Stokesparameter

Stokes parameters are a set of four values that provide a complete description of the polarization state of electromagnetic radiation. They were introduced to quantify both fully and partially polarized light in a way that is convenient for experimentation and data analysis. The four parameters are denoted I, Q, U, and V and together form the Stokes vector S = [I, Q, U, V]^T.

The quantities I, Q, U, and V are defined from the electric field components of a light wave, typically expressed as complex amplitudes E_x and E_y for two orthogonal transverse directions. In terms of time-averaged intensities and correlations, the standard definitions are:

I = ⟨|E_x|^2⟩ + ⟨|E_y|^2⟩,

Q = ⟨|E_x|^2⟩ − ⟨|E_y|^2⟩,

U = 2 Re⟨E_x E_y^*⟩,

V = 2 Im⟨E_x E_y^*⟩.

For a fully polarized plane wave with a Jones vector [E_x, E_y], these reduce to I = |E_x|^2 + |E_y|^2, Q = |E_x|^2 − |E_y|^2, U = 2 Re(E_x E_y^*), and V = 2 Im(E_x E_y^*).

Physically, I is the total intensity; Q and U describe linear polarization with reference to axes, while V describes circular polarization. The degree of polarization is p = sqrt(Q^2 + U^2 + V^2) / I, and the angle of linear polarization is χ = (1/2) arctan2(U, Q). Ellipticity is related to V.

Under rotation of the polarization reference frame by angle θ, Q and U transform as Q' = Q cos 2θ + U sin 2θ and U' = −Q sin 2θ + U cos 2θ, while I and V remain the same. Stokes parameters also form the basis of the Mueller calculus used to describe the effect of optical elements on polarization. Applications span astronomy, remote sensing, and optical communications.