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Optics Express

Optics Express

  • Editor: Michael Duncan
  • Vol. 13, Iss. 24 — Nov. 28, 2005
  • pp: 9758–9765
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Gain-assisted pulse advancement using single and double Brillouin gain peaks in optical fibers

Kwang Yong Song, Miguel González Herráez, and Luc Thévenaz  »View Author Affiliations


Optics Express, Vol. 13, Issue 24, pp. 9758-9765 (2005)
http://dx.doi.org/10.1364/OPEX.13.009758


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Abstract

We report the first experimental demonstration of pulse advancement with gain in optical fibers based on stimulated Brillouin scattering. Two experimental configurations are investigated and compared. One is to make the pulse propagate in a region slightly detuned from a gain peak where the group velocity change is negative and the other is to make use of the large anomalous dispersion appearing between two gain peaks. We experimentally show that the second method produces pulse advancement with lower distortion than the first one.

© 2005 Optical Society of America

1. Introduction

There is an increasing interest in the scientific community to exert an external optical control on the dispersive properties of a material, so as to modify substantially the speed of light pulses travelling through it. To date, many successful experiments for creating slow and fast light have been described [1

1 . R. W. Boyd and D. J. Gauthier , “ ‘Slow’ and ‘Fast’ Light ,” Ch. 6 in Progress in Optics 43 , E. Wolf , Ed. ( Elsevier, Amsterdam , 2002 ), 497 – 530 .

], most of them using special media like cold atomic gases [2

2 . 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 , 594 – 598 ( 1999 ). [CrossRef]

,3

3 . C. Liu , Z. Dutton , C. H. Behroozi , and L. V. Hau . “ Observation of coherent optical information storage in an atomic medium using halted light pulses ,” Nature 409 , 490 – 493 ( 2001 ). [CrossRef] [PubMed]

], hot atomic vapours [4–6

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

] or special crystals with long transition lifetimes [7

7 . M. S. Bigelow , N. N. Lepeshkin , and R. W. Boyd , “ Superluminal and Slow-light propagation in a room-temperature solid ,” Science 301 , 200 – 202 ( 2003 ). [CrossRef] [PubMed]

]. While the former studies were mainly performed using narrow atomic resonances under rigorous experimental conditions, it has been recently shown that slow and fast light propagation in optical fibers can be achieved by use of stimulated Brillouin scattering [8–11

8 . 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.opticsexpress.org/abstract.cfm?URI=OPEX-13-1-82 . [CrossRef] [PubMed]

], Raman scattering [12

12 . 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.opticsexpress.org/abstract.cfm?URI=OPEX-13-16-6092 . [CrossRef] [PubMed]

] or Raman-assisted parametric amplification [13

13 . 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.opticsexpress.org/abstract.cfm?URI=OPEX-13-16-6234 . [CrossRef] [PubMed]

] with more flexibility and a simpler configuration. These experiments make use of an optically-controlled narrowband gain or loss process occurring in the fiber, in which the group velocity of the signal is strongly altered. In all these experiments, the group index can be tuned continuously simply by controlling a pump power level. In particular, the method based on stimulated Brillouin scattering proved that it can reproduce almost all the experimental results achieved by the former studies such as slow light (vg≈71000 km/s), faster-than-light (superluminal) propagation and even negative group velocities [11

11 . 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]

] with a simple bench top experimental setup at room temperatures.

Fast light experiments are particularly challenging and fascinating for the scientific community, since superluminal signal velocities can be achieved (however preserving Einstein’s causality [5

5 . M. D. Stenner , D. J. Gauthier , and M. A. Neifeld , “ The speed of information in a ‘fast-light’ optical medium ,” Nature 425 , 695 – 698 ( 2003 ). [CrossRef] [PubMed]

]). These experiments require the attainment of a very large anomalous dispersion in the medium at the signal frequency. Sharp atomic absorptions and electromagnetically-induced absorption (EIA) [6

6 . A. M. Akulshin , Barreiro S. , and A. Lezema “ Steep anomalous dispersion in a coherently prepared Rb vapor ,” Phys. Rev. Lett. 83 , 4277 ( 1999 ). [CrossRef]

] have provided a mean to obtain this large anomalous dispersion. In fibers, the narrowband loss of stimulated Brillouin scattering has been used to create these conditions [11

11 . 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]

]. All these methods for obtaining fast light, however, have the common drawback of making the pulse propagate in a spectral region of high absorption. To overcome this impairment, two methods have been devised: one is to propagate the pulse in a region slightly detuned from a gain line [14

14 . E. L. Bolda , J. C. Garrison , and R. Y. Chiao , “ Optical pulse propagation at negative group velocities due to a nearby gain ,” Phys. Rev. A 49 , 2938 – 2947 ( 1994 ). [CrossRef] [PubMed]

], where the group velocity change is negative; the other, more sophisticated approach is to make use of the large anomalous dispersion appearing between two gain peaks [4

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

]. These methods have been previously demonstrated in atomic vapours, but never in the optical fiber.

