Abstract

An analytical solution of the basic coupled stimulated Brillouin scattering (SBS) equations is obtained which describes the evolution of a Stokes pulse injected into an extended Brillouin medium excited by CW pump radiation. We show that regardless of the pulse length of the input Stokes pulse the delay of the output Stokes pulse results entirely from the inertia of the acoustic wave excitation via the electrostrictive interaction of the Stokes pulse with CW pump radiation. This delay is the SBS build up time and not the SBS induced group delay normally attributed to slow light.

© 2009 Optical Society of America

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References

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  1. D. J. Gauthier, "Slow light brings faster communications," Phys. World 18, 30-32 (2005).
  2. K. Y. Song, M. G. Herraez, and L. Thevenaz, "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. Zu, 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. K. Y. Song, M. G. Herraez, and L. Thevenaz, "Long optically controlled delays in optical fibers," Opt. Lett. 30, 1782-1784 (2006).
    [CrossRef]
  5. M. G. Herraez, K. Y. Song, and L. Thevenaz, "Arbitrary-bandwidth Brillouin slow light in optical fibers," Opt. Express 14, 1395-1400 (2006).
    [CrossRef]
  6. Z. Lu, Y. Dong, and Q. Li, "Slow light in multi-line Brillouin gain spectrum," Opt. Express 15, 1871-1877 (2007).
    [CrossRef] [PubMed]
  7. K. Y. Song and K. Hotate, "25 GHz bandwidth Brillouin slow light in optical fibers," Opt. Lett. 32, 217-219 (2007).
    [CrossRef] [PubMed]
  8. B. Zang, L. Yan, I. Fazal. L. Zhang, A. E. Willner, Z. Zu, and D. J. Gauthier, "Slow light on Gbit/s differential-phase-shift-keying signals," Opt. Express 15, 1878-1883 (2007).
    [CrossRef]
  9. B. Ya Zeldovich, "Time of establishment of stationary regime of stimulated light scattering," JETP Lett. 15, 158-159 (1972).
  10. B. Ya Zeldovich, N. F. Pilipetskii, and V. V. Shkunov, Principles of phase conjugation (Springer Verlag, Berlin, 1985).
  11. Z. Zhu, D. J. Gauthier, Y. Okawachi, J. E. Sharping, A. L. Gaeta, R. W. Boyd, and A. E. Willner, "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]
  12. I. N. Bronshtein and K. A. Semendyayev. A guide book to mathematics (Verlag Harri Deutsch, Zurich, 1973).
  13. N. Kroll, "Excitation of hypersonic vibrations by means of photoelastic coupling of high-intensity light waves to elastic waves," J. Appl. Phys. 36, 34-43 (1965).
    [CrossRef]
  14. R. L. Carman, F. Shimizu, C. S. Wang, and N. Bloembergen, "Theory of Stokes pulse shapes in transient Raman scattering," Phys. Rev. A 2, 60-72 (1970).
    [CrossRef]
  15. S. A. Akhmanov, K. N. Drabovich, A. P. Sukhorukov, and A. S. Chirkin, "Stimulated Raman scattering in a field of ultrashort light pulses," Sov. Phys. JETP 32, 266-273 (1971).
  16. I. M. Bel’dyugin, V. F. Efimkov, S. I. Mikhailov, and I. G. Zubarev, "Amplification of weak Stokes signals in the transient regime of stimulated Brillouin scattering," J. Russ. Laser Res. 26, 1-12 (2005).
    [CrossRef]
  17. D. Pohl and W. Kaiser, "Time-resolved investigations of stimulated Brillouin scattering in transparent and absorbing media: Determination of phonon lifetimes," Phys. Rev. B 1, 31-43 (1970).
    [CrossRef]
  18. V. I. Kovalev and R. G. Harrison, "Threshold for stimulated Brillouin scattering in optical fiber," Opt. Express 15, 17625-17630 (2007).
    [CrossRef] [PubMed]
  19. D. A. Pinnow, "Guide lines for the selection of acoustooptic materials," IEEE J. Quantum Electron. QE-6, 223-238 (1970).
    [CrossRef]
  20. G. P. Agrawal, Nonlinear Fiber Optics, 2nd ed. (Acadamic, Boston, Mass., 1995).
  21. V. I. Kovalev and R. G. Harrison, "Observation of inhomogeneous spectral broadening of stimulated Brillouin scattering in an optical fiber," Phys. Rev. Lett. 85, 1879-1882 (2000).
    [CrossRef] [PubMed]
  22. V. I. Kovalev and R. G. Harrison, "Waveguide-induced inhomogeneous spectral broadening of stimulated Brillouin scattering in optical fiber," Opt. Lett. 27, 2022-2024 (2002).
    [CrossRef]
  23. V. P. Kalosha, L. Cheng, and X. Bao, "Slow and fast light via SBS in optical fibers for short pulses and broadband pump," Opt. Express 14, 12693-12703 (2006).
    [CrossRef] [PubMed]
  24. A. Sommerfeld, Optics (Lectures on Theoretical Physics 4), (Academic Press, 1954).
  25. V. I. Kovalev, R. G. Harrison, J. C. Knight, and N. E. Kotova, "Waveguide induced spectral bandwidth enhancement of slow light group index caused by stimulated Brillouin scattering in optical fiber," Laser Part. Beams 26, 319-322 (2008).

