Polarization versus spatial characteristics of optical beams at a planar isotropic interface

Three-dimensional monochromatic optical beams of uniform polarization interacting with a planar boundary between two homogeneous, isotropic, and lossless media are analyzed. Generalized Fresnel transmission and reflection coefficients for beam spectra are given. Interrelations induced by cross-polarization coupling between beam profile and phase and beam polarization, or between spin and orbital angular momentum of beams are derived. Beam transmission for normal incidence is discussed in detail. It is shown that elegant Hermite-Gaussian beams of linear polarization and Laguerre-Gaussian beams of circular polarization, all projected on the interface, are normal modes at this interface. Creation and annihilation of these modes at the interface are shown with total angular momentum being conserved on a single photon level.