Novel reduction of complex surface radiation integrals to contour integrals

J.M.L. Bernard (1)

1 CMLA - Centre de Mathématiques et de Leurs Applications

We develop here an efficient method for the reduction of surface radiation integrals to contour integrals, when we suppose known, as in Physical Optics (PO), the analytic expression of surface currents whose electromagnetic radiation is calculated. Although many authors have studied this problem, we present here an original solution, general and practical, leading to simple non-singular contour expressions (without any special function), valid from infinity to a short distance of the source (near-field case), for large plane or moderately curved surfaces : a) in monostatic case, for the radiation of PO currents carried by a perfectly or imperfectly reflective surface, excited by a point source whose radiation can be of arbitrary pattern, without any approximation in the phase of the integrand, b) in bistatic case, when the integrand has a complex phase which is a quadratic function of the coordinates, as in the case of gaussian beam propagation or in second order phase approximation for the free space Green function at large distance. Comparisons with classic surface integration results show excellent agreements for both cases a) and b).

Domaines: Physique mathématique [math-ph]; Variables complexes [math.CV]; Analyse classique [math.CA]; Electromagnétisme; Acoustique [physics.class-ph]; Mathématiques générales [math.GM]

J.M.L. Bernard. Novel reduction of complex surface radiation integrals to contour integrals. 2017. ⟨hal-01446672v1⟩