Beyond Geometrical Optics: Higher Order Diffraction at Thin Curved Dielectric Layers

In this paper, we elaborate the method to successively find higher order terms of the asymptotic expansion of the field diffracted at a thin dielectric layer in 2-D problems (both the cases of E- and H-polarization). Each iteration of this method can be reduced to some standard 1-D boundary problem with a second-order differential equation and boundary conditions of impedance type. The boundary problem solvability and uniqueness are studied. The derivation of the leading asymptotic term is described, along with its geometrical optics meaning. The structure of the second asymptotic term is studied and analyzed with respect to its partial terms. Special attention is given to the partial terms describing the contribution to the diffracted field of the curvature of boundaries and their mutual slope. The results are verified by comparison with a solution obtained with the integral equation method.