Abstract
By formulating Maxwell's equations in perturbation matched curvilinear coordinates, we have derived the rigorous perturbation theory (PT) and coupled mode theory (CMT) expansions that are applicable in the case of generic non-uniform dielectric profile perturbations in high index-contrast waveguides, including photonic band gap fibers, 2D and 3D waveguides. PT is particularly useful in the optimization stage of a component design process where fast evaluation of an optimized property with changing controlling variables is crucial. We demonstrate our method by studying radiation scattering due to common geometric variations in planar 2D photonic crystals waveguides. We conclude the paper by statistical analysis of experimental images of 2D planar PCs to characterize common imperfections in such structures.
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