In this paper we report the first experimental demonstration of pulse advancement with gain and low distortion in optical fibers using stimulated Brillouin scattering (SBS). We test the two methods described above to achieve gain-assisted fast light and demonstrate experimentally that the method based on the double Brillouin gain peak produces pulse advancement with lower distortion. A simple numerical simulation is also performed based on the linear theory and compared to the results. We believe that this observation will have important implications for slow and fast light research based on optical fibers.

2. Theory

The process of SBS is usually described as the interaction of two counterpropagating waves, a strong pump wave and a weak probe wave. If a specific frequency arrangement is satisfied (namely fpump=fprobe+v B, v B being the Brillouin shift), an acoustic wave is generated which scatters photons from the pump to the probe wave, stimulating the process. Since the Brillouin gain bandwidth is as small as 30 MHz in conventional optical fibers, the SBS can be regarded as a narrowband amplification process, in which a strong pump wave produces a narrowband gain in a spectral region around fpump-v B and a loss around fpump+v B. According to the Kramers-Kronig relation, a refractive index change is associated with the Brillouin gain/loss process and a substantial change of the group index ng=n+ω dn/ follows as a result of the sharp index transition.

Fig. 1. Gain, refractive index change An and group index change ∆ng generated in an optical fiber in (a) single peak and (b) double peak configurations: v 1 and v 2, optical frequencies of the Brillouin gain peaks; v 0, central frequency of the probe pulse; ∆v, detuning frequency.

3. Experiments

The experimental configuration is shown in Fig. 2. A conventional optical fiber with a v B of 10.834 GHz and length of 5 km was used as gain medium and a DFB laser diode operating at 1552 nm was used as a light source. The laser output was launched into an electro-optic modulator (EOM-1) to create two first-order sidebands and the carrier wave was suppressed by controlling the DC bias voltage delivered into the EOM with a feedback circuit [15

15 . M. Niklès , L. Thévenaz , and P. Robert , “ Brillouin gain spectrum characterization in single-mode optical fibers ,” J. Lightwave Technol. , LT-15 , 1842 – 1851 ( 1997 ). [CrossRef]

]. The lower-frequency sideband (Stokes wave) was reflected by a narrowband fiber Bragg grating and optically gated to be used as a probe pulse. As a fast optical gate, another EOM was used, resulting in clean and sharp pulses with no ripple.

Our first experiment concerned the use of a single, detuned SBS gain peak to achieve pulse advancement. In this case, the lower frequency sideband at the output of the EOM-1 was amplified to be used as a Brillouin pump wave using a high power Er-doped fiber amplifier (EDFA). The time delay and the envelope of the probe pulse were measured using a photodiode and a digital oscilloscope. The frequency difference between pump and probe was set to v B+∆v, where ∆v was swept from 2 MHz to 50 MHz in 4-MHz step. In the mean time, the output amplitude of the probe pulse on the detector was kept constant using a variable optical attenuator (VOA) to avoid a possible time biasing from an amplitude-dependent time response of the detector.

Fig. 2. Experimental setup for optical delay measurement. Devices surrounded by the dashed box are only inserted for the double peak configuration: LD, laser diode; VOA, variable optical attenuator; EOM, electro-optic modulator; PD, photodiode; EDFA, erbium-doped fiber amplifier.

Our second experiment concerned the use of a double SBS gain peak to achieve pulse advancement. The modulation frequency of the EOM-1 was fixed to the Brillouin shift v B of the fiber and another modulator (EOM-2) was inserted in the setup (dashed box in Fig. 2) to modulate the pump with a frequency ∆v. The bias point of the EOM-2 was controlled as in the EOM-1 to eliminate the DC component. This way, only the two first-order sidebands are used as pumps, creating two gain peaks separated by 2∆v. A similar measurement of the probe pulse was carried out, sweeping the modulation frequency of the EOM-2 from 2 MHz to 50 MHz in 4-MHz step.

