Accession Number : ADP008163

Title :   Local Cardinal Interpolation Spline Method for Solving Coupled Nonlinear Schrodinger Equations: A Comparison with BPM,

Corporate Author : TEXAS A AND M UNIV COLLEGE STATION DEPT OF ELECTRICAL ENGINEERING

Personal Author(s) : Chan, A. K. ; Chui, C. K. ; Zha, Jun ; Bian, Jieren

Report Date : APR 1992

Pagination or Media Count : 2

Abstract : In terms of computational speed, BPM is faster than finite difference method by an order of magnitude or more to achieve a given accuracy. However, it requires relatively small propagation steps and large computing window for artificial absorption on the boundary. A large transverse index change can also jeopardize the method. In solving coupled wave equations. BPM iterates between the equations until a converged solution is obtained. The total efficiency of this algorithm is greatly reduced. In this paper, we present a numerical algorithm which uses the Local Cardinal Interpolation Spline (LCIS) method developed by Chui and Chan to solve the nonlinear Schroedinger equation and the coupled nonlinear Schroedinger equations that are frequently encountered in the analyses of integrated photonic circuit elements and nonlinear optical fiber devices. A comparison with the FFT-BPM is given to demonstrate that our method is about 3 to 4 times faster than BPM for uncoupled nonlinear Schroedinger equation and about 8 times faster for coupled nonlinear Schroedinger equations to achieve a given accuracy. Furthermore, the LCIS method dose not have the disadvantages of BPM mentioned above. Our method has potential for fast and accurate simulations of integrated optical devices.

Descriptors :   *PHOTONICS, *COMPUTER PROGRAMMING, *NUMERICAL METHODS AND PROCEDURES, ABSORPTION, ACCURACY, ALGORITHMS, BOUNDARIES, COMPARISON, EFFICIENCY, EQUATIONS, FIBERS, INDEXES, INTERPOLATION, PROPAGATION, SIMULATION, SPLINES, TRANSVERSE, VELOCITY, WAVE EQUATIONS, FINITE DIFFERENCE THEORY, SOLITONS, BIREFRINGENCE, FAST FOURIER TRANSFORMS, OPTICAL CIRCUITS.

Subject Categories : Electrooptical and Optoelectronic Devices
      Numerical Mathematics
      Computer Programming and Software

Distribution Statement : APPROVED FOR PUBLIC RELEASE