Abstract

An analytical solution of the basic coupled stimulated Brillouin scattering (SBS) equations is obtained in the Fourier domain, which describes the spectral evolution of the medium’s response, and that of a Stokes pulse injected into this medium, when SBS is excited by non-monochromatic CW pump radiation. It shows that spectral broadening of pump radiation by any reasonable amount results in only minute increase of the spectral width of the resonant material’s excitation in SBS, and cannot be effective in modifying the natural group index of the medium for the Stokes pulse.

© 2009 OSA

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. D. J. Gauthier, “Slow light brings faster communications,” Phys. World 18, 30–32 (2005).
  2. K. Y. Song, M. G. Herráez, and L. Thévenaz, “Gain-assisted pulse advancement using single and double Brillouin gain peaks in optical fibers,” Opt. Express 13(24), 9758–9765 (2005).
    [PubMed]
  3. M. D. Stenner, M. A. Neifeld, Z. Zhu, A. M. C. Dawes, and D. J. Gauthier, “Distortion management in slow-light pulse delay,” Opt. Express 13(25), 9995–10002 (2005).
    [PubMed]
  4. M. G. Herráez, K. Y. Song, and L. Thévenaz, “Arbitrary-bandwidth Brillouin slow light in optical fibers,” Opt. Express 14(4), 1395–1400 (2006).
  5. A. Minardo, R. Bernini, and L. Zeni, “Low distortion Brillouin slow light in optical fibers using AM modulation,” Opt. Express 14(13), 5866–5876 (2006).
    [PubMed]
  6. E. Shumakher, N. Orbach, A. Nevet, D. Dahan, and G. Eisenstein, “On the balance between delay, bandwidth and signal distortion in slow light systems based on stimulated Brillouin scattering in optical fibers,” Opt. Express 14(13), 5877–5884 (2006).
    [PubMed]
  7. Z. Zhu and D. J. Gauthier, “Nearly transparent SBS slow light in an optical fiber,” Opt. Express 14(16), 7238–7245 (2006).
    [PubMed]
  8. A. Zadok, A. Eyal, and M. Tur, “Extended delay of broadband signals in stimulated Brillouin scattering slow light using synthesized pump chirp,” Opt. Express 14(19), 8498–8505 (2006).
    [PubMed]
  9. S. Chin, M. G. Herraez, and L. Thévenaz, “Zero-gain slow & fast light propagation in an optical fiber,” Opt. Express 14(22), 10684–10692 (2006).
    [PubMed]
  10. T. Schneider, M. Junker, and K.-U. Lauterbach, “Potential ultra wide slow-light bandwidth enhancement,” Opt. Express 14(23), 11082–11087 (2006).
    [PubMed]
  11. V. P. Kalosha, L. Chen, and X. Bao, “Slow and fast light via SBS in optical fibers for short pulses and broadband pump,” Opt. Express 14(26), 12693–12703 (2006).
    [PubMed]
  12. Z. Zhu, A. M. C. Dawes, D. J. Gauthier, L. Zhang, and A. E. Willner, “Broadband SBS slow light in an optical fiber,” J. Lightwave Technol. 25(1), 201–206 (2007).
  13. K. Y. Song and K. Hotate, “25 GHz bandwidth Brillouin slow light in optical fibers,” Opt. Lett. 32(3), 217–219 (2007).
    [PubMed]
  14. Z. Lu, Y. Dong, and Q. Li, “Slow light in multi-line Brillouin gain spectrum,” Opt. Express 15(4), 1871–1877 (2007).
    [PubMed]
  15. B. Zhang, L. Yan, I. Fazal, L. Zhang, A. E. Willner, Z. Zhu, and D. J. Gauthier, “Slow light on Gbit/s differential-phase-shift-keying signals,” Opt. Express 15(4), 1878–1883 (2007).
    [PubMed]
  16. L. Yi, L. Zhan, W. Hu, and Y. Xia, “Delay of broadband signals using slow light in stimulated Brillouin scattering with phase-modulated pump,” IEEE Photon. Technol. Lett. 19(8), 619–621 (2007).
