Abstract

The electrostrictive contribution to the nonlinear refractive index is investigated by use of frequency-dependent cross-phase modulation with a weak unpolarized cw probe wave and a harmonically modulated pump copropagating in optical fibers. Self-delayed homodyne detection is used to measure the amplitude of the sidebands imposed upon the probe wave as a function of pump intensity for pump modulation frequencies from 10  MHz to 1  GHz. The ratio of the electrostrictive nonlinear coefficient to the cross-phase-modulation Kerr coefficient for unpolarized light is measured to be 1.58:1 for a standard step-index single-mode fiber and 0.41:1 for dispersion-shifted fibers, indicating a larger electrostrictive response in silica fibers than previously expected.

© 1997 Optical Society of America

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References

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  1. G. P. Agrawal, Nonlinear Fiber Optics, 2nd ed. (Academic, Boston, Mass., 1995).
  2. R. M. Shelby, M. D. Levenson, and P. W. Bayer, Phys. Rev. B 314, 5244 (1985).
    [CrossRef]
  3. K. Smith and L. F. Mollenauer, Opt. Lett. 14, 1284 (1989).
    [CrossRef] [PubMed]
  4. E. M. Dianov, A. V. Luchnikov, A. N. Pilipetskii, and A. M. Prokhorov, Appl. Phys. B 54, 175 (1992).
    [CrossRef]
  5. P. D. Townsend, A. J. Alistair, P. J. Hardman, and K. J. Blow, Opt. Lett. 21, 333 (1996).
    [CrossRef] [PubMed]
  6. P. J. Hardman, P. D. Townsend, A. J. Poustie, and K. J. Blow, Opt. Lett. 21, 393 (1996).
    [CrossRef] [PubMed]
  7. T. Kato, Y. Suetsugu, M. Takagi, E. Sasaoka, and M. Nishimura, Opt. Lett. 20, 988 (1995).
    [CrossRef]
  8. E. L. Buckland and R. W. Boyd, Opt. Lett. 21, 1117 (1996).
    [CrossRef] [PubMed]
  9. R. W. Boyd, Nonlinear Optics (Academic, Boston, Mass., 1992).
  10. A. N. Pilipetskii, A. V. Luchnikov, and A. M. Prokhorov, Sov. Lightwave Commun. 3, 29 (1993).
  11. T. Okoshi, K. Kikuchi, and A. Nakayama, Electron. Lett. 16, 630 (1980).
    [CrossRef]
  12. M. Nazarathy, W. V. Sorin, D. M. Baney, and S. A. Newton, J. Lightwave Technol. 7, 1083 (1989).
    [CrossRef]
  13. In the absence of electrostriction, one must multiply the values of n2 obtained in this experiment by 1/2×3/2×8/9=2/3 to compare to self-phase-modulation values obtained by polarized light in randomly birefringent fibers.8
  14. A. Boskovic, S. V. Chernikov, J. R. Taylor, I. Gruner-Nielsen, and O. A. Levring, in Conference on Lasers and Electro-Optics, Vol. 9 of 1996 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1996), paper CMA7.

1996 (3)

1995 (1)

1993 (1)

A. N. Pilipetskii, A. V. Luchnikov, and A. M. Prokhorov, Sov. Lightwave Commun. 3, 29 (1993).

1992 (1)

E. M. Dianov, A. V. Luchnikov, A. N. Pilipetskii, and A. M. Prokhorov, Appl. Phys. B 54, 175 (1992).
[CrossRef]

1989 (2)

M. Nazarathy, W. V. Sorin, D. M. Baney, and S. A. Newton, J. Lightwave Technol. 7, 1083 (1989).
[CrossRef]

K. Smith and L. F. Mollenauer, Opt. Lett. 14, 1284 (1989).
[CrossRef] [PubMed]

1985 (1)

R. M. Shelby, M. D. Levenson, and P. W. Bayer, Phys. Rev. B 314, 5244 (1985).
[CrossRef]

1980 (1)

T. Okoshi, K. Kikuchi, and A. Nakayama, Electron. Lett. 16, 630 (1980).
[CrossRef]

Agrawal, G. P.

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

Alistair, A. J.

Baney, D. M.

M. Nazarathy, W. V. Sorin, D. M. Baney, and S. A. Newton, J. Lightwave Technol. 7, 1083 (1989).
[CrossRef]

Bayer, P. W.

R. M. Shelby, M. D. Levenson, and P. W. Bayer, Phys. Rev. B 314, 5244 (1985).
[CrossRef]

Blow, K. J.

Boskovic, A.

A. Boskovic, S. V. Chernikov, J. R. Taylor, I. Gruner-Nielsen, and O. A. Levring, in Conference on Lasers and Electro-Optics, Vol. 9 of 1996 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1996), paper CMA7.

Boyd, R. W.

E. L. Buckland and R. W. Boyd, Opt. Lett. 21, 1117 (1996).
[CrossRef] [PubMed]

R. W. Boyd, Nonlinear Optics (Academic, Boston, Mass., 1992).

Buckland, E. L.

Chernikov, S. V.

A. Boskovic, S. V. Chernikov, J. R. Taylor, I. Gruner-Nielsen, and O. A. Levring, in Conference on Lasers and Electro-Optics, Vol. 9 of 1996 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1996), paper CMA7.

Dianov, E. M.

E. M. Dianov, A. V. Luchnikov, A. N. Pilipetskii, and A. M. Prokhorov, Appl. Phys. B 54, 175 (1992).
[CrossRef]

Gruner-Nielsen, I.

A. Boskovic, S. V. Chernikov, J. R. Taylor, I. Gruner-Nielsen, and O. A. Levring, in Conference on Lasers and Electro-Optics, Vol. 9 of 1996 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1996), paper CMA7.

