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 the solution reduces to the paraxial Gaussian beam form. The solution is equivalent to the spherical wave of a combined complex point source and sink but has the advantage of being more directly interpretatable.
© 2000 Optical Society of America
Z. Ulanowski and I. K. Ludlow, "Scalar field of nonparaxial Gaussian beams," Opt. Lett. 25, 1792-1794 (2000)