Wave propagation along a dielectric interface

We consider a plane wave as it approaches a dielectric medium that is split along a plane parallel to the wave motion. As the wave penetrates into the two-layered medium, its phase velocity is different in the two regions of index n1 and n2. The deformation of the plane wave is studied. Plots of the field irradiance and phase are obtained by numerical evaluation of an integral. The analysis is based on the expansion of the field in terms of normal modes. Backscattering of the wave incident on the layered medium is ignored. The results presented here are closely related to interference microscopy, because the distortion of the plane wave caused by diffraction may show up as a fringe shift.