Unified treatment of beam interaction with a dielectric interface using modal plane wave expansion

New phenomena have been reported recently in connection with Gaussian beam interaction with a plane dielectric interface, namely, the deterioration of the reflected and refracted beams from shapes predicted by geometric optics, and the generation of higher order components that cause angular beam deflection. Any bounded symmetric beam, that is not necessarily Gaussian, can be comprised in terms of angular spectra of plane waves. Utilizing such a modal expansion, a model of the interaction process that seems to point out the generality of the phenomena involved for bounded symmetrical beams with any cross-section is presented. Results for two examples of beam profiles, a plane wave of limited extent and a Cauchy Profile, are given. Comparison with prior results obtained for the Gaussian beam and careful examination of the respective spectral functions demonstrate close correspondence between the results. This adds credence to the general approach presented here which can be applied to bounded symmetrical beams of general shape.