A Simple Analytic Approximation for the Refracted Field at Gaussian Beam Incidence upon a Boundary of Absorbing Medium

An approximate analytic model is presented to describe spatial structure of refracted electromagnetic field arising at oblique incidence of a Gaussian beam on a plane boundary of an absorbing homogeneous medium. The analytic solution is obtained by asymptotic approximation of a Fourier field integral under the condition of great beam width in comparison with a wavelength (the geometrical-optics approximation). This model can be used also for approximate simulation of refracted field in the cases of beam incidence near the critical angle on transparent or absorbing (amplifying) refracting medium, if one artificially introduces the additional absorption (amplification), whose value is proportional to the ratio of the wavelength and the effective beam width. It is shown that the analytic model reflects the general features of refracted field at total internal reflection.