In this article, we reported self-pumped stimulated Brillouin scattering (SBS)-induced fast light in a micro-resonator. The optically induced thermal effect in the micro-resonator will lead to a shift of the dispersion spectrum and make the SBS gain occurred in the anomalous dispersion regime. The group delay could be experimentally optimized from −91.0 microsecond to 2.6 microsecond by changing the modulation frequency in a microsphere with its diameter of 175 μm. The experimental results will benefit applications utilizing anomalous dispersion such as gyroscope.
© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
The gyroscope plays a great role in the measurement of rotation, which has great applications in the fields of navigation , phone sensor , aircraft [3,4], satellite , and gravito-magnetic effects . The features of compact size and high sensitivity are expected for the future gyroscope. In 2007, M. S. Shahriar etc. demonstrated a resonator-based optical gyroscope whose sensitivity could be enhanced via the fast light from anomalous dispersion . There are various methods to control the dispersion to realize group velocity control, such as electromagnetically induced transparency (EIT) [8,9], population oscillations (PO) in semiconductors , nondegenerate two-wave mixing [11,12], stimulated Brillouin scattering (SBS) in fiber [13–15], stimulated Raman scattering in fiber [16,17] and cavity based on photonic crystals [18–20], among which SBS in fiber was studied universally for its fiber-based configuration and low threshold. With the help of an expensive radio-frequency (RF) signal generator , the signal in the SBS amplifier configuration  could be set in the anomalous dispersion window to generate fast light. Note in a generator configuration , the self-pump SBS only generates slow light because the SBS signal in the configuration works within the normal dispersion window. As the development of high-Q whispering gallery mode (WGM) micro-resonator [22–24], the threshold of the SBS could be controlled as small as tens of microwatt [25,26]. In such cavity, with the help of various complex mechanisms in the WGM resonator such as optically induced thermal effect and opto-mechanic, it is possible to realize a self-pumped fast light in the cavity to make a compact, low cost and low threshold fast light configuration, and thus benefit the development of gyroscope.
In this letter, self-pumped SBS-induced fast light was demonstrated in a micro-sphere cavity, in which no RF signal generator was applied. The group delay from −91.0 to 2.6 μs could be modified by changing the modulation frequency of the pump light, and the optically induced thermal effect in the cavity was found to play an important role in the dispersion modification. The configuration remains the advantages of compact size and low threshold, and it could be applied within the broadband wavelength for the improvement of the future gyroscope.
The SBS effect has been explored for many years and various applications have been proposed. As for group velocity control, both fast light and slow light have been demonstrated in SBS [14, 16]. Typical gain and dispersion curves in a non-cavity SBS medium, and the group index accordingly are shown in Figs. 1(a)-1(c), respectively. When the normalized frequency deviation δω/ΓB was zero, where δω = ω-ωB is the frequency deviation from the Stokes frequency ωB and ΓB is the Brillouin linewidth of the SBS signal, the gain is maximized within the normal dispersion frequency window, and the SBS signal is slow light. In the generation configuration of the SBS in a non-cavity medium, because the SBS signal is self-pumped from the pump light and always generates at the resonant wavelength, it is always located in the frequency window of the normal dispersion and only slow light can be achieved as shown in Figs. 1(b) and 1(c). To get fast light, the SBS signal has to be working at the anomalous dispersion window at an off-resonant wavelength, which is typically controlled by a signal generator under an amplifier configuration. The frequency shift between the typical SBS signal and the pump light is usually around 10 GHz with a gain bandwidth as narrow as tens of MHz, and the radio frequency (RF) signal generator to fulfill the demands is not only expensive but also very large. As the development of the whispering gallery mode (WGM) cavity, low-threshold SBS has been widely studied. With both the pump light and the SBS signal influenced by the Q-factor, the threshold of SBS could be as low as tens of microwatt. At the same time, the high-Q cavity with a small mode volume usually involves obvious optically induced thermal effect, which will cause the resonant wavelength to drift and influence the gain process. The resonant wavelength with thermal effect could be given as 
With the WGM activated by a modulated light, the temperature evolution in the microcavity is much complex, but in general,Eq. (2) is valid for each light with different ΔT and Ih, respectively.
Different temperature evolutions will eventually lead to the change of the spectrum spacing between the two resonant modes involving the SBS process in WGM cavity. With suitable condition, such change will make the SBS gain shifted to the anomalous dispersion area, thus fast light can be expected.
