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OPTICS LETTERS / Vol. 39, No. 17 / September 1, 2014
Brillouin slow light: substantial optical delay in the second-order Brillouin gain spectrum Gabriel K. W. Gan,1 Y. G. Shee,1,* K. S. Yeo,1 G. Amouzad Madhiraji,1 F. R. Mahamd Adikan,1 and M. A. Mahdi2 1
2
Integrated Lightwave Research Group, Department of Electrical Engineering, Faculty of Engineering, University of Malaya, 50603 Kuala Lumpur, Malaysia
Wireless and Photonics Networks Research Center, Faculty of Engineering, Universiti Putra Malaysia, 43400 UPM, Serdang, Selangor, Malaysia *Corresponding author: [email protected] Received June 23, 2014; revised July 16, 2014; accepted July 23, 2014; posted July 25, 2014 (Doc. ID 214516); published August 22, 2014
We experimentally demonstrate optical delay in the second-order Brillouin gain spectrum by incorporating a double Brillouin-frequency shifter into the system. By coinciding the seed signal with the second-order Brillouin gain spectrum, it was found that the seed signal experienced significantly larger delay as compared to the Brillouin slow light generated from the first-order Brillouin spectrum. At a Brillouin gain of 17 dB, the delay was found to be at maximum of 60 ns. This widens the window of promising opportunities into the deployment of all optical tunable delay into the existing optical signal processing. © 2014 Optical Society of America OCIS codes: (060.2310) Fiber optics; (060.4370) Nonlinear optics, fibers; (290.5900) Scattering, stimulated Brillouin; (350.5500) Propagation. http://dx.doi.org/10.1364/OL.39.005118
Microwave photonics can generally be defined as the study of high-speed photonic devices operating at microwave or millimeter wave frequencies [1]. Ever since the development of a high-quality optical fiber with good transmission performance [2], the demand for all-optical microwave signal processing in the optical domain is imminent. One of the basic optical signal processing tools, namely an optical delay line, has attracted many researchers due to its potential applications in optical signal processing. Enabling optical storage to allow for the development of optical buffers and all-optical RAM for future optical packet switched networks [3,4] and quantum computing [5], optical delay lines have envisaged a futuristic all-optical network for light information packets being stored in the optical domain, which will revolutionize modern technologies. Consequently, realizing optical delay lines into the existing communication networks is certainly an attractive approach for maximizing the data traffic flow in future networks [2]. Past research has revealed several ways to delay or slow down light using methods such as electromagnetically induced transparency (EIT) [6], coherent population oscillations (CPO) [7], Brillouin slow light [8], and photonics crystal waveguide slow light [9]. Brillouin slow light, in particular, features a tunable delay capability that excels all of its precedent optical delay line approaches though some might exhibit tunable delay attributes as well. Brillouin slow light evidently inherits four main crucial characteristics: it requires low Brillouin pump (BP) power, it enables delay tunability, a room temperature operation, and most important of all it is an all-optical delay line that can be seamlessly integrated into the existing optical fiber communication system. The EIT or CPO require sophisticated chambers of cryogenic cooling systems and precise use of strong auxiliary laser beams [6,7], which prove to be impractical in system implementation. Song et al. [8] have demonstrated the initiative to control optical group velocity via a Brillouin slow light mechanism. They were able to achieve a maximum delay of 30 ns when the Brillouin gain reached 0146-9592/14/175118-04$15.00/0
30 dB. On the other hand, Okawachi et al. [10] have also demonstrated tunable Brillouin slow light with a 15 ns short pulse to achieve a maximum delay of 20 ns. Zhu et al. [11] have shown 47 ps delay with 75 ps short pulse. As reported by the other researchers, the conventional Brillouin slow light was capable achieving a maximum delay up to ∼30 ns [8]. Beyond this figure, the Brillouin system might undergo pump depletion [12,13], causing the delay time to saturate to a certain value. In addition, all of the abovementioned initiatives made use of the first-order Brillouin resonance by coupling the seed signal into it. However, none has ever investigated the effect of higher-order