NEGATIVE GROUP VELOCITY SUPERLUMINAL PROPAGATION IN OPTICAL FIBERS USING STIMULATED

BRILLOUIN SCATTERING Li Zhan*, Liang Zhang, Jinmei Liu, Qishun Shen, Yuxing Xia

Department of Physics, State Key Lab of Advanced Optical Communication Systems and Networks, Shanghai Jiao Tong University, Shanghai, 200240, China

*lizhan@sjtu.edu.cn

Keywords: fast light, superluminal propagation, negative group velocity, stimulated Brillouin scattering, slow light.

Abstract

We demonstrated the superluminal propagation at negative group velocity using stimulated Brillouin scattering (SBS) in optical fibers. In the scheme, the Stokes wave is circulated back into the ring cavity for Brillouin lasing to enhance the peak loss. The experiment demonstrated the superluminal light propagation can be realized by increasing the input signal power. The largest time advancement of 221.2ns has been observed. Correspondingly, the negative group velocity is -0.15c and the group index is -6.636.

1 Introduction

To control the group velocity of light propagation in different materials have been attracted much interest recently [1-14]. It is becoming an important role in the implementation of all-optical communication system, since it has an inviting application prospects for developing fast-access memories and optically-controlled delay lines. Otherwise, the light superluminal propagation (where, the group velocity

g exceed c) or even with a negative g , have been studied

theoretically [15][16], and also observed experimentally [17][18], e.g., in absorbing medium [19][20], atomic medium [21][22], photonic crystals [23],active optical fibers[24-26], fiber Bragg gratings,[27] corrugated waveguide [28], left- handed materials [29], and saturated absorption medium [30][31]. The consistency of such phenomena with causality has also been verified experimentally [25]. The realization of slowing or advancing light in optical fibers forwards a great step to the all-optical communication systems. Several methods were proposed to control the group velocity of light pulses in fibers based on the nonlinear effects such as stimulated Brillouin scattering (SBS) [4], stimulated Raman scattering (SRS) [5] and parametric amplification [6], or using the group delay reflected from active fiber Bragg gratings (FBG) [7] and the gap solitons in FBGs [8]. Fast or slow light based on SBS in fibers has been proved to be an efficient and flexible method to realize optical advancement or delay, owing to its many advantages such as low pump power level, longer delay, and operating at any wavelength. In early SBS slow-light experiments, the delay is small and the applicable bandwidth is limited to dozens of MHz [9-10].

Further experiments optimized the delay efficiency [11] and extended the bandwidth [12][13]. However, the group velocity can reach neither superluminal nor negative owing to the saturation effect of Stokes wave. In this paper, we observed the superluminal light propagation at negative group velocity using SBS in a fiber ring lasing cavity. The largest advancement of 221.2ns obtained and the negative group was -0.15c and the group index was - 6.636.

2 Experimental setup and principles

The setup to demonstrate superluminal light in fiber ring is shown in Fig. 1. A 10m single-mode optical fiber (SMF) is used as the SBS medium. To generate the signal, we used a tunable laser source (TLS) of 1550 nm, which is modulated using an electro-optic modulator(EOM) to produce a sinusoidally pulse signal of 1 MHz repetition rate. Adjusting the DC bias of function generator applied to the EOM, we can obtain the signal with a DC component which creates the Stokes wave essentially.

Fig. 1. Setup to realize the SBS superluminal light. EOM: electro-optic modulator, EDFA: Erbium-doped fiber amplifier, SMF: single-mode optical fiber.

Then the signal is boosted using a erbium-doped fiber amplifier (EDFA) before it's reached into the SMF. A fiber ring lasing cavity constructed by a optical circulator and the SMF is employed in order to circulate the Stokes light back into the SBS medium for Brillouin lasing. 90% of the back-propagate stokes is served as pump light of SBS in turn. The power of the signal wave and the Stokes wave are observed at optical coupler's output port and the temporal traces of signal light within the fiber is monitored successively by measuring output waveform with the same photodetector and recorded by a digital storage oscilloscope. The phenomenon of fast light appears when the light propagates in the anomalous dispersion medium. If the dispersion is anomalous / 0dn d , then the group velocity

g of a light pulse can exceed the speed in a medium nc / or

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The 9th International Conference on Optical Communications and Networks (ICOCN2010) Nanjing, China, 24-27, October, 2010

