Scattering and guiding of waves by dielectric gratings with arbitrary profiles

Based on an exact solution of the pertinent boundary-value problem, a method is presented for finding the electromagnetic fields scattered or guided by lossy dielectric gratings having arbitrary profiles. This method unifies the treatment of both perpendicular (TE) and parallel (TM) polarizations by expressing the fields in terms of two coupled first-order differential equations. Their solution is obtained by resorting to difference equations in conjunction with the algorithm of Adams-Moulton, which easily leads to accurate results for a large variety of practical problems. To illustrate the application of this approach, quantitative results are presented for the scattering of plane waves by lossy corrugated structures and for the guiding of (leaky) surface waves by triangular gratings with symmetric or asymmetric profiles.