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