Polarimeter
Reports polarization state, normalized Stokes parameters, and a visual linear, circular, elliptical, or unpolarized representation.
Open in the canvas →In the real world
Polarization is the direction the electric field oscillates in as light travels. Describing it fully means describing an ellipse — the figure the field vector traces out in the plane transverse to propagation — with its orientation, its ellipticity, and its handedness. The trouble is that this ellipse is an amplitude description, and amplitude is not something a detector can see. Detectors respond to intensity, so the ellipse "can neither be observed nor measured"[1] directly.
George Gabriel Stokes solved this in 1852 by describing the polarization state with four quantities that are all intensities, and so all measurable. The Stokes parameters are, in the modern convention:
Dividing the last three by S₀ gives normalized parameters s₁, s₂, s₃, each between −1 and +1, and these are the Cartesian coordinates of a point on or inside the Poincaré sphere. The equator holds every linear state, the poles the two circular ones, and everything between is elliptical. A lossless waveplate does not change how polarized the light is, only which state it is in, so it moves the point around the surface — which is why the sphere is such a natural way to think about retarders.
The radius of that point is the degree of polarization:
That last point is what makes the Stokes description more than a change of notation. Unpolarized light is not one state; it is an incoherent mixture of states, and mixtures add as Stokes vectors. Two equally strong orthogonal beams superposed give S₁ = S₂ = S₃ = 0 with S₀ unchanged: the sphere's centre, genuinely unpolarized. No single ellipse can represent that, which is why real sources — sunlight, a lamp, an LED — need the Stokes formalism and not the ellipse.
Measuring the four parameters
A polarimeter is whatever apparatus turns the four definitions above into four numbers. The classical method follows them almost literally: send the beam through a rotatable linear polarizer onto a power meter and record the transmitted intensity at a few analyzer angles. With the analyzer at θ and an optional waveplate of retardance φ in front of it, the transmitted intensity is[1]
It works, but Schaefer and colleagues list its weaknesses plainly[1]: the analyzer has to be aligned accurately at each angle, the waveplate has to be inserted and aligned for the last reading, inserting it absorbs light and so changes the very equations being used, and only four data points are taken — so a single bad reading has nothing to average against.
The rotating quarter-wave plate method fixes all four at once. Put the waveplate first and rotate it through an angle θ, keep the analyzer fixed, and record intensity continuously. Nothing is inserted or removed mid-measurement, only one element moves, and the transmitted intensity becomes a truncated Fourier series[1]:
Thorlabs have a short build video that walks through both methods on a real bench, with a polarizer, a quarter-wave plate and a power meter, and shows the actual mounts and the data reduction[2] — a good companion to the algebra above if you intend to assemble one.
Commercial polarimeters mostly avoid moving parts altogether: a division-of-amplitude instrument splits the beam into four paths with fixed analyzers and reads all four detectors at once, and rotating-waveplate designs are still common where speed matters less than cost. Polarimetry underpins fiber and telecom monitoring, stress birefringence measurement in glass and plastics, ellipsometry for thin-film thickness, remote sensing, and polarization-resolved microscopy of ordered biological structure such as collagen.
In OpticalSetup
Every ray in OpticalSetup carries a normalized Stokes vector, and the polarization elements transform it exactly as the Poincaré-sphere picture says they should. A polarizer projects onto its axis by Malus's law in Stokes form, and a waveplate rotates the vector about the axis set by its own fast axis, through an angle equal to its retardance. Prepared states land where they should: a linear source reads (1, 0, 0), the same beam through a quarter-wave plate at 45° reads (0, 0, −1) — circular — and at 22.5° reads (0.5, 0.5, −0.707), still fully polarized.
The polarimeter reports S₀ as the arriving intensity, the three normalized components scaled to it, the degree of polarization, and a plain description of the state. It gets those from the power-weighted mean of every ray landing on its face — which means partially polarized and unpolarized light are representable, even though no individual ray can be either. Two equally strong counter-polarized beams on one face average to the centre of the sphere and are correctly reported as unpolarized, with S₀ undiminished.
The instrument is a shortcut, not a separate physics
This element does not measure anything: it reads out a vector the tracer has been carrying all along. The measurement it stands in for can nevertheless be performed properly on the bench, out of ordinary parts, because the polarizer really does implement I = ½(S₀ + S₁cos2θ + S₂sin2θ) — the same equation the classical method inverts.
Both published methods have been checked against it. Building the classical four-intensity measurement out of a polarizer, a quarter-wave plate and a plain photodetector, then applying S₀ = I(0°)+I(90°) and the rest, recovers the polarimeter's own numbers to better than one part in 10¹⁵. So does the rotating-waveplate method: sixteen intensities through a rotating quarter-wave plate and a fixed analyzer, Fourier-analyzed into A, B, C, D, give back the same Stokes vector. Both are locked in as regression tests, so the shortcut and the honest measurement cannot drift apart.
Waveplates here are perfectly achromatic: a quarter-wave plate applies exactly 90° of retardance at 405 nm and at 1550 nm alike. A real waveplate is quarter-wave only near its design wavelength, with retardance scaling roughly as 1/λ, so a genuine polarimeter's calibration is wavelength-specific and this one's is not. Polarizers are ideal too — perfect extinction on one axis, no leakage, no wavelength dependence, and no insertion loss beyond the projection itself, so the "inserting the waveplate absorbs light" problem that motivates the rotating method cannot be reproduced here.
Nothing depolarizes. Scattering, stress birefringence, thermal effects and multimode fiber all scramble polarization in reality; here the only route to a partially polarized reading is incoherently mixing distinct beams on one detector face. There is no Mueller-matrix generality either: elements apply their specific transformations rather than an arbitrary 4×4 matrix, so diattenuation and depolarization cannot be authored as element properties.
The readout itself is noiseless and instantaneous — no detector noise, no analyzer misalignment, no waveplate retardance error, and none of the systematic error budget that dominates real polarimetry. And because the tracer works in a 2D meridional plane, the Stokes vector is carried as an abstract state attached to rays rather than as a field orientation in three dimensions; it is exact within that model, but it is not a full vector-field treatment.
Related components
References
- B. Schaefer, E. Collett, R. Smyth, D. Barrett and B. Fraher, “Measuring the Stokes polarization parameters,” American Journal of Physics 75(2), 163–168 (2007)
- Thorlabs Insights — “Build a Polarimeter to Find Stokes Values, Polarization State (Viewer Inspired)” (YouTube, 2021): both the classical and rotating-waveplate methods built on a real bench