Polarimetry Bench

What is modelled

Fully polarized monochromatic light is described by a Stokes vector (S0, S1, S2, S3). An optical rotator turns the linear axis, a linear retarder delays one component and can make the light elliptical, and an ideal analyzer passes the component along its axis.

Equations

• Linear input S = (1, cos 2ψ, sin 2ψ, 0).
• Analyzer I = ½ (S0 + S1 cos 2α + S2 sin 2α), which reduces to Malus's law cos2(α - ψ) for linear light.
• Retarder: rotate Q/U into the fast-axis frame, then rotate U/V by the retardance.
• Scan fit I = A + B cos 2α + C sin 2α by linear least squares.

Checks run in the page

• Malus's law across many angles.
• The total degree of polarization stays 1 through lossless optics.
• The scan fit recovers the linear polarization fraction.
• Quarter- and half-wave plate behaviour.

Honest simplifications

Ideal monochromatic and fully polarized light, ideal wave plates and a leakage term for the analyzer; no depolarization or wavelength dependence.

• Choose Quarter-wave to circular: the analyzer scan becomes flat because circular light passes every angle equally.
• Choose Pure linear and compare the curve with cos squared.
• Raise the detector noise and see how the fit residual grows while the fitted angle stays close.