Super Gaussian beam

Super Gaussian beam equation, assuming that the propagation path equals 0 (z=0), is [1]:

\(E(x,y,z=0) = exp\left[-2\cdot\left(\frac{-\rho^2}{w_{0}^2}\right)^{Gi}\right]\), where \(\rho = \sqrt{x^2+y^2}\)

The \(w_{0}\) is a beam waist and parameter \(Gi\) is an order of Super-Gaussian beam, both of them users can control. Where for \(Gi=1\) Super-Gaussian beam becomes regular Gaussian beam.

The generated amplitude map is presented below, A) for \(w_{0}=2, \\ Gi=2\) and B) \(w_{0}=2, \\ Gi=6\), both \(blazed\) \(grating\) with \(x,y=300\) :

[1] Parent, A., Morin, M. & Lavigne, P. Propagation of super-Gaussian field distributions. Opt Quant Electron 24, S1071–S1079 (1992). https://doi.org/10.1007/BF01588606