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

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.

Document Details

Document Type
Technical Report
Publication Date
Apr 01, 1992
Accession Number
ADP008163

Entities

People

  • A. K. Chan
  • Charles K. Chui
  • Jieren Bian
  • Jun Zha

Organizations

  • Texas A&M University

Tags

Communities of Interest

  • Advanced Electronics

DTIC Thesaurus Topics

  • Absorption
  • Accuracy
  • Algorithms
  • Boundaries
  • Circuits
  • Differential Equations
  • Efficiency
  • Equations
  • Fibers
  • Interpolation
  • Mathematical Analysis
  • Mathematics
  • Optical Fibers
  • Partial Differential Equations
  • Photonic Integrated Circuits
  • Schrodinger Equation
  • Wave Equations

Readers

  • Approximation Theory.
  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)