Abstract

A new method for solving the scalar Helmholtz equation to obtain the propagation of total fields or beams through general optical waveguiding structures is presented. The method is based on converting the partial differential equation into a matrix total differential equation using a collocation method and then solving the resulting equation through standard numerical methods. A comparison with the propagating-beam method shows that the present method has better accuracy and is more efficient numerically.

© 1989 Optical Society of America

Propagation characteristics of optical waveguiding structures by direct solution of the Helmholtz equation for total fields

Swagata Banerjee and Anurag Sharma
J. Opt. Soc. Am. A 6(12) 1884-1894 (1989)

Unconditionally stable procedure to propagate beams through optical waveguides using the collocation method

Anurag Sharma and Anju Taneja
Opt. Lett. 16(15) 1162-1164 (1991)

Propagation of beams through optical waveguiding structures: comparison of the beam-propagation method and the collocation method

Anju Taneja and Anurag Sharma
J. Opt. Soc. Am. A 10(8) 1739-1745 (1993)

Variable-transformed collocation method for field propagation through waveguiding structures

Anurag Sharma and Anju Taneja
Opt. Lett. 17(11) 804-806 (1992)

New method for nonparaxial beam propagation

Anurag Sharma and Arti Agrawal
J. Opt. Soc. Am. A 21(6) 1082-1087 (2004)