4. Results

Figure 3 shows the time waveforms of probe pulses at a few selected detuning frequencies (∆v’s) in the case of single peak (a) and double peak (b) configuration. ∆v indicates the frequency difference from v B in case of single peak and the half of the frequency difference between the two peaks in the double peak experiment, respectively (see Fig. 1). As expected, the largest pulse delays were observed at the minimum ∆v (2 MHz) in both cases and the amount of delay started to decrease with ∆v increasing. The distortion of the pulse envelope was also observed and it was more evident in the case of single peak experiment at larger gain as shown in Fig. 3(a), which could be attributed to the non-symmetric amplitude response of the gain shape at that frequency point and the large third-order dispersion around that spectral region. Meanwhile, the distortion was smaller in the case of double peak configuration as seen in Fig. 3(b), due to the flat and symmetric amplitude response.

Fig. 3. Time waveforms of probe pulses at a few selected ∆v’s in (a) single peak and (b) double peak configuration. The gain values of 10 dB (middle) and 20 dB (bottom) mean the maximum gains at ∆v=0 in both cases. The dashed lines indicate the peak position of the initial 37-ns probe pulse with no Brillouin pump.

Figure 4 shows the gain and the time delay of the probe pulses as a function of the detuning frequency ∆v in the single peak (a) and the double peak (b) configurations, respectively. Since the peak positions of the pulses were difficult to determine in the case of large modification of envelope, we measured the half-maximum point of the front edge as a criterion of pulse delaying and advancement. We believe this is a reasonable point to establish where the detection of the signal takes place in a real communication system. In both cases, the gain curve reflects the Lorentzian shape of the Brillouin gain faithfully and the amount of pulse delay decreases gradually as the detuning frequency (∆v) is increased. The advancement of the pulse (under the dotted line in the figures) is clearly seen for ∆v’s of about 25 MHz or more in all cases. The advancement could be continuously controlled and the maximum advancements were 5.0 ns with a gain of 2.9 dB at ∆v=50 MHz in the case of the single peak and 3.9 ns with a gain of 4.6 dB at ∆v=38 MHz in the case of the double peak, respectively, with 20 dB maximum gain in both cases. These correspond to the group index changes of about -3.0×10-4 and -2.3×10-4 for the single and the double peak configurations, respectively.

Fig. 4. Measured gain and time delay of probe pulses as a function of the detuning frequency ∆v in (a) single peak and (b) double peak configurations, respectively. The gain values of 10 dB (top) and 20 dB (bottom) mean the maximum gains at ∆v=0 in both cases. The dotted line indicates the original (no pump) position of probe pulses.
Fig. 5. The FWHM of probe pulses as a function of ∆v normalized by the initial value (37 ns) in the case of (a) single peak and (b) double peak configurations, respectively. The gain means the maximum gain values at ∆v=0.

The amount of envelope modification can be roughly estimated using the variation of the relative pulse width (FWHM) normalized to the initial value which is shown in Fig. 5. The variation of the pulse width was larger in the case of 20 dB-gain and single peak configuration where the relative pulse width changes as much as 50%. The offset value for ∆v=50 MHz and 20 dB gain results from the strong distortion, as can be seen in Fig. 3(a). On the other hand, the variation was less than 20% in the double peak configuration, which is due to the fact that the group velocity changes within the pulse bandwidth are smaller and the flat magnitude response in the middle of the two gain peaks.

In order to confirm the validity of this result, we performed a numerical simulation using the real shape of the input pulse based on the linear theory [16

16 . S. E. Harris , J. E. Field , and A. Kasapi , “ Dispersive properties of electromagnetically induced transparency ,” Phys. Rev. A 46 , 29 ( 1992 ). [CrossRef]

,17

17 . R. W. Boyd , D. J. Gauthier , A. L. Gaeta , and A. E. Willner , “ Maximum time delay achievable on propagation through a slow-light medium ,” Phys. Rev. A 71 , 023801 ( 2005 ). [CrossRef]

], assuming that the Brillouin gain was uniform along the fiber following a Lorentzian distribution with a 30 MHz FWHM width. The effect of pump depletion is not considered for simplicity and may lead to substantially different results when important [18

18 . Z. Zhu , D. J. Gauthier , Y. Okawachi , J. E. Sharping , A. L. Gaeta , R. W. Boyd , and A. E. Willer , “ Numerical study of all-optical slow-light delays via stimulated Brillouin scattering in an optical fiber ,” J. Opt. Soc. Am. B , 22 , 2378 – 2384 ( 2005 ). [CrossRef]

], but we managed to set our experimental conditions to make it negligible. We calculated the delay and the relative width of the pulse normalized to the initial value as a function of ∆v in 1 MHz step in the single peak and the double peak configurations, setting the maximum gain of 20 dB at ∆v=0 in both cases. The result is shown in Fig. 6.

