Beam

[1]:

import nexus as nx
import numpy as np

# set beam along pi polarization via initialization parameters
beam = nx.Beam(polarization = 1,
               mixing_angle = 0,
               canting_angle = 90,
               id="my beam",
               profile = "g",   # Gaussian beam profile
               fwhm = nx.Var(0.21, min=0, max=1, fit =True, id="beam fwhm")
               )

print(beam)

print(beam.matrix)
print("")

print(beam.jones_vector)
print("")

print(beam.ComplexCoherence())

Beam
  .id: my beam
  .matrix:
[[0.000000e+00+0.j 6.123234e-17+0.j]
 [6.123234e-17+0.j 1.000000e+00+0.j]]
  .jones_vector:
[[nan+nanj]
 [nan+nanj]]
  .profile: g
  .fwhm (mm): Var.value = 0.21, .min = 0.0, .max = 1.0, .fit: True, .id: beam fwhm
  .Polarization(): 1.0
  .Coherence(): nan
  .PhaseDifference() [sigma - pi](rad): nan

[[0.000000e+00+0.j 6.123234e-17+0.j]
 [6.123234e-17+0.j 1.000000e+00+0.j]]

[[nan+nanj]
 [nan+nanj]]

(nan+nanj)

[2]:

beam = nx.Beam(id="new beam")
beam.CircularLeft()

print(beam)

print(beam.ComplexCoherence())

Beam
  .id: new beam
  .matrix:
[[ 0.5+0.j  -0. -0.5j]
 [ 0. +0.5j  0.5+0.j ]]
  .jones_vector:
[[0.70710678+0.j        ]
 [0.        +0.70710678j]]
  .profile: g
  .fwhm (mm): Var.value = 0.0, .min = 0.0, .max = inf, .fit: False, .id: FWHM
  .Polarization(): 1.0
  .Coherence(): 0.9999999999999998
  .PhaseDifference() [sigma - pi](rad): -1.5707963267948966

(-0-0.9999999999999998j)

[3]:

# set coherency matrix for unpolarized beam
beam.SetCoherencyMatrix(np.array([[1,0], [0, 1]], dtype=complex))

print(beam)

print(beam.ComplexCoherence())

Beam
  .id: new beam
  .matrix:
[[1.+0.j 0.+0.j]
 [0.+0.j 1.+0.j]]
  .jones_vector:
[[nan+nanj]
 [nan+nanj]]
  .profile: g
  .fwhm (mm): Var.value = 0.0, .min = 0.0, .max = inf, .fit: False, .id: FWHM
  .Polarization(): 0.0
  .Coherence(): 0.0
  .PhaseDifference() [sigma - pi](rad): 0.0

0j

[4]:

# set Jones vector for a fully sigma polarized beam
beam.SetJonesVector(np.array([1,0], dtype=complex))

print(beam)

print(beam.ComplexCoherence())

Beam
  .id: new beam
  .matrix:
[[1.+0.j 0.+0.j]
 [0.+0.j 0.+0.j]]
  .jones_vector:
[[1.+0.j]
 [0.+0.j]]
  .profile: g
  .fwhm (mm): Var.value = 0.0, .min = 0.0, .max = inf, .fit: False, .id: FWHM
  .Polarization(): 1.0
  .Coherence(): nan
  .PhaseDifference() [sigma - pi](rad): nan

(nan+nanj)

[5]:

beam.LinearSigma()

beam.Rotate(45)

print(beam)

print(beam.ComplexCoherence())

Beam
  .id: new beam
  .matrix:
[[0.5+0.j 0.5+0.j]
 [0.5+0.j 0.5+0.j]]
  .jones_vector:
[[0.70710678+0.j]
 [0.70710678+0.j]]
  .profile: g
  .fwhm (mm): Var.value = 0.0, .min = 0.0, .max = inf, .fit: False, .id: FWHM
  .Polarization(): 1.0
  .Coherence(): 1.0
  .PhaseDifference() [sigma - pi](rad): 0.0

(1+0j)

[6]:

beam.CircularLeft()

print(beam)

print(beam.Polarization())

print(beam.Coherence())

print(beam.PhaseDifference())

print(beam.ComplexCoherence())

Beam
  .id: new beam
  .matrix:
[[ 0.5+0.j  -0. -0.5j]
 [ 0. +0.5j  0.5+0.j ]]
  .jones_vector:
[[0.70710678+0.j        ]
 [0.        +0.70710678j]]
  .profile: g
  .fwhm (mm): Var.value = 0.0, .min = 0.0, .max = inf, .fit: False, .id: FWHM
  .Polarization(): 1.0
  .Coherence(): 0.9999999999999998
  .PhaseDifference() [sigma - pi](rad): -1.5707963267948966

1.0
0.9999999999999998
-1.5707963267948966
(-0-0.9999999999999998j)