Scalar field of non-paraxial Gaussian beams
A family of closed form expressions for the scalar field of strongly focused Gaussian beams in oblate spheroidal coordinates is given. The solutions satisfy the wave equation and are free from singularities. The lowest order solution in the far field closely matches the energy density produced by a sine condition, high-aperture lens illuminated by a paraxial Gaussian beam. At the large waist limit it reduces to the paraxial Gaussian beam form. It is equivalent to the spherical wave of combined complex point source and sink but has the advantage of more direct interpretation.