Evanescent fields produced by totally reflected beams

When the coordinates of a line source are assigned complex values in the free-space Green's function, the resulting field represents a bounded beam. This property is employed to formulate an integral expression for the field transmitted across a plane dielectric interface. Asymptotic evaluation of the integral requires detailed study of the saddle point and steepest descent path configurations, especially when the incident beam is totally reflected. The asymptotic results in that case are employed to chart the power flow lines and to deduce the lateral shift of the reflected beam.