Complete transmission through a two-dimensional diffraction grating

The propagation of a normally incident electromagnetic plane wave through a two-dimensional metallic grating is modeled and analyzed. The period of the structure A is on the order of the incident wave length lambda, but the height of the channel H separating the blocks is very small. Exploiting the small parameter H/A, an approximate transmission coefficient is obtained for the grating. For a fixed frequency this coefficient is O(H/A) except near resonant lengths where it is O(1). That is, for certain widths the structure is transparent. Similarly, for a fixed length the transmission coefficient has the same resonant features as a function of frequency.