3. Experiment and results
To observe SBS effect in the micro-resonator, a configuration of a tapered fiber (TF) coupled microsphere was applied in the experiment . The waist of the tapered fiber used for coupling was about 2.2 μm. The microsphere was made by melting the tip of a piece of commercial fiber and a microsphere with a radius about 175 μm was selected to generate SBS, which had got a suitable mode-density. A smaller sphere with sparser WGMs will hardly fulfill the spectral adjacent for the SBS signal (~10 GHz), while in the bigger one with denser WGMs, frequently mode hoping will make it hard to maintain the pump light and the SBS signal within certain modes.
The experiment configuration to observe self-pumped fast light is shown in Fig. 2. A narrow linewidth tunable laser was applied and amplified by an erbium doped fiber amplifier (EDFA). After modulated by an electro-optical modulator (EOM) driven by a function generator (FG), the laser was coupled to the TF-microsphere system to generate SBS signal, which was collected by a circulator C1. Due to the high Q-value of the microsphere, cascading SBS signals appeared from time to time and Rayleigh scatting was also non-negligible, thus an additional circulator C2 with a piece of fiber Bragg grating (FBG) was connected to filter the first order SBS signal out for the measurement. Note a polarization controller PC was applied before the EOM to optimize the polarization of the light. After we achieved the first order SBS signal, it was divided into two parts by a 99:1 coupler. The weak signal was led to an optical spectrum analyzer to monitor SBS signal and most of the energy was led into a photo detector, where the first order SBS signal was converted to electric signal. The converted signal was monitored with an oscilloscope (OSC) and the driving signal of the EOM was also coupled into a second channel of the OSC to provide time reference for the converted SBS signal. By comparing the delay time of the modulation waveforms in the OSC, we could get the group delay. Note the origin of the group delay in the OSC was not negligible at high modulation frequency because of the phase shift in the electric circuit of the photo-detector and the propagation time of the light in the fiber, and it was pre-measured with the TF-microsphere system replaced by a fiber mirror, the typical value of which was around 1 μs in the experiment.
In the experiment, the wavelength of the laser was set at the 1550 nm around the band edge of the FBG in the beginning. The modulation frequency of the FC was set at 10 kHz. By adjusting the PC before the modulator and the voltage offset in FG, the pump light was confirmed to be sinusoidal modulated before coupled into the microsphere. Then we swept the wavelength of the laser and observed one-order SBS signal at the wavelength of 1550.177 nm in the OSA, where no high order SBS was observed and the SBS signal was about 14 dB larger than the pump scattering. Note the TF was placed in touch with the micro sphere to provide a relative stable coupling and the loaded Q of the WGM was above 107 in the experiment. When the first order SBS signal was maximized, circulator C2 was connected and single out the 1st SBS signal for measurement, whose signal-noise ratio (SNR) was improved to more than 30 dB. By scanning the modulation frequency from 2 kHz to 1 MHz, the waveforms of the SBS signal in the OSC were recorded for further analysis.
The results are shown in Fig. 3, with waveforms measured at frequencies 2 kHz, 27 kHz and 50 kHz shown in Figs. 3(a)-3(c) as typical results, respectively. The black solid curves are the reference signals from the FG and the blue solid curves are the SBS signals measured. By comparing the delay time between the peak intensity of the SBS signal and that of the reference signal in the OSC, the group delay of the SBS signal could be achieved. Both fast light and slow light could be observed in the experiment. Note there was deformation of the SBS signal waveforms when the delay was large as shown in Figs. 3(a) and 3(c), which mainly came from large dispersion. At the same time, unstable coupling from the low frequency vibration was possible reason for the small random deformations of the waveforms.
All the group delays and phase delays accordingly at different frequency are presented in Fig. 3(d). Negative group delays and phase delays indicated the SBS waveforms had got a phase advance and it was fast light accordingly, indicating that the SBS gain occurred within the anomalous dispersion area. The group delay was −91.0 μs at a modulation frequency of 2 kHz, and it would increase as the modulation frequency increased. It was worth noting that, around the frequency of 27 kHz, the group advance was about zero, which corresponded to a very large group velocity. As the modulation frequency was further increased, the waveforms showed the feature of slow light, indicating that the SBS gain occurred within the normal dispersion area. The group delay reached 2.6 µs at 50 kHz and it was the largest group delay we had ever measured in the experiment. As the modulation frequency increased further, the group delay decreased. The phase delays’ tendency was almost the same as the group delays with the largest phase delay around 150 kHz. It is clear that the maximum of the phase delay and group delay is not at the same frequency in the Fig. 3(d). This is because the bandwidth-delay product in the group delay is limited and changing very slowly. With the modulation frequency increased, i. e. the bandwidth of the pump increased, the group delay will decrease rapidly. Both group delays and phase delays varied slower as the modulation frequency was larger than 400 kHz.
