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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 16, Iss. 1 — Jan. 7, 2008
  • pp: 225–230
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Gain-assisted superluminal propagation in tellurite glass fiber based on stimulated Brillouin scattering

Kwang Yong Song, Kazi S. Abedin, and Kazuo Hotate  »View Author Affiliations


Optics Express, Vol. 16, Issue 1, pp. 225-230 (2008)
http://dx.doi.org/10.1364/OE.16.000225


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Abstract

We demonstrate superluminal propagation of optical pulses with amplification in optical fibers based on stimulated Brillouin scattering. A triple gain peak configuration is used for the generation of narrowband anomalous dispersion in 2 m tellurite glass fiber, where the group index change as much as -1.19 is achieved with 6.9 dB amplification in 34 ns Gaussian pulses, leading to the group index of 0.84.

© 2008 Optical Society of America

1. Introduction

Recent studies on the group-index control of optical pulses, i.e. slow and fast light, in optical fibers have attracted much attention in photonics societies, and a number of interesting results have been reported based on stimulated Brillouin scattering (SBS), stimulated Raman scattering (SRS), Raman-assisted optical parametric amplification, and coherent population oscillation (CPO) [1–7

1. R. W. Boyd and D. J. Gauthier, “‘Slow’ and ‘Fast’ Light,” Ch. 6 in Progress in Optics43, E. Wolf, Ed. (Elsevier, Amsterdam, 2002), 497–530.

]. For most of potential applications of the slow and fast light such as optical buffers, optical variable delay lines, phased-array antennas, and optical memories, the amount of the fractional delay, i.e. the product of the bandwidth and the time delay, is regarded as a key parameter rating the device performance. However, the amount of the group index change (Δng) also plays an important role in some applications like a passive resonator gyroscope where the rotational sensitivity is inversely proportional to ng [8

8. 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, 053807 (2007). [CrossRef]

], therefore so called ‘superluminal’ (ng<1) propagation can lead to the enhancement of the sensing performance.

In this paper, we demonstrate gain-assisted fast light propagation in a tellurite-glass fiber based on SBS. A triple Brillouin pump is applied to a 2 m tellurite-glass fiber to introduce anomalous dispersion between gain peaks, and Δn g of -1.19 with 6.93 dB amplification is achieved using 34 ns Gaussian pulses, resulting in the n g of 0.84. To the best of our knowledge, this is the first demonstration of gain-assisted superluminal propagation based on SBS.

2. Principle

Figure 1 shows the relation between Brillouin gain, the phase index change (Δn), and Δng based on the Kramers-Kronig relation. As depicted in Fig. 1(a), a Lorentzian gain with a bandwidth (FWHM) of ΔνB induces sudden changes of Δn and Δng with local maxima δn and δng which are expressed as following equations:

δn=c8πν0gBIP
(1)
δng=4ν0·δnΔνB=c·gBIP2π·ΔνB
(2)

where c, ν0, gB, and Ip are speed of light in vacuum, center frequency of Brillouin gain, Brillouin gain coefficient, and intensity of pump wave, respectively.

Fig. 1. Relation between Brillouin gain, the phase index change (Δn), and the group index change (Δng) based on the Kramers-Kronig relation in the case of a single peak (a) and a double peak (b) configuration.

For the generation of gain-assisted fast light, the frequency region of the minimum Δn g is used which is located at ν0±32ΔvB with the amplitude of -δng/8. In order to reduce the pulse distortion, a double-peak configuration is usually adopted with the peak separation of √3·ΔνB, and the resultant Δng is an addition of the contributions from two peaks as shown in Fig. 1(b) based on the linearity of the Kramers-Kronig relation. Since the efficiency of the double peak is only 1/8 of that of the single peak under the same pump power, the superluminal condition (ng<1) in a conventional single-mode fiber requires over 40 dBm (10 W) of pump power considering the former parameters (Δng~-2 with pump power ~37 dBm) of a single peak experiment [4

4. M. G. Herráez, K. Y. Song, and L. Thévenaz, “Optically controlled slow and fast light in optical fibers using stimulated Brillouin scattering,” Appl. Phys. Lett. 87, 081113 (2005). [CrossRef]

], which is beyond practical pump power level. In this work, a 2 m tellurite-glass fiber with small effective area (9.2 µm2) is used to enhance the efficiency of SBS, and the gain-assisted superluminal condition is demonstrated under the pump power less than 30 dBm (1 W).

