Electromagnetic wave propagation in a periodic array of rectangular dielectric waveguides

The electromagnetic wave propagation in a two dimensional dielectric grating, consisting of a periodic array of rectangular dielectric waveguides, is examined here using the moment method with an adequate electric field expansion inside each rectangular dielectric waveguide. The free space Green's function is obtained by using the volume equivalence theorem. It includes the waveguide coupling through the use of the Floquet's theorem. Curves of normalized phase constant as functions of Floquet's wavenumber are obtained for various waveguide dimensions. Agreement is observed with existing results in the limit of the one dimensional dielectric grating.