Abstract

The numerical algorithm is presented for solving coupled extended nonlinear Schrödinger equations (NLSEs) including higher-order dispersion, retarded nonlinear response, and self-steepening terms. The numerical results show that the influence of the retarded nonlinear response and self-steepening effect on the coupling dynamics in a nonlinear directional coupler (NLDC) is strongly dependent on the input peak power, input pulse width, and product of the dispersion length and the coupling coefficient (L<sub>D</sub>kappa). In the case of L<sub>D</sub>kappa >> 1, the pulse coupling obeys Jensen's equation as long as the input pulse width is broader than 250 fs and the coupler is far from zero dispersion. Both the retarded nonlinear response and the self-steepening effect could be ignored if the normalized amplitude of the input pulse is less than 0.5. It was also found that the retarded nonlinear response improves the energy transfer efficiency between the two coupled waveguides.

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  6. A. K. Atieh, P. Myslinski, J. Chrostowski and P. Galko, "Measuring the Raman time constant (TR) for soliton pulses in standard single mode fiber", J. Lightw. Technol., vol. 17, no. 2, pp. 216-221, Feb. 1999.
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  21. Y. Wang and W. Wang, "A simple and effective numerical method for nonlinear pulse propagation in N-core optical couplers", IEEE Photon. Technol. Lett., vol. 16, no. 4, pp. 1077-1079, Apr. 2004.
  22. P. L. Chu, B. A. Malomed and G. D. Peng, "Soliton switching and propagation in nonlinear fiber couplers: Analytical results", J. Opt. Soc. Amer. B, Opt. Phys., vol. 10, no. 8, pp. 1379-1385, Aug. 1993.
  23. I. M. Uzunov, R. Muschall, M. Gölles, Y. S. Kivshar, B. A. Malomed and F. Lederer, "Pulse switching in nonlinear fiber directional couplers", Phys. Rev. E, Stat. Phys. Plasmas Fluids Relat. Interdiscip. Top., vol. 51, no. 3, pp. 2527-2537, Mar. 1995.
  24. C. Pare and M. Florjanczyk, "Approximate model of soliton dynamics in all-optical couplers", Phys. Rev. A, Gen. Phys., vol. 41, no. 11, pp. 6287-6295, Jun. 1990.
  25. D. Anderson, "Variational approach to nonlinear pulse propagation in optical fibers", Phys. Rev. A, Gen. Phys., vol. 27, no. 6, pp. 3135-3145, Jun. 1983.
  26. K. S. Chiang, "Intermodal dispersion in two-core optical fibers", Opt. Lett., vol. 20, no. 9, pp. 997-999, May 1995.
  27. R. H. Stone, J. P. Gordon, W. J. Tomlinson and H. A. Haus, "Raman response function of silica-core fibers", J. Opt. Soc. Amer. B, Opt. Phys., vol. 6, no. 6, pp. 1159-1166, Jun. 1989.

Other (27)

F. M. Mitschke and L. F. Mollenauer, "Discovery of the soliton self-frequency shift", Opt. Lett., vol. 11, no. 10, pp. 659-661, Oct. 1986.

J. P. Gordon, "Theory of the soliton self-frequency shift", Opt. Lett., vol. 11, no. 10, pp. 662-664, Oct. 1986.

D. Grischkowsky, E. Courtens and J. A. Armstrong, "Observation of self-steepening of optical pulses with possible shock formation", Phys. Rev. Lett., vol. 31, no. 7, pp. 422-425, Aug. 1973.

W. Hodel and H. P. Weber, "Decay of femtosecond higher-order solitons in an optical fiber induced by Raman self-pumping", Opt. Lett., vol. 12, no. 11, pp. 924-926, Nov. 1987.

K. Tai, A. Hasegawa and N. Bekki, "Fission of optical solitons induced by stimulated Raman effect", Opt. Lett., vol. 13, no. 5, pp. 392-394, May 1988.

A. K. Atieh, P. Myslinski, J. Chrostowski and P. Galko, "Measuring the Raman time constant (TR) for soliton pulses in standard single mode fiber", J. Lightw. Technol., vol. 17, no. 2, pp. 216-221, Feb. 1999.

P. V. Mamyshev and S. V. Chernikov, "Ultrashort-pulse propagation in optical fibers", Opt. Lett., vol. 15, no. 19, pp. 1076-1078, Oct. 1990.

G. P. Agrawal, Nonlinear Fiber Optics, London: U.K.: Academic, 2001, ch. 2.

K. J. Blow and D. Wood, "Theoretical description of transient stimulated Raman scattering in optical fiber", IEEE J. Quantum Electron., vol. 25, no. 12, pp. 2665-2673, Dec. 1989.

