GAUSSIAN-BEAM AT A DIELECTRIC INTERFACE

To discuss the reflection and refraction of a Gaussian TE or TM electr omagnetic beam at a dielectric interface S we use a scalar field solut ion of the 2D-paraxial wave equation. the boundary conditions on S for the phase and the amplitude of the beam give generalized Descartes-Sn ell relations and Fresnel formulae that are made explicit in the optic al domain kw0 much-greater-than 1 and in the low frequency domain kw0 much-less-than 1. The parameter w0 is the half-width of the Gaussian b eam at the point where its wave front is plane while k is the wave num ber of the beam. We discuss the main properties of the reflected and r efracted beams in the optical domain.