  17. B. Zhang, L. Zhang, L.-S. Yan, I. Fazal, J.-Y. Yang, and A. E. Willner, “Continuously-tunable, bit-rate variable OTDM using broadband SBS slow-light delay line,” Opt. Express 15(13), 8317–8322 (2007).
    [PubMed]
  18. Z. Shi, R. Pant, Z. Zhu, M. D. Stenner, M. A. Neifeld, D. J. Gauthier, and R. W. Boyd, “Design of a tunable time-delay element using multiple gain lines for increased fractional delay with high data fidelity,” Opt. Lett. 32(14), 1986–1988 (2007).
    [PubMed]
  19. R. Pant, M. D. Stenner, M. A. Neifeld, and D. J. Gauthier, “Optimal pump profile designs for broadband SBS slow-light systems,” Opt. Express 16(4), 2764–2777 (2008).
    [PubMed]
  20. L. Ren and Y. Tomita, “Reducing group-velocity-dispersion-dependent broadening of stimulated Brillouin scattering slow light in an optical fiber by use of a single pump laser,” J. Opt. Soc. Am. B 25(5), 741–746 (2008).
  21. T. Sakamoto, T. Yamamoto, K. Shiraki, and T. Kurashima, “Low distortion slow light in flat Brillouin gain spectrum by using optical frequency comb,” Opt. Express 16(11), 8026–8032 (2008).
    [PubMed]
  22. S. Wang, L. Ren, Y. Liu, and Y. Tomita, “Zero-broadening SBS slow light propagation in an optical fiber using two broadband pump beams,” Opt. Express 16(11), 8067–8076 (2008).
    [PubMed]
  23. T. Schneider, R. Henker, K.-U. Lauterbach, and M. Junker, “Distortion reduction in Slow Light systems based on stimulated Brillouin scattering,” Opt. Express 16(11), 8280–8285 (2008).
    [PubMed]
  24. A. Cheng, M. P. Fok, and C. Shu, “Wavelength-transparent, stimulated-Brillouin-scattering slow light using cross-gain-modulation-based wavelength converter and Brillouin fiber laser,” Opt. Lett. 33(22), 2596–2598 (2008).
    [PubMed]
  25. R. W. Boyd, and D. J. Gauthier, “Slow and fast light,” in Progress in Optics, 43, 497 (2002).
  26. B. Y. Zeldovich, N. F. Pilipetskii, and V. V. Shkunov, Principles of phase conjugation, Springer Verlag, Berlin, 1985.
  27. G. A. Korn, and T. M. Korn, Manual of mathematics, McGraw-Hill, New York, 1967.
  28. C. L. Tang, “Saturation and spectral characteristics of the Stokes emission in the stimulated Brillouin process,” J. Appl. Phys. 37(8), 2945–2955 (1966).
  29. N. Kroll, “Excitation of hypersonic vibrations by means of photoelastic coupling of high-intensity light waves to elastic waves,” J. Appl. Phys. 36(1), 34–43 (1965).
  30. R. L. Carman, F. Shimizu, C. S. Wang, and N. Bloembergen, “Theory of Stokes pulse shapes in transient Raman scattering,” Phys. Rev. A 2(1), 60–72 (1970).
  31. 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).
  32. S. A. Akhmanov, Yu. E. Dyakov, and A. S. Chirkin, Introduction to Statistical Radiophysics and Optics, Berlin, Springer, 1988.
  33. V. I. Kovalev, N. E. Kotova, and R. G. Harrison, “Effect of acoustic wave inertia and its implication to slow light via stimulated Brillouin scattering in an extended medium,” Opt. Express 17(4), 2826–2833 (2009).
    [PubMed]

2009

2008

2007

2006

2005

1971

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

R. L. Carman, F. Shimizu, C. S. Wang, and N. Bloembergen, “Theory of Stokes pulse shapes in transient Raman scattering,” Phys. Rev. A 2(1), 60–72 (1970).