Hardman, P. J.

Kato, T.

Kikuchi, K.

T. Okoshi, K. Kikuchi, and A. Nakayama, Electron. Lett. 16, 630 (1980).
[CrossRef]

Levenson, M. D.

R. M. Shelby, M. D. Levenson, and P. W. Bayer, Phys. Rev. B 314, 5244 (1985).
[CrossRef]

Levring, O. A.

A. Boskovic, S. V. Chernikov, J. R. Taylor, I. Gruner-Nielsen, and O. A. Levring, in Conference on Lasers and Electro-Optics, Vol. 9 of 1996 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1996), paper CMA7.

Luchnikov, A. V.

A. N. Pilipetskii, A. V. Luchnikov, and A. M. Prokhorov, Sov. Lightwave Commun. 3, 29 (1993).

E. M. Dianov, A. V. Luchnikov, A. N. Pilipetskii, and A. M. Prokhorov, Appl. Phys. B 54, 175 (1992).
[CrossRef]

Mollenauer, L. F.

Nakayama, A.

T. Okoshi, K. Kikuchi, and A. Nakayama, Electron. Lett. 16, 630 (1980).
[CrossRef]

Nazarathy, M.

M. Nazarathy, W. V. Sorin, D. M. Baney, and S. A. Newton, J. Lightwave Technol. 7, 1083 (1989).
[CrossRef]

Newton, S. A.

M. Nazarathy, W. V. Sorin, D. M. Baney, and S. A. Newton, J. Lightwave Technol. 7, 1083 (1989).
[CrossRef]

Nishimura, M.

Okoshi, T.

T. Okoshi, K. Kikuchi, and A. Nakayama, Electron. Lett. 16, 630 (1980).
[CrossRef]

Pilipetskii, A. N.

A. N. Pilipetskii, A. V. Luchnikov, and A. M. Prokhorov, Sov. Lightwave Commun. 3, 29 (1993).

E. M. Dianov, A. V. Luchnikov, A. N. Pilipetskii, and A. M. Prokhorov, Appl. Phys. B 54, 175 (1992).
[CrossRef]

Poustie, A. J.

Prokhorov, A. M.

A. N. Pilipetskii, A. V. Luchnikov, and A. M. Prokhorov, Sov. Lightwave Commun. 3, 29 (1993).

E. M. Dianov, A. V. Luchnikov, A. N. Pilipetskii, and A. M. Prokhorov, Appl. Phys. B 54, 175 (1992).
[CrossRef]

Sasaoka, E.

Shelby, R. M.

R. M. Shelby, M. D. Levenson, and P. W. Bayer, Phys. Rev. B 314, 5244 (1985).
[CrossRef]

Smith, K.

Sorin, W. V.

M. Nazarathy, W. V. Sorin, D. M. Baney, and S. A. Newton, J. Lightwave Technol. 7, 1083 (1989).
[CrossRef]

Suetsugu, Y.

Takagi, M.

Taylor, J. R.

A. Boskovic, S. V. Chernikov, J. R. Taylor, I. Gruner-Nielsen, and O. A. Levring, in Conference on Lasers and Electro-Optics, Vol. 9 of 1996 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1996), paper CMA7.

Townsend, P. D.

Appl. Phys. B (1)

E. M. Dianov, A. V. Luchnikov, A. N. Pilipetskii, and A. M. Prokhorov, Appl. Phys. B 54, 175 (1992).
[CrossRef]

Electron. Lett. (1)

T. Okoshi, K. Kikuchi, and A. Nakayama, Electron. Lett. 16, 630 (1980).
[CrossRef]

J. Lightwave Technol. (1)

M. Nazarathy, W. V. Sorin, D. M. Baney, and S. A. Newton, J. Lightwave Technol. 7, 1083 (1989).
[CrossRef]

Opt. Lett. (5)

Phys. Rev. B (1)

R. M. Shelby, M. D. Levenson, and P. W. Bayer, Phys. Rev. B 314, 5244 (1985).
[CrossRef]

Sov. Lightwave Commun. (1)

A. N. Pilipetskii, A. V. Luchnikov, and A. M. Prokhorov, Sov. Lightwave Commun. 3, 29 (1993).

Other (4)

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

R. W. Boyd, Nonlinear Optics (Academic, Boston, Mass., 1992).

In the absence of electrostriction, one must multiply the values of n2 obtained in this experiment by 1/2×3/2×8/9=2/3 to compare to self-phase-modulation values obtained by polarized light in randomly birefringent fibers.8

A. Boskovic, S. V. Chernikov, J. R. Taylor, I. Gruner-Nielsen, and O. A. Levring, in Conference on Lasers and Electro-Optics, Vol. 9 of 1996 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1996), paper CMA7.

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Figures (3)

Fig. 1
Fig. 1

Theoretical predictions of the electrostrictive frequency response for a fiber with a mode (intensity) radius of 3  µm. The solid curve includes the influence of acoustic reflections structurally damped by variations in the outer cladding diameter. The dashed curve is the intrinsic fiber response, equivalent to 100% damping of acoustic reflections.

Fig. 2
Fig. 2

Experimental configuration. SLM, single-longitudinal-mode laser; EDFA, erbium-doped fiber amplifier; WDM’s; wavelength-division multiplexers.

Fig. 3
Fig. 3

Measured nonlinear coefficient n2efff/Aeff versus pump modulation frequency for a standard single-mode fiber (top) and a DSF (bottom). The solid curve in the top plot is a theoretical fit to the data.

Equations (2)

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ΔϕNLt=2πλn2effAeffmP¯Leff cos2πft,
n2eff=2κeffn2fast+n2strHRf,

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