## Improved scalar analysis of integrated optical structures by the mapped Galerkin method and Arnoldi iteration

JOSA A, Vol. 18, Issue 4, pp. 966-974 (2001)

http://dx.doi.org/10.1364/JOSAA.18.000966

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### Abstract

A modified Galerkin method is used to study the modal behavior of generic integrated optical waveguides down to first-order mode cutoff. The scalar Helmholtz equation is solved through nonlinear mapping of the transverse plane and subsequent Fourier decomposition. The differential equation is thus transformed into the eigenproblem for a specific finite-dimension linear operator. The largest eigenvalues, corresponding to the lowest-order guided modes, are in turn determined by an iterative Arnoldi procedure. Therefore actual diagonalization of a huge coefficient matrix is avoided, and a very large number of field frequency components can be considered.

© 2001 Optical Society of America

**OCIS Codes**

(130.2790) Integrated optics : Guided waves

(230.7380) Optical devices : Waveguides, channeled

(350.5500) Other areas of optics : Propagation

**Citation**

Michele A. Forastiere and Giancarlo C. Righini, "Improved scalar analysis of integrated optical structures by the mapped Galerkin method and Arnoldi iteration," J. Opt. Soc. Am. A **18**, 966-974 (2001)

http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-18-4-966

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