Optimization of soliton amplitude in dispersion-decreasing nonlinear optical fibers

The compression of a cw into a periodic train of noninteracting solitons by a dispersion-decreasing fiber is investigated with a variational method. To model the evolution from the cw to the soliton train, an elliptic-function-based expression is used as the trial function in the averaged Lagrangian. Both a continuous dispersion variation and a step dispersion variation in the fiber are considered. By use of an optimization method based on the approximate variational equations, the optimal dispersion profile required for achieving maximum pulse compression in a fixed length of fiber is determined. The solutions of the approximate equations are compared with full numerical solutions of the governing nonlinear Schrodinger equation, and good agreement is found.

[1]  E. Swanson,et al.  40-GHz pulse train generation using soliton compression of a Mach-Zehnder modulator output , 1995, IEEE Photonics Technology Letters.

[2]  William H. Press,et al.  Book-Review - Numerical Recipes in Pascal - the Art of Scientific Computing , 1989 .

[3]  J. Taylor,et al.  Integrated all optical fibre source of multigigahertz soliton pulse train , 1993 .

[4]  John A. Nelder,et al.  A Simplex Method for Function Minimization , 1965, Comput. J..

[5]  Smyth,et al.  Soliton evolution and radiation loss for the nonlinear Schrödinger equation. , 1995, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[6]  Claude Brezinski,et al.  Numerical recipes in Fortran (The art of scientific computing) : W.H. Press, S.A. Teukolsky, W.T. Vetterling and B.P. Flannery, Cambridge Univ. Press, Cambridge, 2nd ed., 1992. 963 pp., US$49.95, ISBN 0-521-43064-X.☆ , 1993 .

[7]  Bengt Fornberg,et al.  A numerical and theoretical study of certain nonlinear wave phenomena , 1978, Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences.

[8]  R. Haberman.  Phase Shift Modulations for Stable, Oscillatory, Traveling, Strongly Nonlinear Waves , 1991 .

[9]  V. A. Semenov,et al.  A single-mode fiber with chromatic dispersion varying along the length , 1991 .

[10]  Alan C. Newell,et al.  Solitons in mathematics and physics , 1987 .

[11]  R. Haberman.  The Modulated Phase Shift for Weakly Dissipated Nonlinear Oscillatory Waves of the Korteweg-deVries Type , 1988 .

[12]  E. M. Dianov,et al.  Generation of fundamental soliton trains for high-bit-rate optical fiber communication lines , 1991 .

[13]  Irene A. Stegun,et al.  Handbook of Mathematical Functions. , 1966 .

[14]  D. Richardson,et al.  Experimental demonstration of 100 GHz dark soliton generation and propagation using a dispersion decreasing fibre , 1994 .

[15]  Jeffrey C. Lagarias,et al.  Convergence Properties of the Nelder-Mead Simplex Method in Low Dimensions , 1998, SIAM J. Optim..

[16]  K. I. M. McKinnon,et al.  Convergence of the Nelder-Mead Simplex Method to a Nonstationary Point , 1998, SIAM J. Optim..

[17]  Akira Hasegawa,et al.  Optical solitons in fibers , 1993, International Commission for Optics.

[18]  Govind P. Agrawal,et al.  Nonlinear Fiber Optics , 1989 .

[19]  D. Richardson,et al.  Soliton pulse compression in dispersion-decreasing fiber. , 1993, Optics letters.

[20]  P. Byrd,et al.  Handbook of Elliptic Integrals for Engineers and Physicists , 2014 .