Laguerre-Gaussian beam

This function is responsible for the generation of the amplitude map of Laguerre-Gaussian beam. Laguerre-Gaussian beam can be defined by the equation [1,2]:

\(LG^l_{p}=\frac{1}{\sqrt{2}}\left(\frac{\rho}{w_{0}}\right)^{|m|}\exp{\left[\frac{-\rho^2}{w_{0}^2}\right]}\mathbb{L}_{p}^l\exp{[jm\phi]},\)

where \(m\) is a topological charge, \(\mathbb{L}_{p}^l\) is Laguerre polynomial. In this case users can specify the azimuthal and radial indexes \(l,p\) and the beam waist \(w_{0}\). An example below represents: A) Laguerre-Gaussian beam \(l = 1\), \(p = 0\) and \(w_{0} = 1\), B) Laguerre-Gaussian beam \(l = 1\), \(p = 3\) and \(w_{0} = 1\):

[1] Marek Wichtowski. Optyka liniowa. Wydawnictwo Naukowe PWN, Warszawa, 2020.

[2] Rüdiger Paschotta. Beam quality deterioration of lasers caused by intracavity beam distortions. Opt. Express, 14(13):6069–6074, Jun 2006