1966

C. L. Tang, “Saturation and spectral characteristics of the Stokes emission in the stimulated Brillouin process,” J. Appl. Phys. 37(8), 2945–2955 (1966).

1965

N. Kroll, “Excitation of hypersonic vibrations by means of photoelastic coupling of high-intensity light waves to elastic waves,” J. Appl. Phys. 36(1), 34–43 (1965).

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.

Bernini, R.

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(1), 60–72 (1970).

Boyd, R. W.

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(1), 60–72 (1970).

Chen, L.

Cheng, A.

Chin, S.

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).

Dahan, D.

Dawes, A. M. C.

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).

Eisenstein, G.

Eyal, A.

Fazal, I.

Fok, M. P.

Gauthier, D. J.

Harrison, R. G.

Henker, R.

Herraez, M. G.

Herráez, M. G.

Hotate, K.

Hu, W.

L. Yi, L. Zhan, W. Hu, and Y. Xia, “Delay of broadband signals using slow light in stimulated Brillouin scattering with phase-modulated pump,” IEEE Photon. Technol. Lett. 19(8), 619–621 (2007).

Junker, M.

Kalosha, V. P.

Kotova, N. E.

Kovalev, V. I.

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(1), 34–43 (1965).

Kurashima, T.

Lauterbach, K.-U.

Li, Q.

Liu, Y.

Lu, Z.

Minardo, A.

Neifeld, M. A.

Nevet, A.

Orbach, N.

Pant, R.

Ren, L.

Sakamoto, T.

Schneider, T.

Shi, Z.

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(1), 60–72 (1970).

Shiraki, K.

Shu, C.

Shumakher, E.

Song, K. Y.

Stenner, M. D.

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).

Tang, C. L.

C. L. Tang, “Saturation and spectral characteristics of the Stokes emission in the stimulated Brillouin process,” J. Appl. Phys. 37(8), 2945–2955 (1966).

Thévenaz, L.

Tomita, Y.

Tur, M.

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(1), 60–72 (1970).

Wang, S.

Willner, A. E.

Xia, Y.

L. Yi, L. Zhan, W. Hu, and Y. Xia, “Delay of broadband signals using slow light in stimulated Brillouin scattering with phase-modulated pump,” IEEE Photon. Technol. Lett. 19(8), 619–621 (2007).

Yamamoto, T.

Yan, L.

Yan, L.-S.

Yang, J.-Y.

Yi, L.

L. Yi, L. Zhan, W. Hu, and Y. Xia, “Delay of broadband signals using slow light in stimulated Brillouin scattering with phase-modulated pump,” IEEE Photon. Technol. Lett. 19(8), 619–621 (2007).

Zadok, A.

Zeni, L.

Zhan, L.

L. Yi, L. Zhan, W. Hu, and Y. Xia, “Delay of broadband signals using slow light in stimulated Brillouin scattering with phase-modulated pump,” IEEE Photon. Technol. Lett. 19(8), 619–621 (2007).

Zhang, B.

Zhang, L.

Zhu, Z.

IEEE Photon. Technol. Lett.

L. Yi, L. Zhan, W. Hu, and Y. Xia, “Delay of broadband signals using slow light in stimulated Brillouin scattering with phase-modulated pump,” IEEE Photon. Technol. Lett. 19(8), 619–621 (2007).

J. Appl. Phys.

C. L. Tang, “Saturation and spectral characteristics of the Stokes emission in the stimulated Brillouin process,” J. Appl. Phys. 37(8), 2945–2955 (1966).

N. Kroll, “Excitation of hypersonic vibrations by means of photoelastic coupling of high-intensity light waves to elastic waves,” J. Appl. Phys. 36(1), 34–43 (1965).