Brillouin gain. A technique has been demonstrated by Shee et al. [14] that generates a secondorder Brillouin Stokes signal by circulating the first-order Brillouin Stokes signal in the cavity. It is called the double Brillouin-frequency shifter [14]. In this Letter, we report the effects and the outcome of stimulated Brillouin scattering (SBS) slow light based on second-order Brillouin gain by incorporating the double Brillouin-frequency shifter system. We then compare the result with the contemporary first-order Brillouin slow light setup by using the same delay measurement technique. It was found that the second-order Brillouin slow light provides a much larger delay with the same Brillouin gain as compared to its first-order Brillouin slow light. Figure 1 depicts the experimental setup for the secondorder Brillouin slow light. The operating principle of the second-order Brillouin slow light is described as follows. The laser from the tunable laser source as the BP is amplified by an erbium-doped fiber amplifier and the output power is controlled by an attenuator (OA1) to be inserted into the double Brillouin-frequency shifter system through the four-port circulator. At a relatively strong BP power, it excites the first-order Brillouin Stokes signal (BS1) to propagate in the counterclockwise direction. This BS1 enters port-2 and exits port-3 of the circulator and it is essentially circulating within the loop. BS1, which circulates in the cavity (anti-clockwise) through © 2014 Optical Society of America
September 1, 2014 / Vol. 39, No. 17 / OPTICS LETTERS
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Fig. 1. Second-order Brillouin slow light configuration. TLS, tunable laser source; EDFA, erbium-doped fiber amplifier; OA, optical attenuator; OC, optical coupler; PM, power meter; PC, polarization controller; EOM, electro-optic modulator; PD, photodetector; OSA, optical spectrum analyzer, BP, Brillouin pump; BS1, first-order Brillouin Stokes signal; BS2, secondorder Brillouin Stokes signal.
port-2 and port-3, stimulates the generation of second-order Brillouin Stokes signal (BS2). BS2, which propagates in the opposite direction of BS1, outputs at port-4 of the circulator. Port-4 outputs only even-order Stokes signal and is henceforth a double Brillouin-frequency shifter. The Brillouin slow light configuration can be done by incorporating a seed signal into the system. A separate tunable laser source is modulated by an electro-optic modulator with a signal generator. This modulated seed signal enters the double Brillouin-frequency shifter through a 50∕50 optical coupler (OC4). The wavelength of the seed signal is tuned to coincide with the gain spectrum of the BS2. A power meter (PM2) reads the power for Brillouin gain measurement while the isolator guides the backward propagating BS1 from destabilizing the laser source or potentially damaging it. At the receiver end, the output power from port-4 of the circulator is controlled via OA2. This is to protect the photodetector from being saturated. An optical spectrum analyzer (OSA) is used to monitor the output spectrum while the photodetector converts the optical signal into an electrical signal before it is fed into an oscilloscope. The tunability of the delay is achieved by varying the OA1, which is monitored at PM1, so that different Brillouin gain can be obtained. A 5 km single-mode fiber (SMF), 10 km SMF, 20 km SMF, and a 23 km dispersion compensating fiber (DCF) were used as the Brillouin gain medium to investigate SBS slow light. The measurements of slow light based on secondorder Brillouin gain are shown in Fig. 2(a). It is the case of using a 20 km spool of SMF and with 10 MHz sine wave modulating signal. Throughout the investigation, BS2 coupled with the modulated seed signal were maintained at approximately 20 dB sideband suppression ratio. The Brillouin gain was varied and the highest gain that can be achieved was 17 dB. Above this level, the BP power is too high that it excited the fourth-order Brillouin Stokes signal (BS4) and this reduced the sideband suppression ratio to less than 20 dB. The rise of BS4 will provide dualfrequency signals (BS2 and BS4) to be heterodyned at the photodetector. This generates a ∼20 GHz RF signal (equivalent to the frequency difference between BS2 and BS4), which is undesired and the delayed signal might be distorted. Figure 2(b) shows the second-order
Fig. 2. (a) Time waveforms for the second-order Brillouin slow light and (b) second-order Brillouin gain spectrum.
