New Physical Optics Approach for an Efficient Treatment of Multiple Bounces in Curved Bodies Defined by an Impedance Boundary Condition

Abstract

<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> A new physical optics (PO) formulation is presented to treat radiation and scattering problems of curved bodies, including multiple reflections between the body parts. The approach uses electric and magnetic PO currents that are expanded as exponential terms. These terms are defined by spatially slow-varying amplitude and exponent functions. All the reflections of a multiple bounce contribution are computed by using PO, considering a very efficient recursive scheme to evaluate the PO integrals using quasi-analytical expressions. The complex problem of obtaining the shadowed areas in curved bodies for multiple reflections is avoided, thanks to the electric and magnetic PO currents chosen. These currents extend over the complete area of the body, including lit or shadowed parts. In the lit parts, the currents provide the reflected field, while in the shadow parts, they give a scattered field that, together with the incident field, causes a total null field in the shadows. The currents do not radiate on their back directions. This approach is useful for the analysis of bodies that can be characterized electrically by an impedance boundary condition (IBC). A combination of these currents with the angular Z-buffer (AZB) ray tracing technique makes it possible to analyze simple or complex cases efficiently. </para>