Super-Gaussian Transverse Profile

Used to define a super-Gaussian transverse laser profile.

The shape of the profile is characterised by the waist \(w_0\) and by one “order parameter” \(n\), where \(n=2\) gives a standard Gaussian profile, and the profile converges to a flat-top when \(n\) goes to infinity.

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class lasy.profiles.transverse.SuperGaussianTransverseProfile(w0, n_order)

Class for the analytic profile of a super-Gaussian laser pulse.

More precisely, the transverse envelope corresponds to:

\[\mathcal{T}(x, y) = \exp\left( -\left({\frac{{x^2 + y^2}}{w_0^2}}\right)^{\dfrac{n}{2}} \right)\]

Parameters:

w0float (in meter)

The waist of the laser pulse, i.e. \(w_0\) in the above formula.

n_orderfloat (in meter)

The shape parameter of the super-gaussian function, i.e. \(n\) in the above formula. If \(n=2\) the super-Gaussian becomes a standard Gaussian function. If \(n=1\) the super-Gaussian becomes a Laplace function.