Brillouin gain spectrum taken from the OSA. Comparing the wavelength of the BP (1549.769 nm) and BS2 (1549.937 nm), they have 0.168 nm wavelength difference. As shown in Fig. 2(b), BS4 starts to rise at high BP power. Therefore, the Brillouin gain was capped at 17 dB so that the peak of BS2 is maintained in such that it has more than 20 dB sideband suppression ratio. The waveforms were normalized to check the phase difference and hence, delay values. The delay values were measured at 0 V of each of the waves. From Fig. 2(a), in accordance with the reference wave (output signal that was measured when BP was turned off), the 5, 10, 15, and 17 dB Brillouin gain induced 40, 43, 52, and 60 ns delay, respectively. In order to investigate further, the second-order Brillouin slow light is then benchmarked with the contemporary first-order Brillouin slow light configuration by using the same delay measurement technique. Figure 3 shows the configuration for the generation of slow light based on the first-order Brillouin gain. The configuration is reassembled so that it satisfies the first-order Brillouin slow light. The BP was injected into port-1 of the circulator and exited at port-2 to propagate in the optical fiber medium for stimulated Brillouin scattering to take place. On the other hand, the modulated seed signal with the wavelength of 1549.937 nm was injected in the same direction as the first-order Brillouin Stokes signal and was directed to port-2 of the circulator. The delayed signal was observed at port-3 of the circulator. The measurements of slow light based on first-order Brillouin gain are shown in Fig. 4. It is the case of using a 20 km spool of SMF and with 10 MHz sine wave frequency. From Fig. 4, the 5, 10, 15, 20, 25, and 30 dB Brillouin gain induced 6, 10, 12, 17, 21, and 31 ns delay, respectively. Evidently, the second-order Brillouin slow light showed significantly larger delay as compared to
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Fig. 3. First-order Brillouin slow light configuration. TLS, tunable laser source; EDFA, erbium-doped fiber amplifier; OA, optical attenuator; OC, optical coupler; PM, power meter; PC, polarization controller; EOM, electro-optic modulator; PD, photodetector; OSA, optical spectrum analyzer, BP, Brillouin pump; BS1, first-order Brillouin Stokes signal; BS2, secondorder Brillouin Stokes signal.
Fig. 5. (a) Optical delays that were induced by first-order Brillouin slow light. (b) Optical delays that were induced by second-order Brillouin slow light.
The time delay can be expressed as [9] G f1 − 32ω − ωs ∕ΓB 2 g; (1) Γ where G g0 I P L, g0 is the line center gain factor, ωs is the Stokes frequency and the peak of the Brillouin gain, and ΓB is the Brillouin linewidth. Evidently, from Figs. 5(a) and 5(b) and Eq. (1), the types and the length of the optical fibers do not play a role in affecting the time delay. By maintaining the Brillouin gain and the Brillouin linewidth ratio regardless of different fiber at different length, the time delay can be kept to almost constant. The delay is at its maximum when the seed frequency is equal to the Stokes frequency, namely ω − ωs 0. Nonetheless, the Brillouin gain and the Stokes frequency are the only parameters that dictate the time delay. We have demonstrated, for the first time to the best of our knowledge, a second-order Brillouin slow light. It is conclusive to state that the second-order Brillouin slow light provides a significantly larger delay than the first. We have benchmarked this by using the same Brillouin gain measurement technique for both first- and secondorder Brillouin slow light for a range of optical fibers and a range of modulated seed signal frequencies. For the second-order Brillouin slow light, the highest delay achieved was 60 ns at 17 dB Brillouin gain before the sideband suppression ratio dropped below 20 dB. ΔT d ≈
Fig. 4. Time waveforms for the first-order Brillouin slow light.
that of the first-order Brillouin slow light given that the Brillouin gains are the same. To draw a closer comparison between the first- and second-order Brillouin slow light, Figs. 5(a) and 5(b) show the optical delay of the waves as a function of the Brillouin gain for both the first- and second-order Brillouin slow light at 10 MHz modulated seed signal. In these experiments, 5 km SMF, 10 km SMF, 20 km SMF, and 23 km DCF were tested. From Figs. 5(a) and 5(b), the results indicate that the delay values for different fibers are approximately the same. Although there are some deviations, the average delays for the first-order Brillouin slow light are 4, 10, 13, 18, 23, and 29 ns with 5, 10, 15, 20, 25, and 30 dB of Brillouin gain, respectively, as shown in Fig. 5(a). On the other hand, the average delays for the second-order Brillouin slow light are 40, 42, 52, and 60 ns with 5, 10, 15, and 17 dB of Brillouin gain, respectively, as shown in Fig. 5(b). For the second-order Brillouin slow light, there was a variation in the time delay (∼9 ns) for the 10 km SMF with the rest of the tested fibers at the 17 dB Brillouin gain. This is attributed by the temperature dependence of SBS gain and frequency. In order to stabilize the gain, the fiber should be placed in a temperature controller. As it can be seen, the second-order Brillouin slow light has an additional delay of 36 ns with the 5 dB Brillouin gain. The first-order Brillouin slow light suggested a linear relation between the delay time and the Brillouin gain, which was reported in [8].