3. Experiments and results

The experimental setup is shown in Fig. 2. A 1550-nm laser diode was used as a light source and the output power was divided by a 50/50 coupler. In one arm, a single-sideband modulator (SSBM) and a microwave generator were used to generate a stable Stokes wave detuned from the carrier wave by stable frequency offset (Δν) near the Brillouin frequency (νB) of a fiber under test (FUT). The output from the SSBM was launched into an intensity modulator (IM) to generate probe pulses. In the other arm, a phase modulator (PM) and a RF generator were used to build multiple-peak Brillouin pump waves, and the output was amplified by a high power Er-doped fiber amplifier (EDFA) and launched into the FUT through a circulator in the opposite direction to the probe waves. The time waveforms of the probe pulses were recorded using a photodiode (PD) and an oscilloscope with the amplitude of the pulses maintained constant by a variable optical attenuator (VOA). In the measurement of Brillouin gain spectrum (BGS), we changed the role of the IM into a chopper for the CW probe wave and a lock-in detection technique was applied (dashed line), while sweeping Δν around νB.

Fig. 2. Setup for slow and fast light experiment with multiple-peak Brillouin pump waves: LD, laser diode; SSBM, single-sideband modulator; PM, phase modulator; EDFA, Er-doped fiber amplifier; IM, intensity modulator; VOA, variable optical attenuator; PD, photodiode; FUT, fiber under test.

As a FUT, a 2 m tellurite-glass single-mode fiber was used with the parameters of Δ (≡Δn/n)~1.6%, refractive index ~2.03, and Aeff ~9.2 µm2. The core was doped with erbium at a concentration of about 1000 ppm, and the propagation loss under saturation condition (power >15 dBm) was about 0.51 dB/m. The splice loss to a lead fiber was about 0.6 dB. From the reported value of gB (1.47~2.16×10-10 m/W) [14

14. K. S. Abedin, “Stimulated Brillouin scattering in single-mode tellurite glass fiber,” Opt. Express 14, 11766–11772 (2006), http://www.opticsinfobase.org/abstract.cfm?URI=oe-14-24-11766. [CrossRef] [PubMed]

], the efficiency of SBS (gB/Aeff) in the FUT was estimated to be about 20 times larger than that of a conventional silica fiber.

Fig. 3. Brillouin gain spectrum measured by lock-in detection in the case of (a) single peak and (b) triple peak configurations of Brillouin gain.

We measured the BGS of the FUT using the lock-in detection with the CW probe wave chopped into a rectangular shape at 100 kHz. As depicted in Fig. 3(a), the νB and the Δν B of a single Brillouin gain peak were measured to be 7.883 GHz and 23.4 MHz, respectively with the PM turned off. Fig. 3(b) shows the BGS with the pump wave phase-modulated at 72 MHz (2Δf) through the PM. A triple Brillouin gain peak with equal amplitude was obtained by controlling the RF power input to the PM, and the Brillouin gain of 20 dB each was achieved with the pump power of 28 dBm.

Fig. 4. (a) Time delay and gain of probe pulses as a function of Δf. (b) Normalized time waveforms of probe pulses in some selected values of Δf. The black curve is the initial shape of the pulse with the initial position of the peak indicated by the dashed line. Note that the pump power is maintained constant to 340 mW.

In order to find the optimum value of Δf, the time delay of the pulse was measured sweeping Δf from 0 to 48 MHz in 4 MHz step with a constant pump power of 25.3 dBm (340 mW). Figure 4(a) shows the time delay and the gain of the probe pulse as a function of Δf. It is noticeable that fast light propagation with negative time delay was observed from Δf of 24 MHz and the maximum advancement was achieved at Δf=36 MHz (dashed arrow), while the Brillouin gain was maintained positive. Some of normalized time waveforms are depicted in Fig. 4(b) where the original peak position is indicated by dashed line. The delay and the advancement by Δf control are clearly seen with resultant broadening and narrowing of the pulses [15

15. K. Y. Song, M. G. Herráez, and L. Thévenaz, “Long optically-controlled delays in optical fibers,” Opt. Lett. 30, 1782–1784 (2005). [CrossRef] [PubMed]

].

Fig. 5. (a) Brillouin gain and time delay of probe pulses as a function of pump power. (b) Time waveforms of probe pulses with the amplitude relatively scaled to the initial value according to the gain. The dashed lines indicate the initial (0 dB) and the final (6.93 dB) position of the pulses.

