Abstract

The pulse coupling dynamics in a nonlinear directional coupler (NLDC) is analyzed by using the new normalized coupled nonlinear Schrödinger equations. The operation of an NLDC can be divided into three regions according to L<sub>D</sub> kappa: Region 1 (L<sub>D</sub> kappa ≤ 1), Region 2 (L<sub>D</sub> kappa > 50), and Region 3 (1 < L<sub>D</sub> kappa ≤ 50). In region 1, an NLDC can exhibit a good switching performance. In region 2, both the pulse coupling and continuous-wave (cw) coupling in an NLDC show the similar energy transfer characteristics. In the case of L<sub>D</sub> kappa ≥ 1000, even an ultrashort pulse coupling can be reduced to the cw coupling and follow Jensen's equations when certain criteria are met. Consequently, many of the applications of NLDC that are suggested under the condition of cw excitation can also be implemented under the condition of ultrashort pulse excitation. In region 3, pulses suffer from pulse compression and serious distortion. The conditions for a pulse following Jensen's equations are presented. A 0.8-ps pulse with a wavelength of 1.55 µm in a silica coupler with a half-beat length of 50 mm follows Jensen's equation. To get a good switching performance, the input optical pulsewidth should be smaller than a certain maximum value. In addition, the intermodal dispersion including the contribution of the material dispersion is derived, and zero intermodal dispersion is predicted.

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  1. S. M. Jensen, "The nonlinear coherent coupler", IEEE J. Quantum Electron., vol. QE-18, no. 10, pp. 1580-1583, Oct. 1982.
  2. A. T. Pham and L. N. Binh, "All-optical modulation and switching using a nonlinear-optical directional coupler", J. Opt. Soc. Amer. B, Opt. Phys., vol. 8, no. 9, pp. 1914-1931, Sep. 1991.
  3. Y. Wang and C. K. Lee, "Effect of the linear mismatch and nonlinear asymmetry in the nonlinear coupler", Appl. Phys. B, Photophys. Laser Chem., vol. 72, no. 4, pp. 417-424, 2001.
  4. 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.
  5. Y. Wang and W. Wang, "Study of ultra-fast optical pulse propagation in a nonlinear directional coupler", Appl. Phys. B, Photophys. Laser Chem., vol. 79, no. 15, pp. 51-55, Oct. 2004.
  6. 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.
  7. 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.
  8. G. P. Agrawal, Nonlinear Fiber Optics, London: U.K.: Academic, 2001, ch. 2 and 4.
  9. 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. Plasma Fluid Relat. Interdiscip. Top., vol. 51, no. 3, pp. 2527-2537, Mar. 1995.
  10. Y. S. Kivshar, "Switching dynamics of solitons in fiber directional couplers", Opt. Lett., vol. 18, no. 1, pp. 7-9, Jan. 1993.
  11. 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.
  12. A. Villeneuve, C. C. Yang, P. G. J. Wigley, G. I. Stegeman, J. S. Aitchison and C. N. Ironside, "Ultrafast all-optical switching in semiconductor nonlinear directional couplers at half the band gap", Appl. Phys. Lett., vol. 61, no. 2, pp. 147-149, Jul. 1992.
  13. C. R. Menyuk, "Stability of solitons in birefringent optical fibers. I: Equal propagation amplitudes", Opt. Lett., vol. 12, no. 8, pp. 614-616, Aug. 1987.
  14. K. J. Blow, N. J. Doran and D. Wood, "Polarization instabilities for solitons in birefringent fibers", Opt. Lett., vol. 12, no. 3, pp. 202-204, Mar. 1987.
  15. M. J. Ablowitz, Z. H. Musslimani and G. Biondini, "Methods for discrete solitons in nonlinear lattices", Phys. Rev. E, Stat. Phys. Plasma Fluids Relat. Interdiscip. Top., vol. 65, no. 2, p. 026602, Feb. 2002.
  16. 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.
  17. 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.
  18. K. S. Chiang, "Intermodal dispersion in two-core optical fibers", Opt. Lett., vol. 20, no. 9, pp. 997-999, May 1995.
  19. 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.
  20. A. W. Snyder and D. Love, Optical Waveguide Theory, London: U.K.: Chapman & Hall, 1983, ch. 27.
  21. 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.
  22. Y. Wang and W. Wang, "Study of ultrafast pulse coupling dynamics considering retarded nonlinear response and self-steepening effects", J. Lightw. Technol., vol. 24, no. 2, pp. 1041-1047, Feb. 2006.
  23. 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.

Other (23)

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

A. T. Pham and L. N. Binh, "All-optical modulation and switching using a nonlinear-optical directional coupler", J. Opt. Soc. Amer. B, Opt. Phys., vol. 8, no. 9, pp. 1914-1931, Sep. 1991.

Y. Wang and C. K. Lee, "Effect of the linear mismatch and nonlinear asymmetry in the nonlinear coupler", Appl. Phys. B, Photophys. Laser Chem., vol. 72, no. 4, pp. 417-424, 2001.

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 and W. Wang, "Study of ultra-fast optical pulse propagation in a nonlinear directional coupler", Appl. Phys. B, Photophys. Laser Chem., vol. 79, no. 15, pp. 51-55, Oct. 2004.

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.

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.

G. P. Agrawal, Nonlinear Fiber Optics, London: U.K.: Academic, 2001, ch. 2 and 4.

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. Plasma Fluid Relat. Interdiscip. Top., vol. 51, no. 3, pp. 2527-2537, Mar. 1995.

Y. S. Kivshar, "Switching dynamics of solitons in fiber directional couplers", Opt. Lett., vol. 18, no. 1, pp. 7-9, Jan. 1993.

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.

A. Villeneuve, C. C. Yang, P. G. J. Wigley, G. I. Stegeman, J. S. Aitchison and C. N. Ironside, "Ultrafast all-optical switching in semiconductor nonlinear directional couplers at half the band gap", Appl. Phys. Lett., vol. 61, no. 2, pp. 147-149, Jul. 1992.

C. R. Menyuk, "Stability of solitons in birefringent optical fibers. I: Equal propagation amplitudes", Opt. Lett., vol. 12, no. 8, pp. 614-616, Aug. 1987.

K. J. Blow, N. J. Doran and D. Wood, "Polarization instabilities for solitons in birefringent fibers", Opt. Lett., vol. 12, no. 3, pp. 202-204, Mar. 1987.

M. J. Ablowitz, Z. H. Musslimani and G. Biondini, "Methods for discrete solitons in nonlinear lattices", Phys. Rev. E, Stat. Phys. Plasma Fluids Relat. Interdiscip. Top., vol. 65, no. 2, p. 026602, Feb. 2002.

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.

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.

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

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.

A. W. Snyder and D. Love, Optical Waveguide Theory, London: U.K.: Chapman & Hall, 1983, ch. 27.

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.

Y. Wang and W. Wang, "Study of ultrafast pulse coupling dynamics considering retarded nonlinear response and self-steepening effects", J. Lightw. Technol., vol. 24, no. 2, pp. 1041-1047, Feb. 2006.

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.

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