output measured at 1% port of OC2 in Fig. 4. There is a 2 dB coupling loss also present in the OSA arm. (b)Evolution of the output power for the first three Stokes components, measured using OSA connected to 10% port of OC-3, as a function of input pump power measured using power meter on 90% port of OC-3.
Figure 5(b) shows the output power vs input pump power for the first three Stokes lines. The pump and the Stokes powers are estimated from the measured optical spectrum and power meter readings. From Fig. 5(b), we observe that when the second Stokes reaches its threshold, the output power for the first Stokes saturates indicating that the first Stokes acts as a pump for the second Stokes. The power transfer from the first Stokes to generate second Stokes results in its saturation.
For single- and multi-Stokes Brillouin lasing, SM1950 based cavity provides better efficiency in terms of almost all the parameters namely the threshold pump power, slope efficiency and output Stokes power when compared to SMF based 2 $\mu$m Brillouin lasers where much higher threshold was observed with longer lengths and similar or higher feedback factors [32,34]. From Eq. 1, it is evident that smaller mode area and larger $g_B$ leads to reduction in threshold for Stokes generation. The recent demonstrations of Brillouin laser and multi-Stokes generation at 1550 nm have used this fact to their advantage and demonstrated small footprint low threshold operations [10,14,16,19,23,24,29,30,35–37]. In our work the better efficiency of SM1950 based Brillouin lasers results from the fact that the mode field diameter (MFD) and thus $A_{eff}$ are 8 $\mu$m and 50 $\mu m^2$, respectively, which are smaller than the MFD (14 $\mu$m) and A$_{eff}$ (154 $\mu m^2$) for SMF at 2 $\mu$m (see Figs. 1(b) and (c)). From Eq. 1, note that for the same length smaller A$_{eff}$ results in reduced threshold. Further reduction in threshold occurs due to 25% greater $g_B$ of SM1950 compared to SMF at 2 $\mu$m. We measured the $g_B$ for both SMF and SM1950 at 2 $\mu$m and found them to be ${4.55(\pm 0.57)\times 10^{-12} m/W}$ and ${5.9(\pm 0.8)\times 10^{-12} m/W}$ respectively.
4. Discussion and conclusion
Brillouin lasers are well known for providing a narrow linewidth coherent source. There are two major technique to measure the linewidth of Brillouin laser. First we can amplify the generated Brillouin laser to generate its own Stokes in another cavity and beat them together to get the linewidth. Second we can measure the linewidth of Brillouin laser using heterodyne techniques, which require splitting the signal into two paths for decorrelating the laser signal using longer length fiber delay lines and use of frequency shifting using modulators. Limited output power from the amplifier and higher loss in long length silica fibers and modulator limits the power budget for measuring the linewidth in our set-up using any of the previously mentioned method. We, therefore, estimate the linewidth of the Brillouin laser using the widely used expression [32,33,38]:
where R is the reflectance of the cavity, c is the speed of light in vacuum, $\Delta \nu _{Stokes}$ is the Stokes linewidth, $\Delta \nu _B$ is the measured Brillouin gain bandwidth (22 MHz), $n$ is the mode index, $L$ is the cavity length, and $\Delta \nu _{pump}$ is measured the pump linewidth (2.4 MHz). By incorporating coupling and other losses in the setup, we obtain the effective feedback factors of 24$\%$ and 45$\%$, respectively, for ring cavities with 50$\%$ and 90$\%$ feedback factors. Using the effective fedback factor, we estimate linewidths of 4.0 kHz and 1.4 kHz for feedback factors of 50$\%$ and 90$\%$, respectively, in a 100 m long ring resonator.In conclusion, we have demonstrated efficient single- and multi-Stokes Brillouin lasing using SM1950 fiber in ring and FP resonator configurations. To the best of our knowledge, the Brillouin threshold for single- and mutli-Stokes Brillouin lasers in our demonstration is three to four times smaller when compared to earlier demonstrations using SMF. Smaller $A_{eff}$ and larger $g_{B}$ of SM1950 fiber compared to SMF contributes to enhanced efficiency. The enhancement is not restricted to reduced lasing threshold but also appears in the form of enhancement of slope efficiency and output Stokes power. We demonstrate that by controlling the feedback factor for a given length, 3-4 fold increase in output Stokes power and slope efficiency can be achieved with a small penalty on threshold. For a multi-Stokes Brillouin laser, four-wave mixing between the pump and Stokes components is critical for generating high repetition rate picosecond pulses via phase locking of the Stokes lines [28,30,39]. For the first time, we observe FWM between pump and Stokes components in a multiwavelength 2 $\mu$m Brillouin laser. In addition to FWM, use of larger pump power with SM1950 will help in further reducing the fiber length for single- and multi-Stokes Brillouin lasing, which will help in achieving the stable phase-lock for GHz repetition rate ps pulses at 2 $\mu$m [31,39]. Large power handling, ease of coupling to optical communication systems, small $A_{eff}$ and large $g_B$ of SM1950 fibers compensates for relevant shortcomings of chalcogenide fibers and SMF and makes it a potential platform for efficient Brillouin fiber lasers at 2 $\mu$m.
Funding
Science and Engineering Research Board, Department of Science and Technology (EMR/2015/000363, SB/S2/RJN-069/2014).
References
1. D. Hanna, R. Percival, R. Smart, and A. Tropper, “Efficient and tunable operation of a tm-doped fibre laser,” Opt. Commun. 75(3-4), 283–286 (1990). [CrossRef]
2. S. D. Jackson and T. A. King, “Theoretical modeling of tm-doped silica fiber lasers,” J. Lightwave Technol. 17(5), 948–956 (1999). [CrossRef]
3. G. J. Koch, J. Y. Beyon, B. W. Barnes, M. Petros, J. Yu, F. Amzajerdian, M. J. Kavaya, and U. N. Singh, “High-energy 2 $\mu$m doppler lidar for wind measurements,” Opt. Eng. 46(11), 116201 (2007). [CrossRef]
4. Z. Li, A. Heidt, J. Daniel, Y. Jung, S. Alam, and D. J. Richardson, “Thulium-doped fiber amplifier for optical communications at 2 $\mu$m,” Opt. Express 21(8), 9289–9297 (2013). [CrossRef]
5. N. M. Fried, “High-power laser vaporization of the canine prostate using a 110 w thulium fiber laser at 1.91 $\mu$m,” Lasers Surg. Med. 36(1), 52–56 (2005). [CrossRef]
6. N. M. Fried and K. E. Murray, “High-power thulium fiber laser ablation of urinary tissues at 1.94 $\mathrm {\mu }$m,” J. Endourol. 19(1), 25–31 (2005). [CrossRef]