(Invited Paper)

even in a vacuum c. If dn/d 1 , a negative group velocity is obtained. The delay time T is negative and a light can propagate sooner than that had travelled the same distance in a vacuum. SBS is a nonlinear process that caused by the interaction between a light wave and an acoustic wave. When a pump

light with a frequency p

propagates through a fiber, a

backward-scattered Stokes wave is generated with a downshifted frequency at p B ( B is the Stokes shift). If

the Stokes light is injected in a back-propagate direction to the pump light, it is amplified in SBS process. Meanwhile, the pump light experiences an absorption , which is the condition of the fast light and superluminal. This narrowband (~30 MHz) gain and loss band of SBS is used to achieve strong changes in the group index of light.

For a continuous wave (CW) or quasi-CW pump, The

group index g g

n c via the SBS process is given by[13] 2

0

2 2

1 [2( ) / ],

{1 [2( ) / ] }p s B

g fB s B

cg In n

(1) where, fn is the group index of fibers without any

nonlinearity effect, 0g is the SBS gain factor, B is the SBS

linewidth, s p B is the peak frequency of SBS gain,

p pump effI P A is the pump intensity, effA is the effective

core area of fiber. Thus, the group index change

g g fgn n n via SBS process is proportional to the pump

power. Thus, the time delay by SBS

0

d 2 2

1 [2( ) / ]T ( ) /

{1 [2( ) / ] }

p s B

g f

B eff s B

g P LL n n c

A

(2)

When 2[2( ) / ] 1s B

, Eq. (2) can be expressed as

0

dT ( ) / p

g f

B eff

g P LL n n c

A

. (3)

To control the speed of the signal, a pump light with the precise frequency is required, pump Bsignal for slow

light and pump Bsignal for fast light. Here, the Stokes

wave generated by spontaneous Brillouin scattering at a frequency downshifted B below the signal, in turn, serve as

a pump light. Above the SBS threshold, the signal power is transferred to the Stokes wave and experiences absorption to achieve the fast light and superluminal propapgation. The group index change is proportional to the backward Stokes power as Eq. (1), which increases as the input signal power increases. In our experiment, the Stokes light is circulated back into the SBS medium for Brillouin lasing by employing a fiber ring lasing cavity which is constructed by a optical circulator and the SMF. Thus, the power of the back-propagating Stokes light is enhanced. The group index change is optimized and the advancement is enlarged. Controllable superluminal light propagation at negative group velocity in optical fibers will be realized by manipulating the input signal power or the loss of fiber ring cavity.

3 Results and discussion

Figure 2 show the observed output signals waveform under different Stokes powers. It is clearly observed that the larger the Stokes power is, the faster the signal pulse propagates.

Fig. 2. Signal pulse after propagating through a 10m SMF for different Stokes powers. Waveform heights are normalized to facilitate comparison.

Figure 3 show the observed output signals under different Stokes powers. There is no SBS effect when the input signal power is below the SBS threshold power. Thus, the output signal is delayed with time of 48.6ns which is signal light propagating time through 10 m-long SMF. As the input power is beyond threshold power, the output signal is closer and closer to the input signal, and then precedes it with a negative group velocity. In Figure 3, the decrease in the pulse width is also observed since the width of the back-propagate stokes light is approximately as small as 35MHz and the SBS effect has a strong frequency dependence. The loss around the signal carrier frequency is stronger than that at other frequency which causes the change of the signal pulse spectrum.

2000 2200 2400 2600 2800 3000 3200

0.0

0.2

0.4

0.6

0.8

1.0

No

rm. A

mp

l

Time / ns

input signal output signal

0.057mW 0.090mW 0.18 mW 1.08 mW 4.08 mW 9.08 mW 13.88mW 29.48mW 41.38mW 43.58mW 60.18mW 74.68mW 85.88mW 99.88mW 118.0mW 138.0mW

2697.2ns2648.6ns

2427.4ns

delt1=48.6ns

delt2=221.2ns

Fig. 3. Input and output signal after propagation through the 10-m length of SMF for different Stokes powers.