J. Lightwave Technol.

J. Opt. Soc. Am. B

Opt. Express

T. Sakamoto, T. Yamamoto, K. Shiraki, and T. Kurashima, “Low distortion slow light in flat Brillouin gain spectrum by using optical frequency comb,” Opt. Express 16(11), 8026–8032 (2008).
[PubMed]

S. Wang, L. Ren, Y. Liu, and Y. Tomita, “Zero-broadening SBS slow light propagation in an optical fiber using two broadband pump beams,” Opt. Express 16(11), 8067–8076 (2008).
[PubMed]

T. Schneider, R. Henker, K.-U. Lauterbach, and M. Junker, “Distortion reduction in Slow Light systems based on stimulated Brillouin scattering,” Opt. Express 16(11), 8280–8285 (2008).
[PubMed]

V. I. Kovalev, N. E. Kotova, and R. G. Harrison, “Effect of acoustic wave inertia and its implication to slow light via stimulated Brillouin scattering in an extended medium,” Opt. Express 17(4), 2826–2833 (2009).
[PubMed]

Z. Lu, Y. Dong, and Q. Li, “Slow light in multi-line Brillouin gain spectrum,” Opt. Express 15(4), 1871–1877 (2007).
[PubMed]

B. Zhang, L. Yan, I. Fazal, L. Zhang, A. E. Willner, Z. Zhu, and D. J. Gauthier, “Slow light on Gbit/s differential-phase-shift-keying signals,” Opt. Express 15(4), 1878–1883 (2007).
[PubMed]

B. Zhang, L. Zhang, L.-S. Yan, I. Fazal, J.-Y. Yang, and A. E. Willner, “Continuously-tunable, bit-rate variable OTDM using broadband SBS slow-light delay line,” Opt. Express 15(13), 8317–8322 (2007).
[PubMed]

R. Pant, M. D. Stenner, M. A. Neifeld, and D. J. Gauthier, “Optimal pump profile designs for broadband SBS slow-light systems,” Opt. Express 16(4), 2764–2777 (2008).
[PubMed]

K. Y. Song, M. G. Herráez, and L. Thévenaz, “Gain-assisted pulse advancement using single and double Brillouin gain peaks in optical fibers,” Opt. Express 13(24), 9758–9765 (2005).
[PubMed]

M. D. Stenner, M. A. Neifeld, Z. Zhu, A. M. C. Dawes, and D. J. Gauthier, “Distortion management in slow-light pulse delay,” Opt. Express 13(25), 9995–10002 (2005).
[PubMed]

M. G. Herráez, K. Y. Song, and L. Thévenaz, “Arbitrary-bandwidth Brillouin slow light in optical fibers,” Opt. Express 14(4), 1395–1400 (2006).

A. Minardo, R. Bernini, and L. Zeni, “Low distortion Brillouin slow light in optical fibers using AM modulation,” Opt. Express 14(13), 5866–5876 (2006).
[PubMed]

E. Shumakher, N. Orbach, A. Nevet, D. Dahan, and G. Eisenstein, “On the balance between delay, bandwidth and signal distortion in slow light systems based on stimulated Brillouin scattering in optical fibers,” Opt. Express 14(13), 5877–5884 (2006).
[PubMed]

Z. Zhu and D. J. Gauthier, “Nearly transparent SBS slow light in an optical fiber,” Opt. Express 14(16), 7238–7245 (2006).
[PubMed]

A. Zadok, A. Eyal, and M. Tur, “Extended delay of broadband signals in stimulated Brillouin scattering slow light using synthesized pump chirp,” Opt. Express 14(19), 8498–8505 (2006).
[PubMed]

S. Chin, M. G. Herraez, and L. Thévenaz, “Zero-gain slow & fast light propagation in an optical fiber,” Opt. Express 14(22), 10684–10692 (2006).
[PubMed]

T. Schneider, M. Junker, and K.-U. Lauterbach, “Potential ultra wide slow-light bandwidth enhancement,” Opt. Express 14(23), 11082–11087 (2006).
[PubMed]

V. P. Kalosha, L. Chen, and X. Bao, “Slow and fast light via SBS in optical fibers for short pulses and broadband pump,” Opt. Express 14(26), 12693–12703 (2006).
[PubMed]

Opt. Lett.

