Stokesvector

The Stokes vector, or Stokes parameters, is a four-element vector that describes the polarization state of electromagnetic radiation. It is commonly written as S = (S0, S1, S2, S3)T, where S0 is the total intensity and S1, S2, S3 encode the polarization content.

The standard definitions relate the components to measured intensities after polarization analysis. S1 = I0° − I90°, S2 = I45° − I135°, and S3 = IR − IL, where Iθ denotes the intensity after a linear polarizer oriented at θ degrees (0° horizontal, 90° vertical, 45° and 135° at ±45°) and IR/IL denote intensities after right- and left-handed circular analyzers. S0 equals the total intensity, equivalently S0 = I0° + I90° = I_H + I_V. In many texts the notation I, Q, U, V is used, with S0 = I, S1 = Q, S2 = U, S3 = V.

The degree of polarization is DoP = sqrt(S1^2 + S2^2 + S3^2) / S0; light is completely polarized when DoP = 1. Stokes parameters are real-valued and can be related to the 2×2 coherency (density) matrix; fully polarized light can also be treated with Jones calculus as a special case.

Optical elements transform polarization according to Mueller calculus: S_out = M S_in, where M is the 4×4 Mueller matrix of the element. The Stokes vector is widely used in optics, astronomy, remote sensing, and communications to characterize and analyze partially polarized light. The concept was introduced by George Gabriel Stokes in 1852.