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Corresponding Author

Samra, A.

Subject Area

Electronics and Communication Engineering

Article Type

Original Study

Abstract

Accurate modeling of photonic devices is essential for the development of new higher performance optical components required by current and future wide bandwidth communication systems. The goal of this paper is to formulate a Wavelet-Galerkin method to solve a paraxial wave equation numerically. The numerical simulation is applied to a teal optical diffraction grating fabricated by a double-ion exchange technique. The Wavelet solutions have much better precision but are slightly slower than the finite difference solutions owing to the need to transform the samples from physical space into Wavelet space and back again. Although the Wavelet solutions require slightly more computational effort than the finite difference solution, the gains in accuracy, particularly with the higher order wavelets, far outweigh the increase in cost. Furthermore, Wavelets have the capability of representing solutions at different levels of resolution, which makes them particularly useful for developing hierarchical solutions to engineer problems.

Keywords

Wavelet-Galerkin Method (WGM); Finite-Difference Beam Propagation Method (FD-BPM); Diffraction Grating; partial Differential Equation (PDE); Methods of Weighted Residuals (MWR)

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