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

AbstractA 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 that governing equations for the components of our solution are represented by the proper Riccati equations of complex value, which has no analytical solution in general case.But we find one of the possible exact solutions which is proved to satisfy to such equations for Gaussian beams