7. K. O. Hill, B. S. Kawasaki, and D. C. Johnson, “CW Brillouin laser,” Appl. Phys. Lett. 28(10), 608–609 (1976). [CrossRef]
8. S. P. Smith, F. Zarinetchi, and S. Ezekiel, “Narrow-linewidth stimulated Brillouin fiber laser and applications,” Opt. Lett. 16(6), 393–395 (1991). [CrossRef]
9. L. Stokes, M. Chodorow, and H. Shaw, “All-fiber stimulated Brillouin ring laser with submilliwatt pump threshold,” Opt. Lett. 7(10), 509–511 (1982). [CrossRef]
10. K. S. Abedin, “Brillouin amplification and lasing in a single-mode as2se3 chalcogenide fiber,” Opt. Lett. 31(11), 1615–1617 (2006). [CrossRef]
11. S. Fu, W. Shi, H. Zhang, Q. Sheng, G. Shi, X. Bai, and J. Yao, “Linewidth-narrowed, linear-polarized single-frequency thulium-doped fiber laser based on stimulated Brillouin scattering effect,” IEEE Photonics J. 9(4), 1–7 (2017). [CrossRef]
12. M. H. Al-Mansoori and M. A. Mahdi, “Multiwavelength l-band Brillouin–erbium comb fiber laser utilizing nonlinear amplifying loop mirror,” J. Lightwave Technol. 27(22), 5038–5044 (2009). [CrossRef]
13. M. Al-Mansoori, M. K. Abd-Rahman, F. M. Adikan, and M. Mahdi, “Widely tunable linear cavity multiwavelength Brillouin-erbium fiber lasers,” Opt. Express 13(9), 3471–3476 (2005). [CrossRef]
14. I. V. Kabakova, R. Pant, D.-Y. Choi, S. Debbarma, B. Luther-Davies, S. J. Madden, and B. J. Eggleton, “Narrow linewidth Brillouin laser based on chalcogenide photonic chip,” Opt. Lett. 38(17), 3208–3211 (2013). [CrossRef]
15. S. Gundavarapu, G. M. Brodnik, M. Puckett, T. Huffman, D. Bose, R. Behunin, J. Wu, T. Qiu, C. Pinho, N. Chauhan, J. Nohava, P. T. Rakich, K. D. Nelson, M. Salit, and D. J. Blumenthal, “Sub-hertz fundamental linewidth photonic integrated Brillouin laser,” Nat. Photonics 13(1), 60–67 (2019). [CrossRef]
16. N. T. Otterstrom, R. O. Behunin, E. A. Kittlaus, Z. Wang, and P. T. Rakich, “A silicon Brillouin laser,” Science 360(6393), 1113–1116 (2018). [CrossRef]
17. W. Loh, A. A. Green, F. N. Baynes, D. C. Cole, F. J. Quinlan, H. Lee, K. J. Vahala, S. B. Papp, and S. A. Diddams, “Dual-microcavity narrow-linewidth Brillouin laser,” Optica 2(3), 225–232 (2015). [CrossRef]
18. J. Li, H. Lee, T. Chen, and K. J. Vahala, “Characterization of a high coherence, Brillouin microcavity laser on silicon,” Opt. Express 20(18), 20170–20180 (2012). [CrossRef]
19. H. Lee, T. Chen, J. Li, K. Y. Yang, S. Jeon, O. Painter, and K. J. Vahala, “Chemically etched ultrahigh-q wedge-resonator on a silicon chip,” Nat. Photonics 6(6), 369–373 (2012). [CrossRef]
20. M. Dong and H. G. Winful, “Unified approach to cascaded stimulated Brillouin scattering and frequency-comb generation,” Phys. Rev. A 93(4), 043851 (2016). [CrossRef]
21. M. H. Al-Mansoori, A. Al-Sheriyani, S. Al-Nassri, and F. N. Hasoon, “Generation of efficient 33 GHz optical combs using cascaded stimulated Brillouin scattering effects in optical fiber,” Laser Phys. 27(6), 065112 (2017). [CrossRef]
22. X. Luo, T. H. Tuan, T. S. Saini, H. P. T. Nguyen, T. Suzuki, and Y. Ohishi, “Brillouin comb generation in a highly nonlinear tellurite single mode fiber,” in Frontiers in Optics / Laser Science, (Optical Society of America, 2018), p. JW4A.33.
