Intrinsic method for the evaluation of beam shape coefficients in spheroidal coordinates for on-axis standard configuration

The generalized Lorenz-Mie theory for spheroids requires the evaluation of beam shape coefficients in spheroidal coordinates. Up to now, this task has been performed by using an extrinsic method in which beam shape coefficients in spheroidal coordinates are expressed in terms of beam shape coefficients in spherical coordinates. For various reasons, in particular with the aim of developing localized beam models in spheroidal coordinates, it would be desirable to possess an intrinsic method as well, in which beam shape coefficients in spheroidal coordinates would be directly expressed in spheroidal coordinates. The aim of the present paper is to provide a solution to the evaluation of beam shape coefficients in spheroidal coordinates by using an intrinsic method, for the case of an on-axis standard configuration and, for the first time, to present numerical results for an intrinsic method in spheroidal coordinates.