Polarisation

Wave plates and circular light

A wave plate delays one polarisation behind the other. A quarter-wave plate with its axis at 45° to linear light turns it circular: the field rotates as the light travels, and an analyser passes half of it at every angle.

What you are looking at

Horizontal light, a quarter-wave plate at 45°, an analyser and a power meter.

How the bench is set up

Laser, a quarter-wave plate, a polariser as analyser and a power meter.

The theory

A retarder with fast axis at $\alpha$ and retardance $\delta$ has the Jones matrix $R(-\alpha)\,\mathrm{diag}(1, e^{i\delta})\,R(\alpha)$ . For $\delta = \pi/2$ and $\alpha = 45°$ , horizontal light becomes

\tfrac{1}{\sqrt2}\begin{pmatrix}1\\ \pm i\end{pmatrix},

circular light, which passes any analyser with half its power.

What to measure

Analyser power against angle: cos² for linear, flat for circular

Turn the analyser: the meter stays at half the laser power.
Set the plate’s axis to 0°: the light stays linear and the meter follows $\cos^2$ .
Try 22.5°: elliptical light, between the two.

What the model leaves out

The plate is a zero-order plate exactly a quarter-wave at the laser’s wavelength.

Things to try

Change the plate to half-wave: it turns linear polarisation by twice the angle between them.
Hover over the beam after the plate to read its polarisation.

References

E. Hecht (2017), Optics, 5th edition, Pearson.
B. E. A. Saleh and M. C. Teich (2019), Fundamentals of Photonics, 3rd edition, Wiley.

More experiments, and how the lab works, are in the laser lab’s overview.