2008 (1)

V. I. Kovalev, R. G. Harrison, J. C. Knight, and N. E. Kotova, "Waveguide induced spectral bandwidth enhancement of slow light group index caused by stimulated Brillouin scattering in optical fiber," Laser Part. Beams 26, 319-322 (2008).

2007 (4)

2006 (3)

2005 (5)

K. Y. Song, M. G. Herraez, and L. Thevenaz, "Observation of pulse delaying and advancement in optical fibers using stimulated Brillouin scattering," Opt. Express 13, 82-88 (2005).
[CrossRef] [PubMed]

Z. Zhu, D. J. Gauthier, Y. Okawachi, J. E. Sharping, A. L. Gaeta, R. W. Boyd, and A. E. Willner, "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]

Y. Okawachi, M. S. Bigelow, J. E. Sharping, Z. Zu, 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]

D. J. Gauthier, "Slow light brings faster communications," Phys. World 18, 30-32 (2005).

I. M. Bel’dyugin, V. F. Efimkov, S. I. Mikhailov, and I. G. Zubarev, "Amplification of weak Stokes signals in the transient regime of stimulated Brillouin scattering," J. Russ. Laser Res. 26, 1-12 (2005).
[CrossRef]

2002 (1)

2000 (1)

V. I. Kovalev and R. G. Harrison, "Observation of inhomogeneous spectral broadening of stimulated Brillouin scattering in an optical fiber," Phys. Rev. Lett. 85, 1879-1882 (2000).
[CrossRef] [PubMed]

1972 (1)

B. Ya Zeldovich, "Time of establishment of stationary regime of stimulated light scattering," JETP Lett. 15, 158-159 (1972).

1971 (1)

S. A. Akhmanov, K. N. Drabovich, A. P. Sukhorukov, and A. S. Chirkin, "Stimulated Raman scattering in a field of ultrashort light pulses," Sov. Phys. JETP 32, 266-273 (1971).

1970 (3)

R. L. Carman, F. Shimizu, C. S. Wang, and N. Bloembergen, "Theory of Stokes pulse shapes in transient Raman scattering," Phys. Rev. A 2, 60-72 (1970).
[CrossRef]

D. Pohl and W. Kaiser, "Time-resolved investigations of stimulated Brillouin scattering in transparent and absorbing media: Determination of phonon lifetimes," Phys. Rev. B 1, 31-43 (1970).
[CrossRef]

D. A. Pinnow, "Guide lines for the selection of acoustooptic materials," IEEE J. Quantum Electron. QE-6, 223-238 (1970).
[CrossRef]

1965 (1)

N. Kroll, "Excitation of hypersonic vibrations by means of photoelastic coupling of high-intensity light waves to elastic waves," J. Appl. Phys. 36, 34-43 (1965).
[CrossRef]

Akhmanov, S. A.

