Solutions to Maxwell's Equations using Spheroidal Coordinates

Analytical solutions to the wave equation in spheroidal coordinates in the short wavelength limit are considered. The asymptotic solutions for the radial function are significantly simplified, allowing scalar spheroidal wave functions to be defined in a form which is directly reminiscent of the Laguerre-Gaussian solutions to the paraxial wave equation in optics. Expressions for the Cartesian derivatives of the scalar spheroidal wave functions are derived, leading to a new set of vector solutions to Maxwell's equations. The results are an ideal starting point for calculations of corrections to the paraxial approximation

New Investigation on the Spheroidal Wave Equations

Changing the spheroidal wave equations into new Schro$dinger's form, the super-potential expanded in the series form of the parameter$\alpha$are obtained in the paper. This general form of the super-potential makes it easy to get the ground eigenfunctions of the spheroidal equations. But the shape-invariance property is not retained and the corresponding recurrence relations of the form (4) could not be extended from the associated Legendre functions to the case of the spheroidal functions

Spherical Wave Functions and Certain of Their Properties

Spheroidal wave functions and addition theorem

The application of prolate spheroidal wave functions to the detection and estimation of bandlimited signals

Prolate spheroidal wave functions for solution of Fredholm equation for bandlimited signal detectio