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