S. A. Akhmanov, K. N. Drabovich, A. P. Sukhorukov, and A. S. Chirkin, "Stimulated Raman scattering in a field of ultrashort light pulses," Sov. Phys. JETP 32, 266-273 (1971).

Bao, X.

Bel’dyugin, I. M.

I. M. Bel’dyugin, V. F. Efimkov, S. I. Mikhailov, and I. G. Zubarev, "Amplification of weak Stokes signals in the transient regime of stimulated Brillouin scattering," J. Russ. Laser Res. 26, 1-12 (2005).
[CrossRef]

Bigelow, M. S.

Y. Okawachi, M. S. Bigelow, J. E. Sharping, Z. Zu, 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]

Bloembergen, N.

R. L. Carman, F. Shimizu, C. S. Wang, and N. Bloembergen, "Theory of Stokes pulse shapes in transient Raman scattering," Phys. Rev. A 2, 60-72 (1970).
[CrossRef]

Boyd, R. W.

Y. Okawachi, M. S. Bigelow, J. E. Sharping, Z. Zu, 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]

Z. Zhu, D. J. Gauthier, Y. Okawachi, J. E. Sharping, A. L. Gaeta, R. W. Boyd, and A. E. Willner, "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]

Carman, R. L.

R. L. Carman, F. Shimizu, C. S. Wang, and N. Bloembergen, "Theory of Stokes pulse shapes in transient Raman scattering," Phys. Rev. A 2, 60-72 (1970).
[CrossRef]

Cheng, L.

Chirkin, A. S.

S. A. Akhmanov, K. N. Drabovich, A. P. Sukhorukov, and A. S. Chirkin, "Stimulated Raman scattering in a field of ultrashort light pulses," Sov. Phys. JETP 32, 266-273 (1971).

Dong, Y.

Drabovich, K. N.

S. A. Akhmanov, K. N. Drabovich, A. P. Sukhorukov, and A. S. Chirkin, "Stimulated Raman scattering in a field of ultrashort light pulses," Sov. Phys. JETP 32, 266-273 (1971).

Efimkov, V. F.

I. M. Bel’dyugin, V. F. Efimkov, S. I. Mikhailov, and I. G. Zubarev, "Amplification of weak Stokes signals in the transient regime of stimulated Brillouin scattering," J. Russ. Laser Res. 26, 1-12 (2005).
[CrossRef]

Fazal, I.

Gaeta, A. L.

Y. Okawachi, M. S. Bigelow, J. E. Sharping, Z. Zu, 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]

Z. Zhu, D. J. Gauthier, Y. Okawachi, J. E. Sharping, A. L. Gaeta, R. W. Boyd, and A. E. Willner, "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]

Gauthier, D. J.

Z. Zhu, D. J. Gauthier, Y. Okawachi, J. E. Sharping, A. L. Gaeta, R. W. Boyd, and A. E. Willner, "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]

Y. Okawachi, M. S. Bigelow, J. E. Sharping, Z. Zu, 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]

D. J. Gauthier, "Slow light brings faster communications," Phys. World 18, 30-32 (2005).

Harrison, R. G.

V. I. Kovalev, R. G. Harrison, J. C. Knight, and N. E. Kotova, "Waveguide induced spectral bandwidth enhancement of slow light group index caused by stimulated Brillouin scattering in optical fiber," Laser Part. Beams 26, 319-322 (2008).

V. I. Kovalev and R. G. Harrison, "Threshold for stimulated Brillouin scattering in optical fiber," Opt. Express 15, 17625-17630 (2007).
[CrossRef] [PubMed]

V. I. Kovalev and R. G. Harrison, "Waveguide-induced inhomogeneous spectral broadening of stimulated Brillouin scattering in optical fiber," Opt. Lett. 27, 2022-2024 (2002).
[CrossRef]

V. I. Kovalev and R. G. Harrison, "Observation of inhomogeneous spectral broadening of stimulated Brillouin scattering in an optical fiber," Phys. Rev. Lett. 85, 1879-1882 (2000).
[CrossRef] [PubMed]

Herraez, M. G.

Hotate, K.

