Whispering gallery eigenmodes of a surface with anisotropic surface impedance

Problem of finding electromagnetic whispering gallery eigenmodes of a three-dimensional curvilinear surface is considered. It is assumed that the wavelength of the eigenmodes is much smaller than principal radii of curvature of the surface (high frequency approximation). It is also assumed that electromagnetic field satisfy anisotropic impedance boundary conditions on the surface. The problem is solved in torsionless approximation using both the perturbation method and the method of reference problem.