7.1.5. Interference of a doughnut laser beam: tilted beams.

#! /usr/bin/env python
"""
    Doughnut_tilt.py

    Interference of a non-collinear zero order beam with a  Laguerre-Gauss
    doughnut beam.
    The interferometer could be a Michelson or a Mach Zehnder instrument.

    cc Fred van Goor, may 2020
"""
from LightPipes import *
import matplotlib.pyplot as plt
if LPversion < "2.0.0":
    print(r'You need to upgrade LightPipes to run this script.' + '\n'+r'Type at a terminal prompt: $ pip install --upgrade LightPipes')
    exit(1)

wavelength=632.8*nm #wavelength of HeNe laser
size=10*mm # size of the grid
N=300 # number (NxN) of grid pixels
w0=3*mm # laser beam radius (in waist)
z1=10*cm # length of arm 1
z2=8*cm # length of arm 2
tx=1.0*mrad # tilt of mirror 1

F=Begin(size,wavelength,N)
F1=GaussBeam(F,w0,doughnut=True,x_shift=-0.2*mm)
Phi=Phase(F1)
F2=GaussBeam(F,w0,tx=tx)
F1=Forvard(z1,F1)
F2=Forvard(z2,F2)
F=BeamMix(F1,F2)
I=Intensity(0,F)


#initiate plots:
fig, axs = plt.subplots(nrows=1, ncols=3,figsize=(11.0,5.0))
#axs=_axs.flatten()
s=r'Interference of a doughnut- and a tilted zero-order Gaussian beam.' +'\n'\
r'Forked interference pattern (Michelson interferometer) due to helical phase of doughnut mode.'
fig.suptitle(s)
fig.subplots_adjust(hspace=0.5)

s=r'Interference pattern'
axs[0].imshow(I,cmap='jet'); axs[0].axis('off'); axs[0].set_title(s)
s=r'Phase distribution'+ '\n' + r'of the doughnut beam.'
axs[1].imshow(Phi,cmap='jet'); axs[1].axis('off'); axs[1].set_title(s)
s = r'LightPipes for Python,' + '\n' + 'Doughnut-mode-interference-tilt.py' + '\n\n'\
    r'$\lambda = {:4.1f}$'.format(wavelength/nm) + r' $nm$' + '\n'\
    r'$size = {:4.2f}$'.format(size/mm) + r' $mm$' + '\n'\
    r'$N = {:4d}$'.format(N) + '\n'\
    r'$w_0 = {:4.2f}$'.format(w0/mm) + r' $mm$'+ '\n'\
    r'$z_1 = {:4.1f}$'.format(z1/cm) + r' $cm$' + '\n'\
    r'$z_2 = {:4.1f}$'.format(z2/cm) + r' $cm$' + '\n'\
    r'$t_x = ' + '{:4.2f}$'.format(tx/mrad) + r' $mrad$' + '\n'\
    r'${\copyright}$ Fred van Goor, May 2020'

axs[2].text(-0.18,0.3,s)
axs[2].axis('off')

plt.show()

(Source code, png, hires.png, pdf)