Kaiser, W.

D. Pohl and W. Kaiser, "Time-resolved investigations of stimulated Brillouin scattering in transparent and absorbing media: Determination of phonon lifetimes," Phys. Rev. B 1, 31-43 (1970).
[CrossRef]

Kalosha, V. P.

Knight, J. C.

V. I. Kovalev, R. G. Harrison, J. C. Knight, and N. E. Kotova, "Waveguide induced spectral bandwidth enhancement of slow light group index caused by stimulated Brillouin scattering in optical fiber," Laser Part. Beams 26, 319-322 (2008).

Kotova, N. E.

V. I. Kovalev, R. G. Harrison, J. C. Knight, and N. E. Kotova, "Waveguide induced spectral bandwidth enhancement of slow light group index caused by stimulated Brillouin scattering in optical fiber," Laser Part. Beams 26, 319-322 (2008).

Kovalev, V. I.

V. I. Kovalev, R. G. Harrison, J. C. Knight, and N. E. Kotova, "Waveguide induced spectral bandwidth enhancement of slow light group index caused by stimulated Brillouin scattering in optical fiber," Laser Part. Beams 26, 319-322 (2008).

V. I. Kovalev and R. G. Harrison, "Threshold for stimulated Brillouin scattering in optical fiber," Opt. Express 15, 17625-17630 (2007).
[CrossRef] [PubMed]

V. I. Kovalev and R. G. Harrison, "Waveguide-induced inhomogeneous spectral broadening of stimulated Brillouin scattering in optical fiber," Opt. Lett. 27, 2022-2024 (2002).
[CrossRef]

V. I. Kovalev and R. G. Harrison, "Observation of inhomogeneous spectral broadening of stimulated Brillouin scattering in an optical fiber," Phys. Rev. Lett. 85, 1879-1882 (2000).
[CrossRef] [PubMed]

Kroll, N.

N. Kroll, "Excitation of hypersonic vibrations by means of photoelastic coupling of high-intensity light waves to elastic waves," J. Appl. Phys. 36, 34-43 (1965).
[CrossRef]

Li, Q.

Lu, Z.

Mikhailov, S. I.

I. M. Bel’dyugin, V. F. Efimkov, S. I. Mikhailov, and I. G. Zubarev, "Amplification of weak Stokes signals in the transient regime of stimulated Brillouin scattering," J. Russ. Laser Res. 26, 1-12 (2005).
[CrossRef]

Okawachi, Y.

Y. Okawachi, M. S. Bigelow, J. E. Sharping, Z. Zu, 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]

Z. Zhu, D. J. Gauthier, Y. Okawachi, J. E. Sharping, A. L. Gaeta, R. W. Boyd, and A. E. Willner, "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]

Pinnow, D. A.

D. A. Pinnow, "Guide lines for the selection of acoustooptic materials," IEEE J. Quantum Electron. QE-6, 223-238 (1970).
[CrossRef]

Pohl, D.

D. Pohl and W. Kaiser, "Time-resolved investigations of stimulated Brillouin scattering in transparent and absorbing media: Determination of phonon lifetimes," Phys. Rev. B 1, 31-43 (1970).
[CrossRef]

Schweinsberg, A.

Y. Okawachi, M. S. Bigelow, J. E. Sharping, Z. Zu, 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. Zu, 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]

Z. Zhu, D. J. Gauthier, Y. Okawachi, J. E. Sharping, A. L. Gaeta, R. W. Boyd, and A. E. Willner, "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]

Shimizu, F.

R. L. Carman, F. Shimizu, C. S. Wang, and N. Bloembergen, "Theory of Stokes pulse shapes in transient Raman scattering," Phys. Rev. A 2, 60-72 (1970).
[CrossRef]

Song, K. Y.

Sukhorukov, A. P.

S. A. Akhmanov, K. N. Drabovich, A. P. Sukhorukov, and A. S. Chirkin, "Stimulated Raman scattering in a field of ultrashort light pulses," Sov. Phys. JETP 32, 266-273 (1971).

Thevenaz, L.

Wang, C. S.

