gaussian_laguerre

hcipy.mode_basis.gaussian_laguerre(p, l, mode_field_diameter=1, grid=None)

Creates a Gaussian-Laguerre mode.

This function evaluates a (p,l) order Gaussian-Laguerre mode on a grid. The definition of the modes are the following,

\[\exp{\left(-\frac{r^2}{w_0^2}\right)} L_p^{|l|}\left(\frac{2r^2}{w_0^2} \right) \left(\sqrt{2}\frac{r}{w_0}\right)\]

Here \(w_0\) is the mode_field_radius, which is \(\mathrm{MFD}/2\). And \(L_p^{|l|}\) are the generalized Laguerre Polynomials. All modes are numerical normalized to have a total power of 1.

More details on generalized Laguerre Polynomials can be found on: http://mathworld.wolfram.com/AssociatedLaguerrePolynomial.html

Parameters

pint

The radial order.

lint

The azimuthal order.

mode_field_diameterscalar

The mode field diameter of the mode.

gridGrid

The grid on which to evaluate the mode.

Returns

Field

The evaluated mode.