Poincaré Sphere Lab · Markus Leipe

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Jones vector

Exercise presets

State readout

Input Jones vector ○
Output Jones vector ●
Output Stokes (s₁, s₂, s₃)
Polarization ellipse
Transmitted intensity I / I₀

Conventions used here

|L⟩ = (1, i)/√2 is left circular and sits at the north pole: s₃ = (|E_L|² − |E_R|²)/S₀, exactly as in Aufgabe 8.2.
Wave plates at lab angle θ: M = R(θ)·diag(1, e^{iδ})·R(−θ), so λ/4 at 0° is diag(1, i) and λ/2 at 0° is diag(1, −1). The phase shifter is the birefringent crystal of Aufgabe 8.3 / the LC modulator of Aufgabe 9.2, with adjustable relative phase δ between the V and H components.
A lab angle θ appears at 2θ on the sphere (angle doubling). A retarder rotates the sphere by δ about its eigenstate axis (cos 2θ, sin 2θ, 0) in the equator plane — the dashed line shown during scans.
For a state at rest the output point's ellipse angles are sketched on the sphere: the ψ arc in the equator plane (azimuth) and the χ arc rising to the state vector (ellipticity). Because of angle doubling these arcs span 2ψ and 2χ; the exact numbers are in the state readout.
Polarizers project onto their transmission axis; the state vector is renormalized afterwards (only fully polarized states are shown) while the lost light is tracked in the intensity readout — Malus’s law lives there.
Scan = the chosen angle runs 0° → 180° (a phase shift δ runs 0° → 360°) in 6 s; the trace shows the output of the whole bench, colored by the scanned value. Wave-plate and polarizer angles act with a 180° period, so a single half-turn already sweeps through every distinct state. A polarizer scan always plots the transmitted intensity I / I₀ versus its angle (Malus’s law) — even the constant ½ on circular light is a result worth seeing. Scanning a wave plate or phase shifter plots I / I₀ only when a polarizer downstream actually modulates the beam; otherwise the colour key stays.

Optical axis