gaussian_hermite

hcipy.mode_basis.gaussian_hermite(n, m, mode_field_diameter=1, grid=None)

Creates a Gaussian-Hermite mode.

This function evaluates a (n, m) order Gaussian-Hermite mode on a grid. The definition of the modes are the following,

\[\exp{\left(-\frac{r^2}{w_0^2}\right)} H_n\left(\sqrt{2}\frac{x}{w_0}\right) H_m\left(\sqrt{2}\frac{y}{w_0}\right).\]

Here \(w_0\) is the mode_field_radius, which is \(\mathrm{MFD}/2\). This defintion follows the Physicists definition of the Hermite polynomials. The modes are numerical normalized to have a total power of 1.

More details on the Hermite Polynomials can be found on: http://mathworld.wolfram.com/HermitePolynomial.html

Parameters:

nint

The x order.

mint

The y order.

mode_field_diameterscalar

The mode field diameter of the Gaussian-Laguerre mode.

gridGrid

The grid on which to evaluate the mode.

Returns:

Field

The evaluated mode.