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Quasi-translational addition expressions of prolate scalar wave functions for thin prolate spheroids

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2 Author(s)
Do-Nhat, T. ; Dept. of Electr. & Comput. Eng., Waterloo Univ., Ont., Canada ; MacPhie, R.H.

The conventional, translational addition theorems for both spherical and prolate spheroidal wave functions applied to incoming or outgoing waves possess a well-known convergence sphere near which the addition series fail to converge rapidly. To overcome this deficiency the quasi-translational addition expressions for prolate wave functions are developed by using a physical-geometrical transformation which allows the separation in the azimuthal direction in the translated prolate spheroidal coordinate system. These quasi-translational addition expressions are valid everywhere and, in particular, exhibit a fast convergence characteristics for thin spheroids which are commonly used in physical and engineering applications

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Antennas and Propagation, IEEE Transactions on  (Volume:44 ,  Issue: 7 )