A concise and universal method for deriving arbitrary paraxial and d'Alembertian cylindrical Gaussian-type light modes. (March 2022) - Radożycki, Tomasz
Highlights: A universal method of obtaining expressions for various paraxial beams is proposed. Expressions for a variety of cylindrical Gaussian-like beams are derived. The applicability for both: paraxial equation and d'Alembert equation is proved. A new beam (g beam) is obtained and briefly studied. Abstract: A concise method of deriving expressions for Gaussian-like solutions of the paraxial and wave equation (i.e. 3 D d'Alembert equation) is presented. This method is based on the Hankel transform. Choosing some Gaussian base functions with slight modifications of the prefactor all basic beams of cylindrical character can be easily obtained. This refers to Gaussian, Bessel-Gaussian, modified Bessel-Gaussian, Laguerre–Gaussian and Kummer-Gaussian (i.e., Hypergeometric-Gaussian) beams although potentially other beams can come into play as well. For instance a new type of a beam that can be derived in this way is described through the incomplete gamma function so it may be called a γ beam.