A ray-tracing/PMM hybrid approach for determining wave propagation through periodic structures

An approach to apply the ray-tracing method and the periodic moment method (PMM) for determining wave propagation through periodic material structures is presented. The PMM can be used to obtain the reflection and transmission properties of the periodic objects for plane-wave incidence. Those PMM solutions may then be employed in the ray-tracing method to simulate wave propagation, which includes scattering due to periodically distributed bodies. In the ray-tracing/PMM hybrid approach, results of specular reflections/transmissions and grating-lobe scattering at certain angles of incidence over both faces of the periodic structures are first evaluated. Then, those data are used in the ray-tracing program to calculate the effects of waves incident upon sections of periodic material structures. When a ray tube (composed of four rays) illuminates the periodic objects, some reflected and transmitted ray tubes are generated by interpolating the PMM data for each ray. Those ray tubes are then further traced to find their contributions at the location of the receiving antenna. Measurements of waves propagating in a staircase at 900 and 1800 MHz have been performed and compared with the ray-tracing/PMM simulations. Each section of the stairs is modeled as a singly periodic wedge panel having material properties similar to those of the reinforced concrete wall. Good agreements have been obtained.