In general, as the increasing of the modulation frequency from 2 kHz to 1 MHz in the experiment, the SBS signal was changed from fast light to slow light, i. e., the SBS gain shifted from the anomalous dispersion window to the normal dispersion window. As the phase delay and the group delay reached their maximum, they decreased as the modulation frequency increased further, which meant the group index was decreased. It agreed with the dispersion evolution of the typical SBS as the frequency swept through the gain spectrum shown in Fig. 1. The fast and slow light came from the changing of the total dispersion which included the dispersion from the cavity modes and the dispersion from Brillouin gain of the material itself (silica in the experiment). The mechanism was complex, because both dispersion of the cavity mode and Brillouin gain of the material [29, 30] would be modified when the temperature in the resonator was changed. But in general, thermal effect played important roles during the process.
It is well known that the thermal relaxation in a WGM resonator is around tens or hundreds microseconds. In the experiment, the initial modulation frequency was set at 10 kHz, which was within the response time of the thermal effect to make the SBS signal valid during the experiment. Compared to the modulation frequency in the experiment, the heating process around nanosecond could be treated as an instant process. When a modulated pump light is coupled into the WGM, the temperature change will lead to the change in the refractive index and thus result in the modulation of the resonant wavelength of the WGM according to Eq. (1). As the increasing of the modulation frequency, especially after it is much larger than the thermal decay time, the temperature in the cavity will approach to a constant value and the group index of the SBS signal will also tend to stable around a constant value, which agrees with the fact that the phase delay was stabled around 0.04 × 2π with the modulation frequency larger than 400 kHz. Meanwhile, almost all the SBS waveforms at low modulation frequency got a flattened bottom, which came from the threshold of the SBS signal. The threshold was not a constant but also related to the thermal effect in the WGM cavity which would change the spectral spacing between the WGMs involved in the SBS process. With the SBS signal generate at off-resonant frequency of the WGM, its threshold will extremely increase and the SBS signal will disappear accordingly when the increased threshold was larger than the intensity of the pump. Until the thermal relaxation in the cavity make the spectrum spacing recovered to its origin state suitable to generate SBS signal, i. e., the threshold decreased lower than the pump again, the SBS signal will show up again. At the same time, the detuning of the pump beam is also important. Even at most of the time in the experiment the pump was thermo-locked to the WGM mode, when the pump was modulated, small detuning of the pump to the WGM might still occur and make the threshold of the SBS signal increased. Generally speaking, thermal effect in the WGM resonator will cause a spectrum sweeping in the cavity during SBS signal generation when the pump is modulated at suitable frequency, and fast light can be achieved under the generation configuration of SBS.
In conclusion, the first self-pumped SBS-induced fast light in a TF-coupled microsphere system was demonstrated experimentally and the fast light could be observed at the suitable modulation frequency due to the SBS gain occurred within the anomalous dispersion window at the off-resonant frequency of WGMs. The structure design has the low threshold of light intensity from the high-Q cavity and is easy to control. The research provides another method to realize dispersion control by a passive spectrum decay process from thermal relaxation other than modify the frequency difference as usual. The technique would benefit the applications based on anomalous dispersion such fast light application in gyroscope.
This work is financially supported by the NSFC (11574161 and 11674181), the 111 Project (B07013), Program for Changjiang Scholars and Innovative Research Team in University (IRT_13R29).