In order to achieve the maximum advancement of the pulse, Δf was fixed to 36 MHz and the pump power was increased up to 29.8 dBm (960 mW). As shown in Fig. 5(a), both the amount of advancement and the gain were gradually increased with the pump power, and the maximum advancement of -7.95 ns was obtained with the gain of 6.93 dB. The maximum pump power was limited to 29.8 dBm due to the onset of SBS noise from the CW pump wave. The time waveforms of the probe pulses with different Brillouin gains are depicted in Fig. 5(b) with the amplitude relatively scaled to the initial value. The advancement of the pulse with gain is clearly seen as the initial and the final position indicated by the dashed lines. Some distortion of the pulse is also observed in the case of large pump power (>29 dBm) which seems to have come from the limited bandwidth accompanied by the gain saturation due to large peak gain (>30 dB for each peak).

Figure 6 shows the time delay and the calculated Δng with respect to the Brillouin gain. The result matches well with the linear fit (red line), and Δng at the maximum gain is -1.19 which corresponds to a condition of superluminal propagation with ng of 0.84 from the reported refractive index 2.03 [14

14. K. S. Abedin, “Stimulated Brillouin scattering in single-mode tellurite glass fiber,” Opt. Express 14, 11766–11772 (2006), http://www.opticsinfobase.org/abstract.cfm?URI=oe-14-24-11766. [CrossRef] [PubMed]

].

Fig. 6. Time delay and Δng of probe pulses as a function of gain.

4. Conclusion

We have demonstrated gain-assisted advancement of optical pulses based on Stimulated Brillouin scattering in a 2 m tellurite fiber. A group index of 0.84, corresponding to the condition of superluminal propagation, has been achieved using a triple gain peak configuration with the pump power level less than 30 dBm (1 W). Although the onset of SBS from the CW pump wave has limited the maximum value (-1.19) of the group index change, it will be avoidable by reducing the fiber length on which the group index change does not have dependence. Therefore the pulse propagation with zero group index with amplification would be possible with shorter length (~1 m) of the tellurite fiber with the pump power level of 30~33 dBm (1~2 W), which may provide a significant contribution to the sensor applications based on the slow and fast light.

Acknowledgments

This work was supported by the Korea Research Foundation Grant funded by the Korean Government (MOEHRD) (KRF-2007-331-C00116), and this experiment was done in Department of Electronic Engineering, The University of Tokyo.

References and links

1.

R. W. Boyd and D. J. Gauthier, “‘Slow’ and ‘Fast’ Light,” Ch. 6 in Progress in Optics43, E. Wolf, Ed. (Elsevier, Amsterdam, 2002), 497–530.

2.

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, 82–88 (2005), http://www.opticsinfobase.org/abstract.cfm?URI=oe-13-1-82. [CrossRef] [PubMed]

3.

Y. Okawachi, M. S. Bigelow, J. E. Sharping, Z. M. 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, 153902 (2005). [CrossRef] [PubMed]

4.

M. G. Herráez, K. Y. Song, and L. Thévenaz, “Optically controlled slow and fast light in optical fibers using stimulated Brillouin scattering,” Appl. Phys. Lett. 87, 081113 (2005). [CrossRef]

5.

J. E. Sharping, Y. Okawachi, and Alexander L. Gaeta, “Wide bandwidth slow light using a Raman fiber amplifier,” Opt. Express 13, 6092–6098 (2005), http://www.opticsinfobase.org/abstract.cfm?URI=oe-13-16-6092. [CrossRef] [PubMed]

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, 6234–6249 (2005), http://www.opticsinfobase.org/abstract.cfm?URI=oe-13-16-6234. [CrossRef] [PubMed]

7.

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, 895–897 (2006). [CrossRef] [PubMed]

8.

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, 053807 (2007). [CrossRef]

9.

K. Y. Song, M. González Herráez, and L. Thévenaz, “Gain-assisted pulse advancement using single and double Brillouin gain peaks in optical fibers,” Opt. Express 13, 9758–9765 (2005), http://www.opticsinfobase.org/abstract.cfm?URI=oe-13-24-9758. [CrossRef] [PubMed]

10.

S. H. Chin, M. González Herráez, and L. Thévenaz, “Zero-gain slow & fast light propagation in an optical fiber,” Opt. Express 14, 10684–10692 (2006), http://www.opticsinfobase.org/abstract.cfm?URI=oe-14-22-10684. [CrossRef] [PubMed]

11.

C. Jauregui, H. Ono, P. Petropoulos, and D. J. Richardson, “Four-fold reduction in the speed of light at practical power levels using Brillouin scattering in a 2-m bismuth-oxide fiber,” in Conference on Optical Fiber Communication (OFC 2006), Paper PDP2 (2006).

12.

K. Y. Song, K. S. Abedin, K. Hotate, M. González Herráez, and L. Thévenaz, “Highly efficient Brillouin slow and fast light using As2Se3 chalcogenide fiber,” Opt. Express 14, 5860–5865 (2006), http://www.opticsinfobase.org/abstract.cfm?URI=oe-14-13-5860. [CrossRef] [PubMed]

13.

