Ray solution for near-zone electromagnetic propagation though a periodic wall

A generalized geometrical optics type locally Floquet field expansion is presented for describing the field transmitted through a plane periodic wall when it is illuminated by a nearby antenna. It is developed from a rigorous plane wave spectral integral for the field associated with this problem, and the integral is evaluated asymptotically via a double stationary phase approach. This ray expansion is potentially useful in through wall radar imaging applications. The accuracy and utility of this ray expansion will be demonstrated.