References and links
1. E. Abbott and D. Powell, “Land-vehicle navigation using GPS,” Proc. IEEE 87(1), 145–162 (1999). [CrossRef]
2. N. D. Lane, E. Miluzzo, H. Lu, D. Peebles, T. Choudhury, and A. T. Campbell, “A survey of mobile phone sensing,” IEEE Commun. Mag. 48(9), 140–150 (2010). [CrossRef]
3. H. Yoon and P. Tsiotras, “Spacecraft adaptive attitude and power tracking with variable speed control moment gyroscopes,” J. Guid. Control Dyn. 25(6), 1081–1090 (2002). [CrossRef]
4. B. Culshaw, “The optical fibre Sagnac interferometer:an overview of its principles and applications,” Meas. Sci. Technol. 17(1), R1–R16 (2006). [CrossRef]
6. F. Bosi, G. Cella, A. D. Virgilio, A. Ortolan, A. Porzio, S. Solimeno, M. Cerdonio, J. P. Zendri, M. Allegrini, J. Belfi, N. Beverini, B. Bouhadef, G. Carelli, I. Ferrante, E. Maccioni, R. Passaquieti, F. Stefani, M. L. Ruggiero, A. Tartaglia, K. U. Schreiber, A. Gebauer, and J.-P. R. Wells, “Measuring gravito-magnetic effects by multi ring-laser gyroscope,” Phys. Rev. D Part. Fields Gravit. Cosmol. 84(12), 12 (2011). [CrossRef]
7. M. S. Shahriar, G. S. Pati, R. Tripathi, V. Gopal, M. Messall, and K. Salit, “Ultrahigh enhancement in absolute and relative rotation sensing using fast and slow light,” Phys. Rev. A 75(5), 053807 (2007). [CrossRef]
8. L. V. Hau, S. E. Harris, Z. Dutton, and C. H. Behroozi, “Light speed reduction to 17 metres per second in an ultracold atomic gas,” Nature 397(6720), 594–598 (1999). [CrossRef]
9. B. Peng, S. K. Özdemir, W. Chen, F. Nori, and L. Yang, “What is and what is not electromagnetically induced transparency in whispering-gallery microcavities,” Nat. Commun. 5(1), 5082 (2014). [CrossRef] [PubMed]
10. P. C. Ku, F. Sedgwick, C. J. Chang-Hasnain, P. Palinginis, T. Li, H. Wang, S. W. Chang, and S. L. Chuang, “Slow light in semiconductor quantum wells,” Opt. Lett. 29(19), 2291–2293 (2004). [CrossRef] [PubMed]
12. F. Gao, J. Xu, G. Q. Zhang, F. Bo, and H. Liu, “Paraxial energy transport of a focused Gaussian beam in ruby with nondegenerate two-wave coupling like mechanism,” Appl. Phys. Lett. 92(2), 021121 (2008). [CrossRef]
13. Y. Okawachi, M. S. Bigelow, J. E. Sharping, Z. Zhu, A. Schweinsberg, D. J. Gauthier, R. W. Boyd, and A. L. Gaeta, “Tunable all-optical delays via Brillouin slow light in an optical fiber,” Phys. Rev. Lett. 94(15), 153902 (2005). [CrossRef] [PubMed]
14. M. González-Herráez, K. Y. Song, and L. Thévenaz, “Optically controlled slow and fast light in optical fibers using stimulated Brillouin scattering,” Appl. Phys. Lett. 87(8), 081113 (2005). [CrossRef]
15. Z. Zhu, A. M. C. Dawes, D. J. Gauthier, L. Zhang, and A. E. Willner, “Broadband SBS Slow Light in an Optical Fiber,” J. Lightwave Technol. 25(1), 201–206 (2007). [CrossRef]
16. L. Thévenaz, “Slow and fast light in optical fibres,” Nat. Photonics 2(8), 474–481 (2008). [CrossRef]
17. D. Dahan and G. Eisenstein, “Tunable all optical delay via slow and fast light propagation in a Raman assisted fiber optical parametric amplifier: a route to all optical buffering,” Opt. Express 13(16), 6234–6249 (2005). [CrossRef] [PubMed]
18. H. Gersen, T. J. Karle, R. J. P. Engelen, W. Bogaerts, J. P. Korterik, N. F. van Hulst, T. F. Krauss, and L. Kuipers, “Real-space observation of ultraslow light in photonic crystal waveguides,” Phys. Rev. Lett. 94(7), 073903 (2005). [CrossRef] [PubMed]
20. T. F. Krauss, “Slow light in photonic crystal waveguides,” J. Phys. D Appl. Phys. 40(9), 2666–2670 (2007). [CrossRef]
21. B. J. Eggleton, C. G. Poulton, and R. Pant, “Inducing and harnessing stimulated Brillouin scattering in photonic integrated circuits,” Adv. Opt. Photonics 5(4), 536–587 (2013). [CrossRef]
23. Y. P. Gao, C. Cao, T. J. Wang, Y. Zhang, and C. Wang, “Cavity-mediated coupling of phonons and magnons,” Phys. Rev. A 96(2), 023826 (2017). [CrossRef]
25. 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]
26. C. Guo, K. Che, Z. Cai, S. Liu, G. Gu, C. Chu, P. Zhang, H. Fu, Z. Luo, and H. Xu, “Ultralow-threshold cascaded Brillouin microlaser for tunable microwave generation,” Opt. Lett. 40(21), 4971–4974 (2015). [CrossRef] [PubMed]
29. E. S. Fry, Y. Emery, X. Quan, and J. W. Katz, “Accuracy limitations on Brillouin lidar measurements of temperature and sound speed in the ocean,” Appl. Opt. 36(27), 6887–6894 (1997). [CrossRef] [PubMed]
30. E. Fry, J. Katz, D. Liu, and T. Walther, “Temperature dependence of the Brillouin linewidth in water,” J. Mod. Opt. 49(3-4), 411–418 (2002). [CrossRef]