A plane wave expansion theorem for cylindrically radiated fields

Summary An asymptotic expansion for two-dimensional outwardly radiating fields is developed from an integral representation of these fields by means of a saddle point integration. The expansion is given in terms of inverse powers of the distance from a point in a fixed region to a point in a circular neighborhood at a large distance from that region. The coefficients are expressed in terms of plane waves and linear combinations of derivatives of plane waves with respect to angle of incidence. The theorem may be employed in scattering problems in reducing scattering of arbitrary two-dimensional fields by arbitrary cylinders to scattering of plane waves by the arbitrary cylinders. Research supported by contract AF19 (628) 3868 with Air Force Cambridge Research Laboratories. The initial research was carried out while one of the authors (N. R. Zitron) was at Harvard University.