الفهرس 
IntroductionOnly 14 pages are availabe for public view
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Abstract
Accurate modeling of photonic devices is essential for the development of new higher performance optical components required by current and future large or wide bandwidth communication systems. This thesis introduces several key techniques for such modeling, many of which are used in commercial design tools. These include several techniques of the beam propagation methods (BPM), such as fast Fourier transform (FFTBPM), wide angle fast Fourier transform (WAFFTBPM), scalar finite difference (FDBPM), scalar wide angle finite difference beam propagation method (WAFDBPM), generalized Douglas finite difference (GDFDBPM), full vectorial finite difference beam propagation method (FVFDBPM) and waveletGalerkin method (WGM). The numerical simulations are applied to a real optical diffraction grating fabricated by a doubleion exchange technique.
The validity of the numerical results is confirmed by the analytical results using Kogelnik`s coupled wave theory. Simple analytical expressions for the profiles of transmitted and diffracted beams in the near field are obtained. The wavelet solutions have much better precision but take slightly slower than the finite difference solution 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 engineering problems.