Closed-Form Dyadic Green’s Functions for Dipole Excitation of Planar Periodic Structures

The analysis of a single source in the vicinity of periodic structures is a very challenging task since the aperiodic source forbids a direct application of a periodic analysis method to the problem. Full wave methods addressing these problems involve infinite summations and double integrations which make the analysis cumbersome. Homogenization based methods reduce this complexity but at the expense of a loss of accuracy and flexibility in handling different kinds of structures. Moreover, the resulting Green’s functions still need integrations as opposed to being in closed-form. In this paper, a novel approach is proposed to obtain closed-form expressions for the Green’s functions of single sources over periodic structures which makes the analysis of these problems efficient while offering more accuracy and flexibility compared to existing homogenization methods in the literature. To compute the fields scattered by the periodic structure, the reflection coefficients are numerically computed for TE and TM polarized incident plane waves with different angles of incidence and they are approximated by complex exponentials. Approximated reflection coefficients are used in conjunction with the plane wave expansion of the fields radiated by the dipole so that the scattered fields can be expressed in closed-form by utilizing Bessel integral identities.