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Perturbation theory is a kind of estimation method based on theorem of Taylorexpansion, and is useful to investigate electromagnetic solutions of smallchanges. By considering a sharp boundary as a limit of smoothed systems,previous study has solved the problem when applying standard perturbationtheory to Maxwell's equations for small shifts in isotropic dielectricinterfaces. However, when dealing with anisotropic materials, an approximationis conducted and leads to an unsatisfactory error. Here we develop a modifiedperturbation theory for small shifts in anisotropically dielectric interfaces.By using optimized smoothing function for each component of permittivity, weobtain a method to calculate the intrinsic frequency shifts of anisotropicpermittivity field when boundaries shift, without approximation. Our methodshows accurate results when calculating eigenfrequency's shifts instrong-anisotropy materials, and can be widely used for small shifts inanisotropically dielectric interfaces.

Perturbation theory for Maxwell's equations in anisotropic materials with shifting boundaries