Abstract

We show that the presence of a cavity modifies the behaviour of Brillouin-assisted slow light and can be used to significantly enhance the achievable pulse delays. Moreover, the cavity introduces an additional wavelength dependence into the delay versus gain relationship which can be used to provide an extra degree of control within a slow light system. The degree of delay enhancement depends critically both on the cavity finesse and the Brillouin pump power. Our experiments show that delay enhancements greater than 100% can be obtained accompanied by only relatively modest increases in pulse distortion.

© 2007 Optical Society of America

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  1. S. Chu and S. Wong, "Linear pulse propagation in an absorbing medium," Phys. Rev. Lett. 48, 738-741 (1982).
    [CrossRef]
  2. J. T. Mok and B. J. Eggleton, "Expect more delays," Nature 433, 811-812 (2005).
    [CrossRef] [PubMed]
  3. J. Marangos, "Slow light in cool atoms," Nature 397, 559-560 (1999).
    [CrossRef]
  4. 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]
  5. H. Altug and J. Vuckovic, "Experimental demonstration of the slow group velocity of light in two-dimensional coupled photonic crystal microcavity arrays," Appl. Phys. Lett. 86, 111102-1 - 111102-3 (2005).
    [CrossRef]
  6. M. González Herráez, K. Y. Song, and L. Thévenaz, "Optically controlled slow and fast light in optical fibers using stimulated Brillouin scattering," Appl. Phys. Lett. 87, 081113 (2005).
    [CrossRef]
  7. Y. Okawachi, M. S. Bigelow, J. E. Sharping, Z. Zhu, A. Schweinsberg, D. J. Gauthier, R. W. Boyd, and A. L. Gaeta, "Tunable all-optical delays via Brillouin slow light in an optical fiber," Phys. Rev. Lett. 94, 153902 (2005).
    [CrossRef] [PubMed]
  8. G. P. Agrawal, Nonlinear Fiber Optics (Academic Press Inc., London, Third Edition, 2001), Chap 9.
  9. M. González Herráez, K. Y. Song, and L. Thévenaz, "Arbitrary-bandwidth Brillouin slow light in optical fibers," Opt. Express 14, 1395-1400 (2006).
    [CrossRef]
  10. Z. Zhu, A. M. C. Dawes, D. J. Gauthier, L. Zhang, and A. E. Willner, "12-GHz-Bandwidth SBS slow light in optical fibers," presented at OFC´2006, Anaheim, California, 5-10 March. 2006, paper PDP1 (Postdeadline).
  11. C. Jáuregui, 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," presented at OFC´2006, Anaheim, California, 5-10 March. 2006, paper PDP2 (Postdeadline).
  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, 5860-5864 (2006).
    [CrossRef] [PubMed]
  13. C. Jáuregui, P. Petropoulos, and D. J. Richardson, "Slowing of pulses to c/10 with sub-watt power levels and low latency using Brillouin amplification in a bismuth oxide optical fiber," J. Lightwave Technol. (to be published).
  14. A. L. Gaeta and R. W. Boyd, "Stimulated Brillouin scattering in the presence of external feedback," Int. J. Nonlinear Opt. Phys. 1, 581-594 (1992).
    [CrossRef]
  15. W. Lu, A. Johnstone and R. G. Harrison, "Deterministic dynamics of simulated scattering phenomena with external feedback," Phys. Rev. A 46, 4114-4122 (1992).
    [CrossRef] [PubMed]
  16. R. L. Street, Analysis and solution of partial differential equations (Brooks/Cole Publishing Company, Monterey, 1973), Chap. 9.

2006 (2)

2005 (3)

J. T. Mok and B. J. Eggleton, "Expect more delays," Nature 433, 811-812 (2005).
[CrossRef] [PubMed]

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

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

1999 (2)

J. Marangos, "Slow light in cool atoms," Nature 397, 559-560 (1999).
[CrossRef]

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]

1992 (2)

A. L. Gaeta and R. W. Boyd, "Stimulated Brillouin scattering in the presence of external feedback," Int. J. Nonlinear Opt. Phys. 1, 581-594 (1992).
[CrossRef]

W. Lu, A. Johnstone and R. G. Harrison, "Deterministic dynamics of simulated scattering phenomena with external feedback," Phys. Rev. A 46, 4114-4122 (1992).
[CrossRef] [PubMed]

1982 (1)

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

Abedin, K. S.