R. L. Carman, F. Shimizu, C. S. Wang, and N. Bloembergen, "Theory of Stokes pulse shapes in transient Raman scattering," Phys. Rev. A 2, 60-72 (1970).
[CrossRef]

Willner, A. E.

Ya Zeldovich, B.

B. Ya Zeldovich, "Time of establishment of stationary regime of stimulated light scattering," JETP Lett. 15, 158-159 (1972).

Yan, L.

Zang, B.

Zhu, Z.

Zu, Z.

Y. Okawachi, M. S. Bigelow, J. E. Sharping, Z. Zu, 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]

Zubarev, I. G.

I. M. Bel’dyugin, V. F. Efimkov, S. I. Mikhailov, and I. G. Zubarev, "Amplification of weak Stokes signals in the transient regime of stimulated Brillouin scattering," J. Russ. Laser Res. 26, 1-12 (2005).
[CrossRef]

IEEE J. Quantum Electron. (1)

D. A. Pinnow, "Guide lines for the selection of acoustooptic materials," IEEE J. Quantum Electron. QE-6, 223-238 (1970).
[CrossRef]

J. Appl. Phys. (1)

N. Kroll, "Excitation of hypersonic vibrations by means of photoelastic coupling of high-intensity light waves to elastic waves," J. Appl. Phys. 36, 34-43 (1965).
[CrossRef]

J. Opt. Soc. Am. B (1)

J. Russ. Laser Res. (1)

I. M. Bel’dyugin, V. F. Efimkov, S. I. Mikhailov, and I. G. Zubarev, "Amplification of weak Stokes signals in the transient regime of stimulated Brillouin scattering," J. Russ. Laser Res. 26, 1-12 (2005).
[CrossRef]

JETP Lett. (1)

B. Ya Zeldovich, "Time of establishment of stationary regime of stimulated light scattering," JETP Lett. 15, 158-159 (1972).

Laser Part. Beams (1)

V. I. Kovalev, R. G. Harrison, J. C. Knight, and N. E. Kotova, "Waveguide induced spectral bandwidth enhancement of slow light group index caused by stimulated Brillouin scattering in optical fiber," Laser Part. Beams 26, 319-322 (2008).

Opt. Express (6)

Opt. Lett. (3)

Phys. Rev. A (1)

R. L. Carman, F. Shimizu, C. S. Wang, and N. Bloembergen, "Theory of Stokes pulse shapes in transient Raman scattering," Phys. Rev. A 2, 60-72 (1970).
[CrossRef]

Phys. Rev. B (1)

D. Pohl and W. Kaiser, "Time-resolved investigations of stimulated Brillouin scattering in transparent and absorbing media: Determination of phonon lifetimes," Phys. Rev. B 1, 31-43 (1970).
[CrossRef]

Phys. Rev. Lett. (2)

Y. Okawachi, M. S. Bigelow, J. E. Sharping, Z. Zu, 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]

V. I. Kovalev and R. G. Harrison, "Observation of inhomogeneous spectral broadening of stimulated Brillouin scattering in an optical fiber," Phys. Rev. Lett. 85, 1879-1882 (2000).
[CrossRef] [PubMed]

Phys. World (1)

D. J. Gauthier, "Slow light brings faster communications," Phys. World 18, 30-32 (2005).

Sov. Phys. JETP (1)

S. A. Akhmanov, K. N. Drabovich, A. P. Sukhorukov, and A. S. Chirkin, "Stimulated Raman scattering in a field of ultrashort light pulses," Sov. Phys. JETP 32, 266-273 (1971).

Other (4)

I. N. Bronshtein and K. A. Semendyayev. A guide book to mathematics (Verlag Harri Deutsch, Zurich, 1973).

G. P. Agrawal, Nonlinear Fiber Optics, 2nd ed. (Acadamic, Boston, Mass., 1995).

B. Ya Zeldovich, N. F. Pilipetskii, and V. V. Shkunov, Principles of phase conjugation (Springer Verlag, Berlin, 1985).

A. Sommerfeld, Optics (Lectures on Theoretical Physics 4), (Academic Press, 1954).

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Figures (5)

Fig. 1.
Fig. 1.