K. S. Abedin, G. W. Lu, and T. Miyazaki, “Stimulated Brillouin scattering assisted slow light generation in single mode tellurite fiber,” in Conference on Lasers and Electro-Optics (CLEO 2007), Paper CThH6 (2007).

14.

K. S. Abedin, “Stimulated Brillouin scattering in single-mode tellurite glass fiber,” Opt. Express 14, 11766–11772 (2006), http://www.opticsinfobase.org/abstract.cfm?URI=oe-14-24-11766. [CrossRef] [PubMed]

15.

K. Y. Song, M. G. Herráez, and L. Thévenaz, “Long optically-controlled delays in optical fibers,” Opt. Lett. 30, 1782–1784 (2005). [CrossRef] [PubMed]

OCIS Codes
(060.2310) Fiber optics and optical communications : Fiber optics
(060.4370) Fiber optics and optical communications : Nonlinear optics, fibers
(070.6020) Fourier optics and signal processing : Continuous optical signal processing
(290.5900) Scattering : Scattering, stimulated Brillouin
(350.5500) Other areas of optics : Propagation

ToC Category:
Slow and Fast Light

History
Original Manuscript: November 9, 2007
Revised Manuscript: December 18, 2007
Manuscript Accepted: December 19, 2007
Published: January 2, 2008

Citation
Kwang Yong Song, Kazi S. Abedin, and Kazuo Hotate, "Gain-assisted superluminal propagation in tellurite glass fiber based on stimulated Brillouin scattering," Opt. Express 16, 225-230 (2008)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-1-225


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References

  1. R. W. Boyd and D. J. Gauthier, "‘Slow’ and ‘Fast’ Light," in Progress in Optics43, E. Wolf, ed., (Elsevier, Amsterdam, 2002), Chap. 6, pp. 497-530.
  2. K. Y. Song, M. G. Herráez and L. Thévenaz, "Observation of pulse delaying and advancement in optical fibers using stimulated Brillouin scattering," Opt. Express 13,82-88 (2005). [CrossRef] [PubMed]
  3. Y. Okawachi, M. S. Bigelow, J. E. Sharping, Z. M. 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, 153902 (2005). [CrossRef] [PubMed]
  4. M. G. Herráez, K. Y. Song and L. Thévenaz, "Optically controlled slow and fast light in optical fibers using stimulated Brillouin scattering," Appl. Phys. Lett. 87,081113 (2005). [CrossRef]
  5. J. E. Sharping, Y. Okawachi and AlexanderL. Gaeta, "Wide bandwidth slow light using a Raman fiber amplifier," Opt. Express 13,6092-6098 (2005). [CrossRef] [PubMed]
  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 13,6234-6249 (2005). [CrossRef] [PubMed]
  7. 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, 895-897 (2006). [CrossRef] [PubMed]
  8. 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, 053807 (2007). [CrossRef]
  9. K. Y. Song, M. González Herráez, and L. Thévenaz, "Gain-assisted pulse advancement using single and double Brillouin gain peaks in optical fibers," Opt. Express 13, 9758-9765 (2005). [CrossRef] [PubMed]
  10. S. H. Chin, M. González Herráez, and L. Thévenaz, "Zero-gain slow & fast light propagation in an optical fiber," Opt. Express 14, 10684-10692 (2006). [CrossRef] [PubMed]
  11. C. Jauregui, H. Ono, P. Petropoulos and D. J. Richardson, "Four-fold reduction in the speed of light at practical power levels using Brillouin scattering in a 2-m bismuth-oxide fiber," in Conference on Optical Fiber Communication (OFC 2006), Paper PDP2 (2006).
  12. K. Y. Song, K. S. Abedin, K. Hotate, M. González Herráez and L. Thévenaz, "Highly efficient Brillouin slow and fast light using As2Se3 chalcogenide fiber," Opt. Express 14, 5860-5865 (2006). [CrossRef] [PubMed]
  13. K. S. Abedin, G. W. Lu, and T. Miyazaki, "Stimulated Brillouin scattering assisted slow light generation in single mode tellurite fiber," in Conference on Lasers and Electro-Optics (CLEO 2007), Paper CThH6 (2007).
  14. K. S. Abedin, "Stimulated Brillouin scattering in single-mode tellurite glass fiber," Opt. Express 14, 11766-11772 (2006). [CrossRef] [PubMed]
  15. K. Y. Song, M. G. Herráez and L. Thévenaz, "Long optically-controlled delays in optical fibers," Opt. Lett. 30, 1782-1784 (2005). [CrossRef] [PubMed]

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