Fig. 6. Calculated time delays and relative pulse widths normalized to the initial value according to the detuning frequency based on linear theory in (a) single peak and (b) double peak configurations. A uniform Brillouin gain of a Lorentzian shape with a FWHM of 30 MHz is assumed through the fiber and the maximum gain at ∆v=0 is set to 20 dB.

We could see decent correlation between the simulation and the experimental results in terms of the gradual decrease of the time delay and the overall behavior in the variation of the relative width. It is also remarkable that there was a difference in the ∆’s for zero time delay in the experiment, and this feature matches well with the calculation results. The considerable difference in the real values of relative widths in both cases is thought to come from non-uniform Brillouin gain, and we believe it needs further investigation for better understanding.

5. Conclusion

We have reported the first experimental demonstration of pulse advancement with gain in optical fibers based on stimulated Brillouin scattering. Two experimental configurations were proposed and compared - one is to propagate the pulse in a region slightly detuned from a single SBS gain peak and the other is to make use of the anomalous dispersion appearing between two gain peaks. We experimentally showed that the latter produces pulse advancement with lower distortion, and this was explained in terms of the flatter and symmetric amplitude response of the system in the two gain peak configuration. We expect that this result will have important implications for all-optical signal processing.

We acknowledge the support from the Swiss National Science Foundation through project 200021-109773. MGH also acknowledges funding from the University of Alcalá through project UAH PI 2005/076.

References and links

1 .

R. W. Boyd and D. J. Gauthier , “ ‘Slow’ and ‘Fast’ Light ,” Ch. 6 in Progress in Optics 43 , E. Wolf , Ed. ( Elsevier, Amsterdam , 2002 ), 497 – 530 .

2 .

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 , 594 – 598 ( 1999 ). [CrossRef]

3 .

C. Liu , Z. Dutton , C. H. Behroozi , and L. V. Hau . “ Observation of coherent optical information storage in an atomic medium using halted light pulses ,” Nature 409 , 490 – 493 ( 2001 ). [CrossRef] [PubMed]

4 .

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

5 .

M. D. Stenner , D. J. Gauthier , and M. A. Neifeld , “ The speed of information in a ‘fast-light’ optical medium ,” Nature 425 , 695 – 698 ( 2003 ). [CrossRef] [PubMed]

6 .

A. M. Akulshin , Barreiro S. , and A. Lezema “ Steep anomalous dispersion in a coherently prepared Rb vapor ,” Phys. Rev. Lett. 83 , 4277 ( 1999 ). [CrossRef]

7 .

M. S. Bigelow , N. N. Lepeshkin , and R. W. Boyd , “ Superluminal and Slow-light propagation in a room-temperature solid ,” Science 301 , 200 – 202 ( 2003 ). [CrossRef] [PubMed]

8 .

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.opticsexpress.org/abstract.cfm?URI=OPEX-13-1-82 . [CrossRef] [PubMed]

9 .

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

10 .

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]

11 .

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]

12 .

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.opticsexpress.org/abstract.cfm?URI=OPEX-13-16-6092 . [CrossRef] [PubMed]

13 .

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.opticsexpress.org/abstract.cfm?URI=OPEX-13-16-6234 . [CrossRef] [PubMed]

14 .

E. L. Bolda , J. C. Garrison , and R. Y. Chiao , “ Optical pulse propagation at negative group velocities due to a nearby gain ,” Phys. Rev. A 49 , 2938 – 2947 ( 1994 ). [CrossRef] [PubMed]

15 .

M. Niklès , L. Thévenaz , and P. Robert , “ Brillouin gain spectrum characterization in single-mode optical fibers ,” J. Lightwave Technol. , LT-15 , 1842 – 1851 ( 1997 ). [CrossRef]

16 .

