Source code for lasy.profiles.transverse.super_gaussian_profile
from lasy.backend import xp
from .transverse_profile import TransverseProfile
[docs]
class SuperGaussianTransverseProfile(TransverseProfile):
r"""
Class for the analytic profile of a super-Gaussian laser pulse.
More precisely, the transverse envelope corresponds to:
.. math::
\mathcal{T}(x, y) = \exp\left( -\left({\frac{{x^2 + y^2}}{w_0^2}}\right)^{\dfrac{n}{2}} \right)
Parameters
----------
w0 : float (in meter)
The waist of the laser pulse, i.e. :math:`w_0` in the above formula.
n_order : float (in meter)
The shape parameter of the super-gaussian function, i.e. :math:`n` in the above formula.
If :math:`n=2` the super-Gaussian becomes a standard Gaussian function.
If :math:`n=1` the super-Gaussian becomes a Laplace function.
"""
def __init__(self, w0, n_order):
super().__init__()
self.w0 = w0
self.n_order = n_order
def _evaluate(self, x, y):
"""
Return the transverse envelope.
Parameters
----------
x, y : ndarrays of floats
Define points on which to evaluate the envelope
These arrays need to all have the same shape.
Returns
-------
envelope : ndarray of complex numbers
Contains the value of the envelope at the specified points
This array has the same shape as the arrays x, y
"""
envelope = xp.exp(-xp.power((x**2 + y**2) / self.w0**2, self.n_order / 2))
return envelope