The work was supported in part by Ministry of Higher Education, Malaysia, under High Impact Research Grant A000007-50001, and in part by the University of Malaya under the PPP (PG004-2012B) research grant. References 1. D. Jager and A. Stohr, in Proceedings of the German Microwave Conference, W. Menzel, ed. (Ulm, Germany, 2005), p. 136.
September 1, 2014 / Vol. 39, No. 17 / OPTICS LETTERS 2. L. Thevenaz, Nat. Photonics 2, 474 (2008). 3. R. S. Tucker, P. C. Ku, and C. J. Chang-Hasnain, J. Lightwave Technol. 23, 4046 (2005). 4. J. B. Khurgin, J. Opt. Soc. Am. B 22, 1062 (2005). 5. L. Ren and Y. Tomita, Proc. SPIE 7226, 722605 (2009). 6. J. B. Khurgin, Adv. Opt. Photon. 2, 287 (2010). 7. D. J. Gauthier, A. L. Gaeta, and R. W. Boyd, Photonics Spectra 40, 44 (2006). 8. K. Y. Song, M. G. Herraez, and L. Thevenaz, Opt. Express 13, 82 (2005).
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9. N. Zhu, Y. Wang, Q. Ren, L. Zhu, M. Yuan, and G. An, Opt. Laser Technol. 57, 154 (2014). 10. Y. Okawachi, M. S. Bigelow, J. E. Sharping, Z. Zhu, A. Schweinsberg, D. J. Gauthier, R. W. Boyd, and A. L. Gaeta, Phys. Rev. Lett. 94, 153902 (2005). 11. Z. Zhu, A. M. Dawes, D. J. Gauthier, L. Zhang, and A. E. Willner, J. Lightwave Technol. 25, 201 (2007). 12. G. P. Agrawal, Nonlinear Fiber Optics (Academic, 2007). 13. R. W. Boyd, Nonlinear Optics (Academic, 2003). 14. Y. G. Shee, M. H. Al-Mansoori, A. Ismail, S. Hitam, and M. A. Mahdi, Appl. Opt. 49, 3956 (2010).
OPTICS LETTERS / Vol. 39, No. 17 / September 1, 2014
Brillouin slow light: substantial optical delay in the second-order Brillouin gain spectrum Gabriel K. W. Gan,1 Y. G. Shee,1,* K. S. Yeo,1 G. Amouzad Madhiraji,1 F. R. Mahamd Adikan,1 and M. A. Mahdi2 1
2
Integrated Lightwave Research Group, Department of Electrical Engineering, Faculty of Engineering, University of Malaya, 50603 Kuala Lumpur, Malaysia
Wireless and Photonics Networks Research Center, Faculty of Engineering, Universiti Putra Malaysia, 43400 UPM, Serdang, Selangor, Malaysia *Corresponding author: [email protected] Received June 23, 2014; revised July 16, 2014; accepted July 23, 2014; posted July 25, 2014 (Doc. ID 214516); published August 22, 2014
We experimentally demonstrate optical delay in the second-order Brillouin gain spectrum by incorporating a double Brillouin-frequency shifter into the system. By coinciding the seed signal with the second-order Brillouin gain spectrum, it was found that the seed signal experienced significantly larger delay as compared to the Brillouin slow light generated from the first-order Brillouin spectrum. At a Brillouin gain of 17 dB, the delay was found to be at maximum of 60 ns. This widens the window of promising opportunities into the deployment of all optical tunable delay into the existing optical signal processing. © 2014 Optical Society of America OCIS codes: (060.2310) Fiber optics; (060.4370) Nonlinear optics, fibers; (290.5900) Scattering, stimulated Brillouin; (350.5500) Propagation. http://dx.doi.org/10.1364/OL.39.005118
Microwave photonics can generally be defined as the study of high-speed photonic devices operating at microwave or millimeter wave frequencies [1]. Ever since the development of a high-quality optical fiber with good transmission performance [2], the demand for all-optical microwave signal processing in the optical domain is imminent. One of the basic optical signal processing tools, namely an optical delay line, has attracted many researchers due to its potential applications in optical signal processing. Enabling optical storage to allow for the development of optical buffers and all-optical RAM for future optical packet switched networks [3,4] and quantum computing [5], optical delay lines have envisaged a futuristic all-optical network for light information packets being stored in the optical domain, which will revolutionize modern technologies. Consequently, realizing optical delay lines into the existing communication networks is certainly an attractive