Phys. Rev. A

R. L. Carman, F. Shimizu, C. S. Wang, and N. Bloembergen, “Theory of Stokes pulse shapes in transient Raman scattering,” Phys. Rev. A 2(1), 60–72 (1970).

Phys. World

D. J. Gauthier, “Slow light brings faster communications,” Phys. World 18, 30–32 (2005).

Sov. Phys. JETP

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

S. A. Akhmanov, Yu. E. Dyakov, and A. S. Chirkin, Introduction to Statistical Radiophysics and Optics, Berlin, Springer, 1988.

R. W. Boyd, and D. J. Gauthier, “Slow and fast light,” in Progress in Optics, 43, 497 (2002).

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

G. A. Korn, and T. M. Korn, Manual of mathematics, McGraw-Hill, New York, 1967.

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (1)

Fig. 1
Fig. 1

(a) LHS and RHS halves of the (symmetrical) spectra of |Fρ (ω)| (dashed) and of |ρ˜(ω)| (solid) respectively for the widths of Fρ (ω) 0.02(1), 0.2(2), 2(3) and 20(4) GHz, when ΓB = 0.2 GHz and δΩ = 0. The dotted line 5 is the Lorentzian with ΓB = 0.2 GHz; (b) spectra of |ρ˜(ω)| for the same spectral widths of Fρ (ω) when δΩ = 0.1 GHz.

Equations (18)

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

2δρt2vs22δρA2δρt=ρ0ερ116π2|Ε(z,t)|2,
2δρt2+ΩB2δρ+ΓB2δρt=ρ0ερ18π2z2[Εp(z,t)ΕS(z,t)].
2ΕSz2εc22ΕSt2=1c2ερ2t2[δρ(z,t)Εp(z,t)].
ρt+(ΓB2+iδΩ)ρ=iρ0ερΩB8πvs2Ep(t)ES*(z,t),
ESz+ncESt=iωS2cnερρ*(z,t)Ep(t).
S[f(t)]=f(t)eiωtdt,   S[ddtf(t)]=iωS[f(t)],   and   S[f1(t)f2(t)]=12πF1(ν)F2(ων)dν,
(ΓB2i(ω+δΩ))ρ˜*(z,ω)=iρ0ερΩB8πvs212πE˜p'*(ν)E˜S'(z,ων)dν,
dE˜S(z,ω)dz+iωncE˜S(z,ω)=iωS2cnερ12πE˜p(ν)ρ˜*(z,ων)dν.
ρ˜*(z,ω)=iρ0ερΩB8πvs2Fρ(z,ω)(ΓB/2i(ω+δΩ)),
Fρ(z,ω)=12πE˜p*(ν)E˜S(z,ων)dν
|E˜S(z,ω)|=|eiωncz[E˜S(0,ω)+iωS2ncερ0zFE(x,ω)eiωncxdx]|,
FE(z,ω)=12πE˜p(ν)ρ˜*(z,ων)dν
ES(z)=ES(0)eg0|EpEp*|z2(1i2δΩΓB1),
dES(z)dz=[g0|EpEp*|2(1i2δΩΓB1)]ES(z).
dES(z)dz=[g0(Ep'*ES'(z))2(1i2δΩΓB1)]Ep.
|ρ˜(ω)|=ρ0ερΩB8πvs2|Fρ(ω)|ΓB2/4+(ω+δΩ)2.
ng(ω')=ρ0(ερ)2ΩBIpIS16πn0vs2ω'(ω'ΩB)δωρ2[ΓB2/2+2(ω'ΩB)2+δωρ2][ΓB2/2+(ω'ΩB)2]32e(ω'ΩB)2δωρ2.
ng(ωS)=2BωSδωρ2eωS2/δωρ2,

Metrics