Simple Jones vector and Jones matrices manipulation

Polarization

By Daniel Côté dccote@cervo.ulaval.ca

Polarization is a simple module to manage optical polarization with Jones and Stokes vectors. You create a JonesVector or use on of the pre-defined ones, then you apply your JonesMatrix or you use one of the many pre-defined ones. You can visualize the field with JonesVector.show()

You need matplotlib, which is a fairly standard Python module and numpy. If you do not have it, installing Anaconda is your best option. Python 3.6 or later is required. There are several ways to install the module:

1. Simplest pip install --upgrade polarization

1. If you need to install pip, download getpip.py and run it with python getpip.py
2. If you download the source of the module, then you can type: python setup.py install

3. From GitHub, you can get the latest version (including bugs, which are 153% free!) and then type python setup.py install

4. If you are completely lost, copying the folder polarization (the one that includes __init__.py) from the source file into the same directory as your own script will work.

• To see the example code, type python -m polarization. The example code is below and will get printed to your console after it has executed.

You can visualize the field with v.show() or v.show("movie.mp4") to save it.

Example of arbitrary polarization (it is a movie, but GitHub does not allow them: movie available here)

from polarization import *

# Define the vector with Ex and Ey
print("\n\nDefine horizontal polarization with JonesVector(Ex=1, Ey=0)")
print("===========================================================")
v = JonesVector(Ex=1, Ey=0) # horizontal
print("Components are {0}".format(v))
v.show()
#v.show("horizontal.mp4") #to save movie

print("\n\nDefine other polarizations with JonesVector(Ex, Ey),\ncan be normalized with .normalize()")
print("====================================================")
v = JonesVector(Ex=1, Ey=1).normalize() # +45°
print("Components are {0}".format(v))
v.show()
#v.show("plus45.mp4") #to save movie

print("\n\nMany predefined vectors exist")
print("=============================")
# Many predefined vectors:
# JonesVector.vertical()
# JonesVector.horizontal()
# JonesVector.plus45()
# JonesVector.minus45()
# JonesVector.rightCircular()
# JonesVector.leftCircular()

print("\nJonesVector.rightCircular()")
print("-----------------------------")
v = JonesVector.rightCircular()
print("Components are {0}".format(v))
v.show()

print("\nJonesVector.leftCircular()")
print("-----------------------------")
v = JonesVector.leftCircular() # Many predefined vectors
print("Components are {0}".format(v))
v.show()

# Arbitrary polarization
print("\n\nArbitrary polarization JonesVector(Ex=1*exp(1j*0.3), Ey=0.5).normalize()")
print("========================================================================")
v = JonesVector(Ex=1*exp(1j*0.3), Ey=0.5).normalize()
print("Components are {0}".format(v))
v.show()

# Many properties are defined:
print("\n\nMany properties to access polarization state")
print("============================================")
print("For vector {0}".format(v))
print("v.orientation (0=horizontal) = {0}".format(v.orientation))
print("v.isLinearlyPolarized        = {0}".format(v.isLinearlyPolarized))
print("v.isEllipticallyPolarized    = {0}".format(v.isEllipticallyPolarized))
print("v.isCircularlyPolarized      = {0}".format(v.isCircularlyPolarized))
print("v.isRightCircularlyPolarized = {0}".format(v.isRightCircularlyPolarized))
print("v.isLeftCircularlyPolarized  = {0}".format(v.isLeftCircularlyPolarized))

# Vectors can be transformed by JonesMatrices
# Any matrix can be created with JonesMatrix(A,B,C,D)
# but there are many predefined matrices:
#
# HorizontalPolarizer(): polarizer at theta=0°
# VerticalPolarizer(): polarizer at theta=90°
# Plus45Polarizer(): polarizer at theta=45°
# Minus45Polarizer(): polarizer at theta=-45°
# HWP(theta=pi/4) : halfwave plate at 45°
# QWP(theta=pi/4) : quarterwave plate at 45°
# RightCircularPolarizer(): right circular polarizer
# LeftCircularPolarizer(): left circular polarizer
# PhaseRetarder(): arbitrary retarder

print("\n\nTransform the JonesVector with JonesMatrices")
print("============================================")
print("horizontal vector going through quarter waveplate")

vIn = JonesVector.horizontal()
v = QWP(theta=pi/4)*vIn

print("Input components are {0}".format(vIn))
print("Output components are {0}".format(v))
print("isCircular {0}".format(v.isCircularlyPolarized))
v.show()

print("\n\nApply several JonesMatrices sequentially")
print("============================================")

vIn = JonesVector.horizontal()
v = HWP(theta=pi/2)*QWP(theta=pi/3)*vIn

print("Input components are {0}".format(vIn))
print("Output components are {0}".format(v))
print("v.isLinearlyPolarized        = {0}".format(v.isLinearlyPolarized))
print("v.isEllipticallyPolarized    = {0}".format(v.isEllipticallyPolarized))
print("v.isCircularlyPolarized      = {0}".format(v.isCircularlyPolarized))
print("v.isRightCircularlyPolarized = {0}".format(v.isRightCircularlyPolarized))
print("v.isLeftCircularlyPolarized  = {0}".format(v.isLeftCircularlyPolarized))
v.show()

print("Malus law example")
print("=================")
x = []
y = []
vIn = JonesVector.horizontal()
for theta in range(0,190,10):
vOut = pol*vIn

x.append(theta)
y.append(vOut.intensity)

plt.title("\n\nMalus Law: horizontal beam intensity after linear polarizer")
plt.xlabel(r"Polarizer orientation $\theta$ from horizontal [°]")
plt.ylabel(r"Intensity [arb. unit]")
plt.plot(x,y,'ko')
plt.show()


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