Exact solution of Helmholtz equation for the case of non-paraxial Gaussian beams.

A new type of exact solutions of the full 3 dimensional spatial Helmholtz equation for the case of non-paraxial Gaussian beams is presented here. We consider appropriate representation of the solution for Gaussian beams in a spherical coordinate system by substituting it to the full 3 dimensional spatial Helmholtz Equation. Analyzing the structure of the final equation, we obtain one of the possible exact solution which is proved to satisfy to such an equation for Gaussian beams. Also the proper examples of implementing of the paraxial approximation for Gaussian beam could easily be obtained for a new type of exact solution of Helmholtz equation