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Exact solution of Helmholtz equation for the case of non-paraxial Gaussian beams
Journal of King Saud University: Science
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 that governing equations for the components of our solution are represented by the proper Riccati equations ofdoi:10.1016/j.jksus.2015.02.005 fatcat:mguqoifvsvc7hfvb77c24ohzim