approach for maximizing the data traffic flow in future networks [2]. Past research has revealed several ways to delay or slow down light using methods such as electromagnetically induced transparency (EIT) [6], coherent population oscillations (CPO) [7], Brillouin slow light [8], and photonics crystal waveguide slow light [9]. Brillouin slow light, in particular, features a tunable delay capability that excels all of its precedent optical delay line approaches though some might exhibit tunable delay attributes as well. Brillouin slow light evidently inherits four main crucial characteristics: it requires low Brillouin pump (BP) power, it enables delay tunability, a room temperature operation, and most important of all it is an all-optical delay line that can be seamlessly integrated into the existing optical fiber communication system. The EIT or CPO require sophisticated chambers of cryogenic cooling systems and precise use of strong auxiliary laser beams [6,7], which prove to be impractical in system implementation. Song et al. [8] have demonstrated the initiative to control optical group velocity via a Brillouin slow light mechanism. They were able to achieve a maximum delay of 30 ns when the Brillouin gain reached 0146-9592/14/175118-04$15.00/0
30 dB. On the other hand, Okawachi et al. [10] have also demonstrated tunable Brillouin slow light with a 15 ns short pulse to achieve a maximum delay of 20 ns. Zhu et al. [11] have shown 47 ps delay with 75 ps short pulse. As reported by the other researchers, the conventional Brillouin slow light was capable achieving a maximum delay up to ∼30 ns [8]. Beyond this figure, the Brillouin system might undergo pump depletion [12,13], causing the delay time to saturate to a certain value. In addition, all of the abovementioned initiatives made use of the first-order Brillouin resonance by coupling the seed signal into it. However, none has ever investigated the effect of higher-order Brillouin gain. A technique has been demonstrated by Shee et al. [14] that generates a secondorder Brillouin Stokes signal by circulating the first-order Brillouin Stokes signal in the cavity. It is called the double Brillouin-frequency shifter [14]. In this Letter, we report the effects and the outcome of stimulated Brillouin scattering (SBS) slow light based on second-order Brillouin gain by incorporating the double Brillouin-frequency shifter system. We then compare the result with the contemporary first-order Brillouin slow light setup by using the same delay measurement technique. It was found that the second-order Brillouin slow light provides a much larger delay with the same Brillouin gain as compared to its first-order Brillouin slow light. Figure 1 depicts the experimental setup for the secondorder Brillouin slow light. The operating principle of the second-order Brillouin slow light is described as follows. The laser from the tunable laser source as the BP is amplified by an erbium-doped fiber amplifier and the output power is controlled by an attenuator (OA1) to be inserted into the double Brillouin-frequency shifter system through the four-port circulator. At a relatively strong BP power, it excites the first-order Brillouin Stokes signal (BS1) to propagate in the counterclockwise direction. This BS1 enters port-2 and exits port-3 of the circulator and it is essentially circulating within the loop. BS1, which circulates in the cavity (anti-clockwise) through © 2014 Optical Society of America
September 1, 2014 / Vol. 39, No. 17 / OPTICS LETTERS
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Fig. 1. Second-order Brillouin slow light configuration. TLS, tunable laser source; EDFA, erbium-doped fiber amplifier; OA, optical attenuator; OC, optical coupler; PM, power meter; PC, polarization controller; EOM, electro-optic modulator; PD, photodetector; OSA, optical spectrum analyzer, BP, Brillouin pump; BS1, first-order Brillouin Stokes signal; BS2, secondorder Brillouin Stokes signal.
