finesse.cymath.laguerre.compute_lg_mode

finesse.cymath.laguerre.compute_lg_mode(int p, int l, double w0, double z, double wavelength, ndarray x, ndarray y, helical=True) → np.ndarray[np.complex128]

Compute a Laguerre-Gaussian mode.

Parameters

pint

Radial index of the Laguerre-Gaussian mode.

lint

Azimuthal index of the Laguerre-Gaussian mode.

w0double

Beam waist.

zdouble

Propagation distance.

wavelengthdouble

Wavelength of the beam.

xnp.ndarray[double, ndim=1]

Array of x-coordinates.

ynp.ndarray[double, ndim=1]

Array of y-coordinates.

helicalbool

True if this is a helical LG mode, False for Sinusoidal

Returns

np.ndarray[np.complex128]

2D array of complex values representing the Laguerre-Gaussian mode at the given coordinates.

Examples

>>> import finesse
>>> from finesse.cymath import laguerre as lg
>>> import numpy as np
>>> import matplotlib.pyplot as plt
>>> finesse.init_plotting()
>>>
>>> fig, axes = plt.subplots(3, 3, figsize=(8, 8))
>>>
>>>  w0 = 1e-3
>>>  z = 0
>>>  x = np.linspace(-4 * w0, +4 * w0, 50)
>>>  y = np.linspace(-4 * w0, +4 * w0, 51)
>>>  X, Y = np.meshgrid(x, y)
>>>  helical = False  # whether to plot helical LG modes or sinusoidal LG modes
>>>
>>> for i, p in enumerate([0, 1, 2]):
>>>    for j, l in enumerate([0, 1, 2]):
>>>        E = lg.compute_lg_mode(p, l, w0, z, 1064e-9, x, y, helical)
>>>        intensity = np.abs(E) ** 2
>>>        ax = axes[i, j]
>>>        C = ax.contourf(X, Y, intensity.T, levels=100)
>>>        C.set_edgecolor("face")
>>>        ax.set_title(f"LG Mode p={p}, l={l}")
>>>        ax.set_aspect("equal")
>>>
>>> for ax in axes.flatten():
>>>     ax.set_xticks([])
>>>     ax.set_yticks([])
>>> plt.tight_layout()
>>> plt.show()