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Approximate modeling of scattering by systems of coaxial prolate spheroids

In this paper, an approximate method is described for solving the problem of electromagnetic scattering by two coaxial prolate spheroids, with their major axes along the common axis. The incident wave is considered to be a monochromatic uniform plane electromagnetic wave of arbitrary polarization, and angle of incidence. The method is based on the exact solution to scattering of a plane wave by a single spheroid. To account for the multiple interactions between the spheroids, the total field seen by each spheroid is written as the sum of the fields corresponding to the incident plane wave and to another plane wave of unknown magnitude propagating along the common axis from the other spheroid. Thus the total far field scattered by each spheroid can be written as the sum of the field scattered due to the incident plane wave and the field scattered due to the plane wave of unknown magnitude, propagating axially. The total far field scattered by one spheroid can also be written as the sum of the field scattered by that spheroid due to the incident plane wave and the field scattered due to the total far field scattered by the other spheroid, acting as an incident plane wave on the first spheroid. Equating the two different expressions of the total far field scattered by each of the spheroids, corresponding to transverse electric (TE) and transverse magnetic (TM) polarizations separately, yields a set of simultaneous linear equations, whose solution gives finally the total far scattered field at any given point in space.