port-2 and port-3, stimulates the generation of second-order Brillouin Stokes signal (BS2). BS2, which propagates in the opposite direction of BS1, outputs at port-4 of the circulator. Port-4 outputs only even-order Stokes signal and is henceforth a double Brillouin-frequency shifter. The Brillouin slow light configuration can be done by incorporating a seed signal into the system. A separate tunable laser source is modulated by an electro-optic modulator with a signal generator. This modulated seed signal enters the double Brillouin-frequency shifter through a 50∕50 optical coupler (OC4). The wavelength of the seed signal is tuned to coincide with the gain spectrum of the BS2. A power meter (PM2) reads the power for Brillouin gain measurement while the isolator guides the backward propagating BS1 from destabilizing the laser source or potentially damaging it. At the receiver end, the output power from port-4 of the circulator is controlled via OA2. This is to protect the photodetector from being saturated. An optical spectrum analyzer (OSA) is used to monitor the output spectrum while the photodetector converts the optical signal into an electrical signal before it is fed into an oscilloscope. The tunability of the delay is achieved by varying the OA1, which is monitored at PM1, so that different Brillouin gain can be obtained. A 5 km single-mode fiber (SMF), 10 km SMF, 20 km SMF, and a 23 km dispersion compensating fiber (DCF) were used as the Brillouin gain medium to investigate SBS slow light. The measurements of slow light based on secondorder Brillouin gain are shown in Fig. 2(a). It is the case of using a 20 km spool of SMF and with 10 MHz sine wave modulating signal. Throughout the investigation, BS2 coupled with the modulated seed signal were maintained at approximately 20 dB sideband suppression ratio. The Brillouin gain was varied and the highest gain that can be achieved was 17 dB. Above this level, the BP power is too high that it excited the fourth-order Brillouin Stokes signal (BS4) and this reduced the sideband suppression ratio to less than 20 dB. The rise of BS4 will provide dualfrequency signals (BS2 and BS4) to be heterodyned at the photodetector. This generates a ∼20 GHz RF signal (equivalent to the frequency difference between BS2 and BS4), which is undesired and the delayed signal might be distorted. Figure 2(b) shows the second-order
Fig. 2. (a) Time waveforms for the second-order Brillouin slow light and (b) second-order Brillouin gain spectrum.
Brillouin gain spectrum taken from the OSA. Comparing the wavelength of the BP (1549.769 nm) and BS2 (1549.937 nm), they have 0.168 nm wavelength difference. As shown in Fig. 2(b), BS4 starts to rise at high BP power. Therefore, the Brillouin gain was capped at 17 dB so that the peak of BS2 is maintained in such that it has more than 20 dB sideband suppression ratio. The waveforms were normalized to check the phase difference and hence, delay values. The delay values were measured at 0 V of each of the waves. From Fig. 2(a), in accordance with the reference wave (output signal that was measured when BP was turned off), the 5, 10, 15, and 17 dB Brillouin gain induced 40, 43, 52, and 60 ns delay, respectively. In order to investigate further, the second-order Brillouin slow light is then benchmarked with the contemporary first-order Brillouin slow light configuration by using the same delay measurement technique. Figure 3 shows the configuration for the generation of slow light based on the first-order Brillouin gain. The configuration is reassembled so that it satisfies the first-order Brillouin slow light. The BP was injected into port-1 of the circulator and exited at port-2 to propagate in the optical fiber medium for stimulated Brillouin scattering to take place. On the other hand, the modulated seed signal with the wavelength of 1549.937 nm was injected in the same direction as the first-order Brillouin Stokes signal and was directed to port-2 of the circulator. The delayed signal was observed at port-3 of the circulator. The measurements of slow light based on first-order Brillouin gain are shown in Fig. 4. It is the case of using a 20 km spool of SMF and with 10 MHz sine wave frequency. From Fig. 4, the 5, 10, 15, 20, 25, and 30 dB Brillouin gain induced 6, 10, 12, 17, 21, and 31 ns delay, respectively. Evidently, the second-order Brillouin slow light showed significantly larger delay as compared to
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Fig. 3. First-order Brillouin slow light configuration. TLS, tunable laser source; EDFA, erbium-doped fiber amplifier; OA, optical attenuator; OC, optical coupler; PM, power meter; PC, polarization controller; EOM, electro-optic modulator; PD, photodetector; OSA, optical spectrum analyzer, BP, Brillouin pump; BS1, first-order Brillouin Stokes signal; BS2, secondorder Brillouin Stokes signal.
Fig. 5. (a) Optical delays that were induced by first-order Brillouin slow light. (b) Optical delays that were induced by second-order Brillouin slow light.