Behroozi, C. H.

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]

Bigelow, M. S.

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

Boyd, R. W.

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

A. L. Gaeta and R. W. Boyd, "Stimulated Brillouin scattering in the presence of external feedback," Int. J. Nonlinear Opt. Phys. 1, 581-594 (1992).
[CrossRef]

Chu, S.

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

Dutton, Z.

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]

Eggleton, B. J.

J. T. Mok and B. J. Eggleton, "Expect more delays," Nature 433, 811-812 (2005).
[CrossRef] [PubMed]

Gaeta, A. L.

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

A. L. Gaeta and R. W. Boyd, "Stimulated Brillouin scattering in the presence of external feedback," Int. J. Nonlinear Opt. Phys. 1, 581-594 (1992).
[CrossRef]

Gauthier, D. J.

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

González Herráez, M.

Harris, S. E.

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]

Harrison, R. G.

W. Lu, A. Johnstone and R. G. Harrison, "Deterministic dynamics of simulated scattering phenomena with external feedback," Phys. Rev. A 46, 4114-4122 (1992).
[CrossRef] [PubMed]

Hau, L. V.

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]

Hotate, K.

Jáuregui, C.

C. Jáuregui, P. Petropoulos, and D. J. Richardson, "Slowing of pulses to c/10 with sub-watt power levels and low latency using Brillouin amplification in a bismuth oxide optical fiber," J. Lightwave Technol. (to be published).

Johnstone, A.

W. Lu, A. Johnstone and R. G. Harrison, "Deterministic dynamics of simulated scattering phenomena with external feedback," Phys. Rev. A 46, 4114-4122 (1992).
[CrossRef] [PubMed]

Lu, W.

W. Lu, A. Johnstone and R. G. Harrison, "Deterministic dynamics of simulated scattering phenomena with external feedback," Phys. Rev. A 46, 4114-4122 (1992).
[CrossRef] [PubMed]

Marangos, J.

J. Marangos, "Slow light in cool atoms," Nature 397, 559-560 (1999).
[CrossRef]

Mok, J. T.

J. T. Mok and B. J. Eggleton, "Expect more delays," Nature 433, 811-812 (2005).
[CrossRef] [PubMed]

Okawachi, Y.

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

Petropoulos, P.

C. Jáuregui, P. Petropoulos, and D. J. Richardson, "Slowing of pulses to c/10 with sub-watt power levels and low latency using Brillouin amplification in a bismuth oxide optical fiber," J. Lightwave Technol. (to be published).

Richardson, D. J.

C. Jáuregui, P. Petropoulos, and D. J. Richardson, "Slowing of pulses to c/10 with sub-watt power levels and low latency using Brillouin amplification in a bismuth oxide optical fiber," J. Lightwave Technol. (to be published).

Schweinsberg, A.

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

Sharping, J. E.

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

Song, K. Y.

Thévenaz, L.

Wong, S.

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

Zhu, Z.

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

Appl. Phys. Lett. (1)

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

Int. J. Nonlinear Opt. Phys. (1)

A. L. Gaeta and R. W. Boyd, "Stimulated Brillouin scattering in the presence of external feedback," Int. J. Nonlinear Opt. Phys. 1, 581-594 (1992).
[CrossRef]

J. Lightwave Technol. (1)

C. Jáuregui, P. Petropoulos, and D. J. Richardson, "Slowing of pulses to c/10 with sub-watt power levels and low latency using Brillouin amplification in a bismuth oxide optical fiber," J. Lightwave Technol. (to be published).

Nature (3)

J. T. Mok and B. J. Eggleton, "Expect more delays," Nature 433, 811-812 (2005).
[CrossRef] [PubMed]

J. Marangos, "Slow light in cool atoms," Nature 397, 559-560 (1999).
[CrossRef]

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]

Opt. Express (2)

Phys. Rev. A (1)

W. Lu, A. Johnstone and R. G. Harrison, "Deterministic dynamics of simulated scattering phenomena with external feedback," Phys. Rev. A 46, 4114-4122 (1992).
[CrossRef] [PubMed]

Phys. Rev. Lett. (2)

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

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

Other (5)

G. P. Agrawal, Nonlinear Fiber Optics (Academic Press Inc., London, Third Edition, 2001), Chap 9.

Z. Zhu, A. M. C. Dawes, D. J. Gauthier, L. Zhang, and A. E. Willner, "12-GHz-Bandwidth SBS slow light in optical fibers," presented at OFC´2006, Anaheim, California, 5-10 March. 2006, paper PDP1 (Postdeadline).