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The 9th International Conference on Optical Communications and Networks (ICOCN2010) Nanjing, China, 24-27, October, 2010

Fig. 4 shows the group index change is proportional to the Stokes power. In our experiment, the maximum measured superluminal group velocity was 3.14c and the group index was 0.318. With the stokes power of 12 mW, the minimum negative group was -4.902c and the group index was -0.204. The maximum negative group was -0.151 and the group index was -6.636 with the stokes power of 124.2 mW.

-2 0 2 4 6 8 10 12 14-8

-7

-6

-5

-4

-3

-2

-1

0

1

2

3

4-2 0 2 4 6 8 10 12 14 16

-8

-7

-6

-5

-4

-3

-2

-1

0

1

2

3

4

Gro

up

Ind

ex

Gro

up

Ve

loc

ity

/c

PStokes

/mW

Fig. 4. Signal advancement as a function of the average Stokes power

In our experiment, the maximum signal power is limited by the saturation power of the EDFA. Larger advancement can be realized if using a higher power EDFA or a fiber with a smaller effective area. The scheme shows many advantages including self advancing, lower threshold power and higher unsaturated gain. The advancement induced by SBS is proportional to the back-scattered Stokes power. Controllable superluminal light propagation will be realized by simply manipulating the input signal power. 4 Conclusion

We have firstly experimentally demonstrated the self-induced SBS superluminal light propagation at negative group velocity in optical fibers by employing a fiber ring lasing cavity. The scheme shows some advantages including self advancing, lower threshold power and higher unsaturated gain. Our experiments show that the largest advancement of 221.2 ns is observed, the maximum negative group was -0.15c and the group index was -6.636. In conformity with the theory, the advancement depends on the Stokes power with a high slope efficiency of 20.5 ns/mW. The advancement of the signal can be controlled by modifying its input power

Acknowledgements

The authors acknowledge the support from the National Natural Science Foundation of China (Grant 10874118), the key project of the Ministry of Education of China (Grant 109061), and the “SMC Young Star” scientist Program of Shanghai Jiao Tong University.

References

[1] R. W. Boyd and D. J. Gauthier, “‘Slow’ and ‘Fast’ light,” Ch. 6 in Progress in Optics 43, E. Wolf, ed., pp..497-530, (Elsevier, Amsterdam, 2002).

[2] L. V. Hau, S. E. Harris, and Z. Dutton, “Light speed reduction to 17 metres per second in an ultracold atomic gas”, Nature, 397, pp. 594-598 (1999).

[3] M. S. Bigelow, N. N. Lepeshkin, and R. W. Boyd, “Superluminal and slow light propagation in a room- temperature Solid,” Science, 301, pp. 200-202 (2003).

[4] K. Y. Song, M. Gonzalez Herráez, and L. Thévenaz, “Observation of pulse delaying and advancement in optical fibers using stimulated Brillouin scattering,” Opt. Express, 13, pp. 82-88 (2005).

[5] J. E. Sharping, Y. Okawachi and A.L. Gaeta, “Wide bandwidth slow light using a Raman fiber amplifier,” Opt. Express, 13, pp. 6092-6098 (2005).

[6] 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, pp. 6234-6249 (2005).

[7] K. Qian, L. Zhan, H. G. Li, X. Hu, J. S. Peng, L. Zhang, and Y. X. Xia, “Tunable delay slow-light in an active fiber Bragg grating,” Opt. Express, 17, pp. 22217-22222 (2009).

[8] J. T. Mok, C. M. De Sterke, I. C. M. Littler, and B. J. Eggleton, “Dispersionless slow light using gap solitons,” Nat. Phys., 2, pp.775–780 (2006).

[9] K. Y. Song, M. G. Herráez, and L. Thévenaz, “Optically-controlled delays in optical fibres using Brillouin- generated slow and fast light”, Proc. SPIE, 5855, pp. 142–145(2005).

[10] Y. Okawachi, M. S. Bigelow, J. E. Sharping, Z. Zhu, A. Schweinsberg, D. J. Gauthier, R. W. Boyd, A. L.Gaeta, “Tunable all-optical delays via Brillouin slow light in an optical fiber”, Phys. Rev. Lett. 94, 153902 (2005).

[11] K. Y. Song, M. G. Herraez, and L. Thevenaz, “Long optically controlled delays in optical fibers”, Opt. Lett. 30, pp. 1782-1784 (2005).