The time delay can be expressed as [9] G f1 − 32ω − ωs ∕ΓB 2 g; (1) Γ where G g0 I P L, g0 is the line center gain factor, ωs is the Stokes frequency and the peak of the Brillouin gain, and ΓB is the Brillouin linewidth. Evidently, from Figs. 5(a) and 5(b) and Eq. (1), the types and the length of the optical fibers do not play a role in affecting the time delay. By maintaining the Brillouin gain and the Brillouin linewidth ratio regardless of different fiber at different length, the time delay can be kept to almost constant. The delay is at its maximum when the seed frequency is equal to the Stokes frequency, namely ω − ωs 0. Nonetheless, the Brillouin gain and the Stokes frequency are the only parameters that dictate the time delay. We have demonstrated, for the first time to the best of our knowledge, a second-order Brillouin slow light. It is conclusive to state that the second-order Brillouin slow light provides a significantly larger delay than the first. We have benchmarked this by using the same Brillouin gain measurement technique for both first- and secondorder Brillouin slow light for a range of optical fibers and a range of modulated seed signal frequencies. For the second-order Brillouin slow light, the highest delay achieved was 60 ns at 17 dB Brillouin gain before the sideband suppression ratio dropped below 20 dB. ΔT d ≈
Fig. 4. Time waveforms for the first-order Brillouin slow light.
that of the first-order Brillouin slow light given that the Brillouin gains are the same. To draw a closer comparison between the first- and second-order Brillouin slow light, Figs. 5(a) and 5(b) show the optical delay of the waves as a function of the Brillouin gain for both the first- and second-order Brillouin slow light at 10 MHz modulated seed signal. In these experiments, 5 km SMF, 10 km SMF, 20 km SMF, and 23 km DCF were tested. From Figs. 5(a) and 5(b), the results indicate that the delay values for different fibers are approximately the same. Although there are some deviations, the average delays for the first-order Brillouin slow light are 4, 10, 13, 18, 23, and 29 ns with 5, 10, 15, 20, 25, and 30 dB of Brillouin gain, respectively, as shown in Fig. 5(a). On the other hand, the average delays for the second-order Brillouin slow light are 40, 42, 52, and 60 ns with 5, 10, 15, and 17 dB of Brillouin gain, respectively, as shown in Fig. 5(b). For the second-order Brillouin slow light, there was a variation in the time delay (∼9 ns) for the 10 km SMF with the rest of the tested fibers at the 17 dB Brillouin gain. This is attributed by the temperature dependence of SBS gain and frequency. In order to stabilize the gain, the fiber should be placed in a temperature controller. As it can be seen, the second-order Brillouin slow light has an additional delay of 36 ns with the 5 dB Brillouin gain. The first-order Brillouin slow light suggested a linear relation between the delay time and the Brillouin gain, which was reported in [8].
The work was supported in part by Ministry of Higher Education, Malaysia, under High Impact Research Grant A000007-50001, and in part by the University of Malaya under the PPP (PG004-2012B) research grant. References 1. D. Jager and A. Stohr, in Proceedings of the German Microwave Conference, W. Menzel, ed. (Ulm, Germany, 2005), p. 136.
September 1, 2014 / Vol. 39, No. 17 / OPTICS LETTERS 2. L. Thevenaz, Nat. Photonics 2, 474 (2008). 3. R. S. Tucker, P. C. Ku, and C. J. Chang-Hasnain, J. Lightwave Technol. 23, 4046 (2005). 4. J. B. Khurgin, J. Opt. Soc. Am. B 22, 1062 (2005). 5. L. Ren and Y. Tomita, Proc. SPIE 7226, 722605 (2009). 6. J. B. Khurgin, Adv. Opt. Photon. 2, 287 (2010). 7. D. J. Gauthier, A. L. Gaeta, and R. W. Boyd, Photonics Spectra 40, 44 (2006). 8. K. Y. Song, M. G. Herraez, and L. Thevenaz, Opt. Express 13, 82 (2005).
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9. N. Zhu, Y. Wang, Q. Ren, L. Zhu, M. Yuan, and G. An, Opt. Laser Technol. 57, 154 (2014). 10. Y. Okawachi, M. S. Bigelow, J. E. Sharping, Z. Zhu, A. Schweinsberg, D. J. Gauthier, R. W. Boyd, and A. L. Gaeta, Phys. Rev. Lett. 94, 153902 (2005). 11. Z. Zhu, A. M. Dawes, D. J. Gauthier, L. Zhang, and A. E. Willner, J. Lightwave Technol. 25, 201 (2007). 12. G. P. Agrawal, Nonlinear Fiber Optics (Academic, 2007). 13. R. W. Boyd, Nonlinear Optics (Academic, 2003). 14. Y. G. Shee, M. H. Al-Mansoori, A. Ismail, S. Hitam, and M. A. Mahdi, Appl. Opt. 49, 3956 (2010).
