Elliptical polarization

Elliptical polarisation is the generic polarisation state of a monochromatic transverse wave. The electric field vector traces an ellipse in the plane perpendicular to k as the wave oscillates, with the ellipse characterised by its semi-major axis, semi-minor axis, orientation angle, and handedness (left or right). Linear polarisation is the degenerate case where the ellipse collapses to a line (semi-minor = 0); circular polarisation is the degenerate case where the ellipse is a circle (semi-major = semi-minor).

Any coherent superposition of two linear polarisations with a relative phase difference produces elliptical polarisation — zero phase difference gives linear polarisation at an intermediate angle, ±90° with equal amplitudes gives circular, anything else gives an ellipse. The Poincaré sphere provides the standard geometric representation: each point on a unit sphere corresponds to a polarisation state, with poles at RCP/LCP, equator at all linear polarisations, and interior points at elliptical states. Optical components like quarter-wave plates and half-wave plates rotate points on the Poincaré sphere in well-defined ways, which is the basis for every polarisation-analysis instrument from laboratory ellipsometers to satellite polarimetric imagers.