23. R. Pant, E. Li, D.-Y. Choi, C. Poulton, S. J. Madden, B. Luther-Davies, and B. J. Eggleton, “Cavity enhanced stimulated Brillouin scattering in an optical chip for multiorder stokes generation,” Opt. Lett. 36(18), 3687–3689 (2011). [CrossRef]
24. J. Li, H. Lee, and K. J. Vahala, “Microwave synthesizer using an on-chip Brillouin oscillator,” Nat. Commun. 4(1), 2097 (2013). [CrossRef]
25. Z. C. Tiu, S. N. Aidit, N. A. Hassan, M. F. B. Ismail, and H. Ahmad, “Single and double Brillouin frequency spacing multi-wavelength Brillouin erbium fiber laser with micro-air gap cavity,” IEEE J. Quantum Electron. 52(9), 1–5 (2016). [CrossRef]
26. H. Ahmad, S. Aidit, and Z. Tiu, “Multi-wavelength praseodymium fiber laser using stimulated Brillouin scattering,” Opt. Laser Technol. 99, 52–59 (2018). [CrossRef]
27. N. A. B. Ahmad, S. H. Dahlan, N. A. Cholan, H. Ahmad, and Z. C. Tiu, “Switchable 10, 20, and 30 ghz region photonics-based microwave generation using thulium-doped fluoride fiber laser,” J. Opt. Soc. Am. B 35(7), 1603–1608 (2018). [CrossRef]
28. S. Loranger, V. L. Iezzi, and R. Kashyap, “Demonstration of an ultra-high frequency picosecond pulse generator using an sbs frequency comb and self phase-locking,” Opt. Express 20(17), 19455–19462 (2012). [CrossRef]
29. T. F. Büttner, M. Merklein, I. V. Kabakova, D. D. Hudson, D.-Y. Choi, B. Luther-Davies, S. J. Madden, and B. J. Eggleton, “Phase-locked, chip-based, cascaded stimulated Brillouin scattering,” Optica 1(5), 311–314 (2014). [CrossRef]
30. T. F. Büttner, I. V. Kabakova, D. D. Hudson, R. Pant, C. G. Poulton, A. C. Judge, and B. J. Eggleton, “Phase-locking and pulse generation in multi-frequency Brillouin oscillator via four wave mixing,” Sci. Rep. 4(1), 5032 (2015). [CrossRef]
31. V. L. Iezzi, T. F. Büttner, A. Tehranchi, S. Loranger, I. V. Kabakova, B. J. Eggleton, and R. Kashyap, “Temporal characterization of a multi-wavelength Brillouin–erbium fiber laser,” New J. Phys. 18(5), 055003 (2016). [CrossRef]
32. K. Hu, I. V. Kabakova, T. F. S. Büttner, S. Lefrancois, D. D. Hudson, S. He, and B. J. Eggleton, “Low-threshold Brillouin laser at 2$\mu$m based on suspended-core chalcogenide fiber,” Opt. Lett. 39(16), 4651–4654 (2014). [CrossRef]
33. Y. Luo, Y. Tang, J. Yang, Y. Wang, S. Wang, K. Tao, L. Zhan, and J. Xu, “High signal-to-noise ratio, single-frequency 2$\mu$m Brillouin fiber laser,” Opt. Lett. 39(9), 2626–2628 (2014). [CrossRef]
34. X. Wang, P. Zhou, X. Wang, H. Xiao, and L. Si, “Multiwavelength Brillouin-thulium fiber laser,” IEEE Photonics J. 6(1), 1–7 (2014). [CrossRef]
35. J. H. Lee, Z. Yusoff, W. Belardi, M. Ibsen, T. M. Monro, and D. J. Richardson, “Investigation of Brillouin effects in small-core holey optical fiber: lasing and scattering,” Opt. Lett. 27(11), 927–929 (2002). [CrossRef]
36. N. Broderick, T. Monro, P. Bennett, and D. Richardson, “Nonlinearity in holey optical fibers: measurement and future opportunities,” Opt. Lett. 24(20), 1395–1397 (1999). [CrossRef]
37. A. B. Matsko and V. S. Ilchenko, “Optical resonators with whispering gallery modes i: basics,” IEEE J. Sel. Top. Quantum Electron 12(1), 3–14 (2006). [CrossRef]
38. A. Debut, S. Randoux, and J. Zemmouri, “Linewidth narrowing in Brillouin lasers: Theoretical analysis,” Phys. Rev. A 62(2), 023803 (2000). [CrossRef]
39. M. W. Bowers and R. W. Boyd, “Phase locking via Brillouin-enhanced four-wave-mixing phase conjugation,” IEEE J. Quantum Electron. 34(4), 634–644 (1998). [CrossRef]