C. Jáuregui, 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," presented at OFC´2006, Anaheim, California, 5-10 March. 2006, paper PDP2 (Postdeadline).

H. Altug and J. Vuckovic, "Experimental demonstration of the slow group velocity of light in two-dimensional coupled photonic crystal microcavity arrays," Appl. Phys. Lett. 86, 111102-1 - 111102-3 (2005).
[CrossRef]

R. L. Street, Analysis and solution of partial differential equations (Brooks/Cole Publishing Company, Monterey, 1973), Chap. 9.

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Figures (4)

Fig. 1.
Fig. 1.

The experimental setup for the cavity induced delay enhancement. A 2m long highly nonlinear Bismuth-oxide fiber is used as the active medium to generate Brillouin assisted slow-light using a continuous wave pump and a counter-propagating pulsed probe. Partially reflecting splices between the Bismuth-oxide fiber and conventional single-mode fibers are used to define a low finesse Fabry-Perot cavity. The inset shows a trace from a high resolution OTDR used to locate and characterise the cavity. In the figure: P.C.- polarization controller; B.P.F.- bandpass filter; V.O.A.- variable optical attenuator; FBG- fiber Bragg grating; E.D.F.A.- Erbium-doped fiber amplifier.

Fig. 2.
Fig. 2.

Experimental results. a) the waveforms are progressively delayed as the pump power is increased. The modest distortion introduced in the waveforms is clearly visible. b) A comparison of the experimental results with the theoretical predictions (that assume splice reflectivities of 2.3%). The lower plot shows the measured delay versus Brillouin gain (red dotted line) together with the theoretical prediction from the cavity model (blue solid line) and that from a simple analytic model that describes a single pass through the fiber (green solid line). The nonlinear delay enhancement due to the cavity is evident. The upper plot shows the pulse duration as a function of the Brillouin gain as measured in our experiments (red line with diamonds) and as predicted by our model (blue dashed line) compared to that of the single pass theory (green dashed line). It can be seen that an increasing amount of pulse broadening accompanies the delay enhancement.

Fig. 3.
Fig. 3.

(inset) A schematic illustrating all the interactions simultaneously taking place in the Bismuth-oxide fiber cavity. The Brillouin interaction results in an energy transfer between the pump and the probe that leads to probe amplification. However, this process is affected by the relative positions of both the pump and probe with respect to the Fabry-Perot transmission spectrum. (main plot) Dependence of the delay versus gain relationship on the relative position of the pump wavelength with respect to the cavity spectrum. The graph shows the degree of variation attainable in the delay-gain profile when changing the relative position of the pump with respect to the spectrum of the cavity. The solid lines give the theoretical predictions for maximum (red line) and minimum (black line) delays obtained at positions of transmission maxima and minima for the cavity respectively. The crosses and circles represent experimental measurements for different relative positions of the pump with respect to the spectrum of the cavity. It can be seen that the experimental measurements are contained between the limits given by the theoretical predictions.

Fig. 4.
Fig. 4.

Dependence of pulse delay (a) and broadening factor (b) on the reflectivity of the end facets of the cavity. The maximum pump power inside the cavity is given by the labels in each case and roughly corresponds to the lasing threshold.

Equations (10)

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A p + z + 1 v g A p + t = α 2 A p + + j γ ( A p + 2 + 2 A s 2 ) A p + g B 2 A s Q
A s z + 1 v g A s t = α 2 A s + j γ ( A s 2 + 2 A p + 2 ) A s + g B 2 A p + Q *
T B Q t + ( 1 + j δ ) Q = A p + A s *
δ = ( ω p ω s Ω B ) T B
A s + z + 1 v g A s + t = α 2 A s + + j γ ( A s 2 + 2 A p + 2 ) A s +
A p z + 1 v g A p t = α 2 A p + j γ ( A s 2 + 2 A p + 2 ) A p
A s + ( t , 0 ) = r 1 A s ( t , 0 ) e j β s L
A s ( t , L ) = r 2 A s + ( t , L ) e j β s L + A si ( t )
A p + ( t , 0 ) = r 1 A p ( t , 0 ) e j β p L + A pi ( t )
A p ( t , L ) = r 2 A p + ( t , L ) e j β p L

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