A concise and universal method for deriving arbitrary paraxial and non-paraxial cylindrical Gaussian-type light modes

Abstract

A concise method of deriving expressions for Gaussian-like solutions of the paraxial and d'Alembert equations 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 $\gamma$ beam.

8 pages, 2 figures, ReVTeX

References in corpus (10)

• Hypergeometric-Gaussian Modes
• The role of the Riemann-Silberstein vector in classical and quantum theories of electromagnetism
• Gaussian beams diffracting in time
• Integral transformation solution of free-space cylindrical vector beams and prediction of modified-Bessel-Gaussian vector beams
• A simple and effective method for the analytic description of important optical beams, when truncated by finite apertures
• Cylindrically polarized Bessel-Gauss beams
• On the dual-cone nature of the conical refraction phenomenon
• Exact solution of Helmholtz equation for the case of non-paraxial Gaussian beams
• Knotted trajectories of neutral and charged particles in Gaussian light beams
• Knotted nodal lines in superpositions of Bessel-Gaussian light beams

Cited by in corpus (2)

• Constructing various paraxial beams out of regular and modified Bessel-Gaussian modes
• Paraxial Dirac equation