Angular shifts of paraxial beams by refraction in a plane dielectric/dielectric interface

Abstract

The longitudinal and transverse angular shifts in the refraction of a paraxial beam are calculated by using the plane-wave decomposition of the amplitude of the electric field distribution of the incident beam. The transmission coefficients are expanded into powers of the spatial frequencies. In this paper these spatial frequencies need to be within the paraxial approach around the main direction of propagation of the beam. The beam is characterized by the moments of the square of the modulus of the angular spectrum of the electric field. To compute them, it is necessary to calculate how the spatial frequencies of the beam change along the refraction. The state of polarization of the beam is also included in the analysis. Numerical results are obtained to show the dependence of the angular shifts on the polarization’s state and the symmetry of the beam.