slmsuite.holography.toolbox.phase.laguerre_gaussian#

laguerre_gaussian(grid, l, p=0, w=None)[source]#

Returns the phase farfield for a Laguerre-Gaussian beam. Uses the formalism described by this paper.

Note

Without radial order (p = 0), this function distills to a vortex waveplate of given azimuthal order l.

Tip

This function is especially useful to hone and validate SLM alignment. Perfect alignment will result in concentric and uniform fringes for higher order beams. Focusing issues, aberration, or pointing misalignment will mitigate this.

Parameters:

grid ((array_like, array_like) OR SLM) – Meshgrids of normalized \(\frac{x}{\lambda}\) coordinates corresponding to SLM pixels, in (x_grid, y_grid) form. These are precalculated and stored in any SLM, so such a class can be passed instead of the grids directly.
l (int) – The azimuthal wavenumber, or orbital angular momentum. Can be negative.
p (int) – The radial wavenumber. Should be non-negative.
w (float OR None) – See _determine_source_radius().

Returns:

The phase for this function.

Return type:

numpy.ndarray