Electromagnetic scattering of two-dimensional surface-relief dielectric gratings

We employed the rigorous vector coupled-wave theory [J. Opt. Soc. Am. 73, 1105 (1983)] to analyze the electromagnetic scattering from two dimensional (2-D) surface-relief dielectric gratings. A shoot-back method was developed for the numerical solution of the resulting coupled differential equations. This method allowed numerical solutions to be found for grating structures of arbitrary profiles and relatively deep grooves. It was most suitable where the grating medium refractive index was not too large and where only a small number of propagating orders existed. Experiments confirmed the numerically predicted reflectivities for 2-D surface-relief dielectric sinusoidal gratings. Reflectivity measurements were made on 2-D sinusoidal gratings fabricated on photoresist and on polycarbonate. The grating periodicities were of the order of 3000 lines/mm such that only the zero-order diffracted waves were propagating in the incident region, and possibly a few forward orders in the transmission region. The embossing technique that was used for replicating the grating patterns from photoresist onto polycarbonate proved to be a feasible method for the production of such gratings.