Abstract

A method is described for modeling two-dimensional reflecting structures based on a solution of the scalar Helmholtz equation. The equation is solved by use of an alternating-direction-implicit iterative method together with a semioptimum sequence of acceleration parameters similar to those introduced decades ago for the solution of elliptic equations with positive-definite operators. The resulting technique is efficient and simple to program, permits the simulation of complex structures with modest storage requirements, and is of very general applicability.

© 1994 Optical Society of America

Numerical method based on the solution of integral equations for the calculation of the band structure and reflectance of one- and two-dimensional photonic crystals

Alberto Mendoza-Suárez, Francisco Villa-Villa, and Jorge A. Gaspar-Armenta
J. Opt. Soc. Am. B 23(10) 2249-2256 (2006)

Accurate numerical solution of the Helmholtz equation by iterative Lanczos reduction

R. P. Ratowsky and J. A. Fleck
Opt. Lett. 16(11) 787-789 (1991)

Inverse scattering for the one-dimensional Helmholtz equation: fast numerical method

Oleg V. Belai, Leonid L. Frumin, Evgeny V. Podivilov, and David A. Shapiro
Opt. Lett. 33(18) 2101-2103 (2008)

Finite-element solution of Maxwell’s equations with Helmholtz forms

Keith D. Paulsen
J. Opt. Soc. Am. A 11(4) 1434-1444 (1994)

Accurate solution of the Helmholtz equation by Lanczos orthogonalization for media with loss or gain

R. P. Ratowsky, J. A. Fleck, and M. D. Feit
Opt. Lett. 17(1) 10-12 (1992)