Output Stokes pulse shapes for a) tp = 200 ns (≫τ ) and G = 0 (1), 1(0.42), 4(0.026), 8(0.0006), and 12(0.000012) and b) for tp = 18 ns (=τ ) and G = 0(1), 1(0.9), 2(0.6), 4(0.2), 8(0.09), and 12(0.00026), where numbers in brackets are the amplitude magnification factors. The numbers on curves are Gs.

Fig. 2.
Fig. 2.

Output Stokes pulse shapes for a) tp = 4 ns (<τ) and G = 0(1), 2(1), 4(1), 6(1), 8(0.2), and 12(0.007), and b) for tp = 0.5 ns (≪τ) and G = 0(1), 4(1), 8(1), and 12(1 at the first peak and 0.3 at the tail). LHS of b) is temporally stretched to show profiles.

Fig. 3.
Fig. 3.

Output Stokes pulse a) delay, b) broadening factor, and c) effective exponential gain at peak of output pulse vs gain G for pulse durations tp = 200 (dashed), 18 (dotted), 4 (thick solid in the main graph and in the insert), and 0.5 ns (dashed in the insert). Thin solid lines in a) and c) are ΔTd = 9G ns and Gef = G dependencies respectively.

Fig. 4.
Fig. 4.

(a) Dynamics and (b) spectra of the normalised acoustic wave amplitude (solid lines) for Stokes pulses of the shape given by Eq. (10) (dashed lines) with tp = 200(1), 18(2), 4(3) and 0.5 ns(4), τ= 18 ns. The dotted line 5 in (b) is the Lorentzian-shaped spectrum with τ= 18 ns. Note, curves in (b) show half spectra of the pulses at LHS and of corresponding to them medium’s response at RHS.

Fig. 5.
Fig. 5.

Relation between the spectra of a Stokes pulse and of the group index induced by this pulse for tp = 200 a), 18 b), 4 c), and 0.5 ns d). Horizontal scales are in GHz.

Equations (11)

Equations on this page are rendered with MathJax. Learn more.

E S z + n c E S t = i 4 π ω S 2 cn P S ( z , t ) ,
P S ( z , t ) = Δ ε ( z , t ) 4 π E P = 1 4 π ε ρ ( ρ ' ( z , t ) ) * E P ,
ρ ' t + ( Γ 0 2 + Ω ) ρ ' = i ρ 0 ε ρ Ω B 8 π v 2 E p E S * ( z , t ) .
E S z = i ω S 2 cn ε ρ ( ρ ' ( t ' ) ) * E p ,
ρ ' t ' + 1 τ ρ ' = i ρ 0 ε ρ Ω B 8 π v 2 E p E S * ( t ' ) .
E S ( z , t ' ) = E S 0 ( t ' ) + g I p z τ 0 t ' ( e t ' ϑ τ ) I 1 ( 2 g I p z t ' ϑ τ ) 2 g I p z t ' ϑ τ E S 0 ( ϑ )
ρ ' ( t ' ) = i ρ 0 ε ρ Ω B 8 πτ v 2 E p 0 t ' ( e t ' ϑ τ ) I 0 ( 2 g I p z t ' ϑ τ ) E S 0 * ( ϑ )
g = 10 7 ω S 2 ρ 0 τ 4 n c 3 v ( ε ρ ) 2 [ cm / W ] .
I S ( z = 0 , t ) = E S ( z = 0 , t ) 2 = I S 0 ( 3.5 t / t p ) 2 e 3.5 t / t p ,
ρ ' ( t ) = A { 2 ( 2 b τ ) 2 [ 2 τb ( e t τ e t 2 b ) + ( 2 b τ ) t e t 2 b ] } ,
ρ ' ( ω ) = A 2 π 4 τb ( 2 b τ ) 2 [ t 1 + iτω 1 + ( τω ) 2 2 b 1 + i 2 1 + ( 2 ) 2 ] + 2 π 8 b 2 ( 2 b τ ) [ 1 + i 4 ( 2 ) 2 [ 1 + ( 2 ) 2 ] 2 ] .

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