S. E. Harris , J. E. Field , and A. Kasapi , “ Dispersive properties of electromagnetically induced transparency ,” Phys. Rev. A 46 , 29 ( 1992 ). [CrossRef]

17 .

R. W. Boyd , D. J. Gauthier , A. L. Gaeta , and A. E. Willner , “ Maximum time delay achievable on propagation through a slow-light medium ,” Phys. Rev. A 71 , 023801 ( 2005 ). [CrossRef]

18 .

Z. Zhu , D. J. Gauthier , Y. Okawachi , J. E. Sharping , A. L. Gaeta , R. W. Boyd , and A. E. Willer , “ Numerical study of all-optical slow-light delays via stimulated Brillouin scattering in an optical fiber ,” J. Opt. Soc. Am. B , 22 , 2378 – 2384 ( 2005 ). [CrossRef]

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:
Research Papers

History
Original Manuscript: October 10, 2005
Revised Manuscript: October 10, 2005
Published: November 28, 2005

Citation
Kwang Yong Song, Miguel González Herráez, and Luc 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/oe/abstract.cfm?URI=oe-13-24-9758


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References

  1. R. W. Boyd and D. J. Gauthier, “‘Slow’ and ‘Fast’ Light,” Ch. 6 in Progress in Optics 43, E. Wolf, Ed. (Elsevier, Amsterdam, 2002), 497-530.
  2. 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, 594-598 (1999). [CrossRef]
  3. C. Liu, Z. Dutton, C. H. Behroozi and L. V. Hau. “Observation of coherent optical information storage in an atomic medium using halted light pulses,” Nature 409, 490-493 (2001). [CrossRef] [PubMed]
  4. L. J. Wang, A. Kuzmich and A. Dogariu, “Gain-assisted superluminal light propagation,” Nature 406, 277-279 (2000). [CrossRef] [PubMed]
  5. M. D. Stenner, D. J. Gauthier and M. A. Neifeld, “The speed of information in a ‘fast-light’ optical medium,” Nature 425, 695-698 (2003). [CrossRef] [PubMed]
  6. A. M. Akulshin, S. Barreiro and A. Lezema “Steep anomalous dispersion in a coherently prepared Rb vapor,” Phys. Rev. Lett. 83, 4277 (1999). [CrossRef]
  7. M. S. Bigelow, N. N. Lepeshkin and R. W. Boyd, “Superluminal and Slow-light propagation in a room-temperature solid,” Science 301, 200-202 (2003). [CrossRef] [PubMed]
  8. 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), <a href= "http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-1-82">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-1-82<a>. [CrossRef] [PubMed]
  9. K. Y. Song, M. G. Herráez and L. Thévenaz, “Long optically controlled delays in optical fibers,” Opt. Lett. 30, 1782-1784 (2005). [CrossRef] [PubMed]
  10. 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]
  11. 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]
  12. J. E. Sharping, Y. Okawachi and Alexander L. Gaeta, “Wide bandwidth slow light using a Raman fiber amplifier,” Opt. Express 13, 6092-6098 (2005), <a href= "http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-16-6092">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-16-6092</a>. [CrossRef] [PubMed]
  13. 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), <a href= "http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-16-6234">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-16-6234</a>. [CrossRef] [PubMed]
  14. E. L. Bolda, J. C. Garrison and R. Y. Chiao, “Optical pulse propagation at negative group velocities due to a nearby gain,” Phys. Rev. A 49, 2938-2947 (1994). [CrossRef] [PubMed]
  15. M. Niklès, L. Thévenaz and P. Robert, “Brillouin gain spectrum characterization in single-mode optical fibers,” J. Lightwave Technol., LT-15, 1842-1851 (1997). [CrossRef]
  16. S. E. Harris, J. E. Field and A. Kasapi, “Dispersive properties of electromagnetically induced transparency,” Phys. Rev. A 46, 29 (1992). [CrossRef]
  17. R. W. Boyd, D. J. Gauthier, A. L. Gaeta and A. E. Willner, “Maximum time delay achievable on propagation through a slow-light medium,” Phys. Rev. A 71, 023801 (2005). [CrossRef]
  18. Z. Zhu, D. J. Gauthier, Y. Okawachi, J. E. Sharping, A. L. Gaeta, R. W. Boyd and A. E. Willer, “Numerical study of all-optical slow-light delays via stimulated Brillouin scattering in an optical fiber,” J. Opt. Soc. Am. B, 22, 2378-2384 (2005). [CrossRef]

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