[12] L. L. Yi, L. Zhan, W. S. Hu, Y. X. Xia, “Delay of broadband signals using slow light in stimulated Brillouin scattering with phase-modulated pump”, IEEE Photon. Technol. Lett., 19, pp. 619-621 (2007).

[13] K. Y. Song, and K. Hotate, “25 GHz bandwidth Brillouin slow light in optical fibers”, Opt. Lett., 32, pp. 217-219 (2007).

[14] S. Chin, M. Gonzalez-Herraez1, and L. Thévenaz, “Self-advanced fast light propagation in an optical fiber based on Brillouin scattering”, Opt. Express, 16, pp. 12181-12189, (2008).

[15] L. Brillouin, Wave Propagation and Group Velocity. (New York: Academic, 1960).

[16] C. G. B. Garrett and D. E. McCumber, “Propagation of a Gaussian light pulse through an anomalous dispersion medium”, Phys. Rev. A, 1, pp. 305–313, (1970).

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The 9th International Conference on Optical Communications and Networks (ICOCN2010) Nanjing, China, 24-27, October, 2010

[17] D. Mugnai, A. Ranfagni, and R. Ruggeri, “Observation of superluminal behaviors in wave propagation”, Phys. Rev. Lett., 84, pp. 4830-4833, (2000).

[18] H. Chang and D. D. Smith, “Gain-assisted superluminal propagation in coupled optical resonators”, J. Opt. Soc. Am. B, 22, pp. 2237-2241, (2005).

[19] S. Chu and S. Wong, “Linear pulse propagation in an absorbing medium,” Phys. Rev. Lett., 48, pp. 738-741, (1982).

[20] M. A. I. Talukder, Y. Amagishi, and M. Tomita. “Superluminal to subluminal transition in the pulse propagation in a resonantly absorbing medium”, Phys. Rev. Lett. 86, pp. 3546-3549, (2001).

[21] L. J. Wang, A. Kuzmich, and A. Dogariu, “Gain-assisted superluminal light propagation,” Nature, 406, pp. 277–279, (2000).

[22] W. G. A. Brown, R. McLean, A. Sidorov, P. Hannaford, and A. Akulshin, “Anomalous dispersion and negative group velocity in a coherence-free cold atomic medium”, arXiv:0805, 2993 (2008).

[23] A. M. Steinberg, P. G. Kwiat, and R. Y. Chiao, “Measurement of the single-photon tunneling time,” Phys. Rev. Lett., 71, pp. 708–711, (1993).

[24] K. Y. Song, M. G. Herráez, and L. Thévenaz, “Observation of pulse delaying and advancement in optical fibers using stimulated Brillouin scattering,” Opt. Express, 13, pp. 82–88, (2005).

[25] G. M. Gehring, A. Schweinsberg, C. Barsi, N. Kostinski, and R. W. Boyd, "Observation of backward pulse propagation through a medium with a negative group velocity", Science, 312, pp. 895-897, (2006).

[26] K. Y. Song, K. S. Abedin and K. Hotate, “Gain-assisted superluminal propagation in tellurite glass fiber based on stimulated Brillouin scattering”, Opt. Express, 16, pp. 225-230, (2008).

[27] S. Longhi, M. Marano, and P. Laporta, "Superluminal optical pulse propagation at 1.5 μm in periodic fiber Bragg gratings", Phys. Rev. E, 64, 055602, (2001)

[28] R. B. Hwang, “Negative group velocity and anomalous transmission in a one-dimensionally periodic waveguide”, IEEE Trans. Anten. Prop., 54, pp. 755-760, (2006).

[29] J. F. Woodley and M. Mojahedi, “Negative group velocity and group delay in left-handed media,” Phys. Rev. E, 70, 046603, (2004).

[30] H. Wang, Y. Zhang, N. Wang, W. Yan, H. Tian, W. Qiu, and P. Yuan, "Observation of superluminal propagation at negative group velocity in C60 solution", Appl. Phys. Lett., 90, 121107, (2007).

[31] H. Wang, Y. Zhang, H. Tian, N.Wang, L. Ma, P. Yuan, "Direct observation of signal evolution of slow and fast light in media with saturated and reverse saturated absorption", Appl. Phys. B, 92, pp 487–491, (2008)

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