## Influence of two-photon absorption on modulational instability

JOSA B, Vol. 18, Issue 8, pp. 1144-1149 (2001)

http://dx.doi.org/10.1364/JOSAB.18.001144

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### Abstract

The instability of a plane wave in an optical medium with two-photon absorption is studied. The analysis is based on the modified nonlinear Schrödinger equation. The linearized equation for the modulation is shown to have an exact solution in terms of confluent hypergeometric functions. It is found that the gain spectrum varies with position. This may result in a change of the wave dynamics and in a decrease of the repetition rate of the pulse train developed from the plane wave. The application of the results to the optical pulse propagation in semiconductor gratings and fiber gratings is discussed.

© 2001 Optical Society of America

**OCIS Codes**

(050.2770) Diffraction and gratings : Gratings

(190.0190) Nonlinear optics : Nonlinear optics

(190.3100) Nonlinear optics : Instabilities and chaos

**Citation**

E. N. Tsoy, C. M. de Sterke, and F. Kh. Abdullaev, "Influence of two-photon absorption on modulational instability," J. Opt. Soc. Am. B **18**, 1144-1149 (2001)

http://www.opticsinfobase.org/josab/abstract.cfm?URI=josab-18-8-1144

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### References

- V. I. Bespalov and V. I. Talanov, “Filamentary structure of light beams in nonlinear liquids,” JETP 3, 307–310 (1966).
- T. B. Benjamin and J. E. Feir, “The disintegration of wave trains on deep water,” J. Fluid Mech. 27, 410–430 (1967).
- G. P. Agrawal, Nonlinear Fiber Optics (Academic, San Diego, Calif., 1995).
- D. Anderson and M. Lisak, “Modulational instability of coherent optical-fiber transmission signals,” Opt. Lett. 9, 468–470 (1984).
- A. Hasegawa and K. Tai, “Effects of modulational instability on coherent transmission systems,” Opt. Lett. 14, 512–513 (1989).
- M. Karlsson, “Modulational instability in lossy optical fibers,” J. Opt. Soc. Am. B 12, 2071–2077 (1995).
- V. A. Vysloukh and N. A. Sukhostova, “Influence of third-order dispersion on the generation of a train of picosecond pulses in fiber waveguides due to self-modulation instability,” Sov. J. Quantum Electron. 17, 1509–1511 (1987).
- F. Kh. Abdullaev, S. A. Darmanyan, S. Bishoff, P. L. Christiansen, and M. P. Sørensen, “Modulational instability in optical fibers near the zero dispersion point,” Opt. Commun. 108, 60–64 (1994).
- K. J. Blow and D. Wood, “Theoretical description of transient stimulated Raman scattering in optical fibers,” IEEE J. Quantum Electron. 25, 2665–2673 (1989).
- F. Kh. Abdullaev, S. A. Darmanyan, A. Kobyakov, and F. Lederer, “Modulational instability in optical fibers with variable dispersion,” Phys. Lett. A 220, 213–218 (1996).
- F. Kh. Abdullaev, S. A. Darmanyan, S. Bischoff, and M. P. Sørensen, “Modulational instability of electromagnetic waves in media with varying nonlinearity,” J. Opt. Soc. Am. B 14, 27–33 (1997).
- F. T. Gratton, G. Gnavi, R. M. O. Galvao, and L. Gomberoff, “Self-modulation of a strong electromagnetic wave in a positron–electron plasma induced by relativistic temperatures and phonon damping,” Phys. Rev. E 55, 3381–3392 (1997).
- P. Millar, R. M. De La Rue, T. F. Krauss, J. S. Aitchison, N. G. R. Broderick, and D. J. Richardson, “Nonlinear propagation effects in AlGaAs Bragg grating filter,” Opt. Lett. 24, 685–687 (1999).
- B. J. Eggleton, R. E. Slusher, C. M. de Sterke, P. A. Krug, and J. E. Sipe, “Bragg grating solitons,” Phys. Rev. Lett. 76, 1627–1630 (1996).
- C. M. de Sterke and J. E. Sipe, “Gap solitons,” in Progress in Optics XXXIII, E. Wolf, ed. (Elsevier, Amsterdam, 1994), Chap. 3, pp. 203–260.
- Y. Silberberg, “Solitons and two-photon absorption,” Opt. Lett. 15, 1005–1007 (1990).
- V. V. Afanasjev, J. S. Aitchison, and Y. S. Kivshar, “Splitting of high-order spatial solitons under the action of two-photon absorption,” Opt. Commun. 116, 331–338 (1995).
- V. Mizrahi, K. W. DeLong, G. I. Stegeman, M. I. Saifi, and M. J. Andrejco, “Two-photon absorption as a limitation to all-optical switching,” Opt. Lett. 14, 1140–1142 (1989).
- M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions (Wiley, New York, 1972).
- L. J. Slater, Confluent Hypergeometric Functions (Cambridge University, London, 1960).
- J. S. Aitchison, D. C. Hutchings, J. U. Kang, G. I. Stegeman, and A. Villeneuve, “The nonlinear properties of AlGaAs at the half band gap,” IEEE J. Quantum Electron. 33, 341–348 (1997).
- B. J. Eggleton, C. M. de Sterke, A. B. Acevez, J. E. Sipe, T. A. Strasser, and R. E. Slusher, “Modulational instability and tunable multiple soliton generation in apodized fiber gratings,” Opt. Commun. 149, 267–271 (1998).

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