Filtering effect of metal-strip gratings printed on optical planar dielectric slabs

Optical periodic guiding structures made up of multilayered dielectric materials have been investigated for practical applications of such integrated optics as Bragg-reflection filters, distributed-feedback lasers and grating couplers. Analogous structures based on periodic dielectric guides can be successfully used in the microwave and millimeter-wave range. In most cases, they can be easily fabricated by printing metal-strip gratings on the surface of dielectric slabs. The electromagnetic problems associated with filtering properties have been studied by means of a variety of methods that usually include a mixture of analytical and computer-based techniques. However, these techniques are often unable to provide information on all the effects produced by the metal-strip gratings with finite-thickness. To achieve the objective, in this paper we present a rigorous modal transmission-line theory and obtain a novel result for the dominant TE mode.