Elegant Hermite-Gaussian and Laguerre-Gaussian beams at a dielectric interface

Basic features of narrow optical beam interactions with a dielectric interface are analysed. It is shown that two types of paraxial beams - elegant Hermite-Gaussians of linear polarization and elegant Laguerre-Gaussians of circular polarization - can be treated as vector normal modes of the interface. Excitation of higher-order modes by cross-polarization coupling is described and changes of mode indices induced by transmission and reflection matrices are evaluated. Optical vortex excitation and splitting are theoretically predicted and confirmed by numerical simulations.