Polarized Electric Fields

Scott Prahl

Feb 2026

This module shows that the basic idea in polarized light is that there is a fixed phase relationship between the electric fields in the horizontal and vertical directions.

Details of the assumptions are given in the Jupyter notebook on Conventions

%config InlineBackend.figure_format = 'retina'

import sys
import numpy as np
import matplotlib.pyplot as plt

plt.rcParams["animation.html"] = "jshtml"

if sys.platform == "emscripten":
    import micropip

    await micropip.install("pypolar")

from pypolar import jones
from pypolar import visualization as vis

2D represention of a 3D vector fields

Light is propagating in the z-direction. The graphs below are x-y cross sections. The horizontal axis corresponds to the \(E_x\) field and the vertical axis is the \(E_y\) field. The graphs can thought of as time exposures: the blue line shows all values that the polarization field can have.

theta = 0
v = jones.field_linear(np.radians(theta))
print("Jones vector for %d° linearly polarized light (horizontal)" % theta)
vis.draw_jones_animated(v, nframes=32)

Jones vector for 0° linearly polarized light (horizontal)

Once Loop Reflect

theta = 90
v = jones.field_linear(np.radians(theta))
print("Jones vector for %d° linearly polarized light (vertical)" % theta)
vis.draw_jones_animated(v, nframes=32)

Jones vector for 90° linearly polarized light (vertical)

Once Loop Reflect

theta = 45
v = jones.field_linear(np.radians(theta))
print("Jones vector for %d° linearly polarized light" % theta)
vis.draw_jones_animated(v, nframes=32)

Jones vector for 45° linearly polarized light

Once Loop Reflect

v = jones.field_right_circular()
print("Jones vector for right circularly polarized light")
vis.draw_jones_animated(v, nframes=32)

Jones vector for right circularly polarized light

Once Loop Reflect

v = jones.field_left_circular()
print("Jones vector for left circularly polarized light")
vis.draw_jones_animated(v, nframes=32)

Jones vector for left circularly polarized light

Once Loop Reflect