S. M. Jensen, "The nonlinear coherent coupler", IEEE J. Quantum Electron., vol. QE-18, no. 10, pp. 1580-1583, Oct. 1982.

S. R. Friberg, Y. Silberberg, M. K. Oliver, M. J. Andrejco, M. A. Saifi and P. W. Smith, "Ultrafast all-optical switching in a dual-core fiber nonlinear coupler", Appl. Phys. Lett., vol. 51, no. 15, pp. 1135-1137, Oct. 1987.

Y. Wang, "Nonlinear optical limiter and digital optical switch by cascaded nonlinear couplers: Analysis", J. Lightw. Technol., vol. 17, no. 2, pp. 292-297, Feb. 1999.

S. Trillo, S. Wabnitz, E. M. Wright and G. I. Stegman, "Soliton switching in fiber nonlinear directional couplers", Opt. Lett., vol. 13, no. 8, pp. 672-674, Aug. 1988.

E. Caglioti, S. Trillo, S. Wabnitz, B. Crosignani and P. Di Porto, "Finite-dimensional description of nonlinear pulse propagation in optical-fiber couplers with applications to soliton switching", J. Opt. Soc. Amer. B, Opt. Phys., vol. 7, no. 3, pp. 374-385, Mar. 1990.

Y. Wang and J. Liu, "All-fiber logical devices based on the nonlinear directional coupler", IEEE Photon. Technol. Lett., vol. 11, no. 1, pp. 72-74, Jan. 1999.

A. M. Weiner, Y. Silberberg, H. Fouckhardt, D. E. Leaird, M. A. Saifi, M. J. Andrejco and P. W. Smith, "Use of femtosecond square pulses to avoid pulse breakup in all-optical switching", IEEE J. Quantum Electron., vol. 25, no. 12, pp. 2648-2654, Dec. 1989.

B. A. Malomed, I. M. Skinner and R. S. Tasgal, "Solitons in a nonlinear optical coupler in the presence of the Raman effect", Opt. Commun., vol. 139, no. 4, pp. 247-251, Jul. 1997.

F. S. Locati, M. Romagnoli, A. Tajani and S. Wabnitz, "Adiabatic femtosecond soliton active nonlinear directional coupler", Opt. Lett., vol. 17, no. 11, pp. 1213-1215, 1992.

Y. Wang and W. Wang, "Study of ultra-fast optical pulse propagation in a nonlinear directional coupler", Appl. Phys. B, Photophys. Laser Chem., vol. B79, no. 1, pp. 51-55, Jul. 2004.

C. R. Paiva, A. L. Topa and A. M. Barbosa, "Influence of intermodal dispersion on the switching of solitons at different wavelengths in twin-core fiber couplers", J. Opt. Soc. Amer. B, Opt. Phys., vol. 16, no. 10, pp. 1636-1641, Oct. 1999.

Y. Wang and W. Wang, "A simple and effective numerical method for nonlinear pulse propagation in N-core optical couplers", IEEE Photon. Technol. Lett., vol. 16, no. 4, pp. 1077-1079, Apr. 2004.

P. L. Chu, B. A. Malomed and G. D. Peng, "Soliton switching and propagation in nonlinear fiber couplers: Analytical results", J. Opt. Soc. Amer. B, Opt. Phys., vol. 10, no. 8, pp. 1379-1385, Aug. 1993.

I. M. Uzunov, R. Muschall, M. Gölles, Y. S. Kivshar, B. A. Malomed and F. Lederer, "Pulse switching in nonlinear fiber directional couplers", Phys. Rev. E, Stat. Phys. Plasmas Fluids Relat. Interdiscip. Top., vol. 51, no. 3, pp. 2527-2537, Mar. 1995.

C. Pare and M. Florjanczyk, "Approximate model of soliton dynamics in all-optical couplers", Phys. Rev. A, Gen. Phys., vol. 41, no. 11, pp. 6287-6295, Jun. 1990.

D. Anderson, "Variational approach to nonlinear pulse propagation in optical fibers", Phys. Rev. A, Gen. Phys., vol. 27, no. 6, pp. 3135-3145, Jun. 1983.

K. S. Chiang, "Intermodal dispersion in two-core optical fibers", Opt. Lett., vol. 20, no. 9, pp. 997-999, May 1995.

R. H. Stone, J. P. Gordon, W. J. Tomlinson and H. A. Haus, "Raman response function of silica-core fibers", J. Opt. Soc. Amer. B, Opt. Phys., vol. 6, no. 6, pp. 1159-1166, Jun. 1989.

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