Waveplate
A waveplate delays one polarisation against the other: a quarter-wave plate turns linear light circular, and a half-wave plate rotates linear light. Rays pass straight through it; only their polarisation changes.
The model
A waveplate is a thin plane across the beam. It retards the polarisation along its slow axis by \(\Gamma\) waves against the polarisation along its fast axis. With its fast axis at \(\theta\) from p, on the Jones vector \((E_p, E_s)\) it is
\[J(\theta, \Gamma) = \begin{pmatrix} \cos^2\theta + e^{i2\pi\Gamma}\sin^2\theta & \left(1 - e^{i2\pi\Gamma}\right)\cos\theta\sin\theta \\ \left(1 - e^{i2\pi\Gamma}\right)\cos\theta\sin\theta & \sin^2\theta + e^{i2\pi\Gamma}\cos^2\theta \end{pmatrix}.\]- A quarter-wave plate (\(\Gamma = 1/4\)) at 45° turns linear light circular, and circular light linear.
- A half-wave plate (\(\Gamma = 1/2\)) at \(\theta\) rotates linear light by \(2\theta\).
- Any other retardance gives elliptical light.
The matrix acts on each ray, and on each sample of the diffracted field, so a waveplate changes what interferes with what, and how a polarising beam splitter after it divides the light.
A waveplate rolled about its normal by its Roll \(\rho\) turns its axis with it. The roll is counted right-handed about the part’s normal, the opposite way to \(\theta\), so for light along its normal a plate at \(\theta\) rolled \(\rho\) acts as one at \(\theta - \rho\). A plate rolled with a rolled source keeps the same angle to its light.
Settings
| Field | Default | Meaning |
|---|---|---|
length | 25.4 | mm aperture. |
retard | 0.25 | retardance in waves (0.25 quarter-wave, 0.5 half-wave, or any value). |
axis | 45 | degrees: the fast axis from p. |
From the tool's own tables, file format version 1: the names are those in a .jekray file.
Assumptions
- The retardance is taken as given at every wavelength: a zero-order, achromatic plate. A real multi-order plate’s retardance changes with wavelength.
- The plate has no thickness, so it adds no optical path and no refraction.
- The retardance does not change with the angle of incidence.
Related
- Polariser.
- Beam splitter: a half-wave plate before a polarising cube makes a variable splitter.
- Free-space optics: polarisation along a ray.