Abstract

For non-conducting passive two-dimensional dielectric periodic structures, the wave equation with a source term J(x,y,t) for an electric dipole can be written as, where $J(\text{x},\text{y},\text{t})=J(\text{x},\text{y})\text{J}(\text{t})=I_0\Omega d\delta \left(\text{x}-{\text{x}}_0\right)\left(\text{y}-{\text{y}}_0\right)\theta (\text{t}){\text{e}}^{-i\Omega \text{t}}$. The dyadic Green's function $\overline{G}\left(\text{x},\text{y},\text{t};{\text{x}}^{\prime },{\text{y}}^{\prime },{\text{t}}^{\prime }\right)$ satisfies, $\overline{G}\left(\text{x},\text{y},\text{t};{\text{x}}^{\prime },{\text{y}}^{\prime },{\text{t}}^{\prime }\right)$ can be constructed with the eigen solutions of the homogeneous wave equation, The eigen solutions of (4) with properly normalized eigenvectors can be readily obtained by the plane wave method.

© 1995 Optical Society of America