Stokes parameters

The Stokes parameters are a set of values that describe the polarization state of electromagnetic radiation. They were defined by George Gabriel Stokes in 1852, as a mathematically convenient alternative to the more common description of incoherent or partially polarized radiation in terms of its total intensity (I), (fractional) degree of polarization (p), and the shape parameters of the polarization ellipse. The effect of an optical system on the polarization of light can be determined by constructing the Stokes vector for the input light and applying Mueller calculus, to obtain the Stokes vector of the light leaving the system. The original Stokes paper was discovered independently by Francis Perrin in 1942 and by Subrahamanyan Chandrasekhar in 1947, who named it as the Stokes parameters. The Stokes parameters are a set of values that describe the polarization state of electromagnetic radiation. They were defined by George Gabriel Stokes in 1852, as a mathematically convenient alternative to the more common description of incoherent or partially polarized radiation in terms of its total intensity (I), (fractional) degree of polarization (p), and the shape parameters of the polarization ellipse. The effect of an optical system on the polarization of light can be determined by constructing the Stokes vector for the input light and applying Mueller calculus, to obtain the Stokes vector of the light leaving the system. The original Stokes paper was discovered independently by Francis Perrin in 1942 and by Subrahamanyan Chandrasekhar in 1947, who named it as the Stokes parameters. The relationship of the Stokes parameters S0, S1, S2, S3 to intensity and polarization ellipse parameters is shown in the equations below and the figure at right. Here I p {displaystyle Ip} , 2 ψ {displaystyle 2psi } and 2 χ {displaystyle 2chi } are the spherical coordinates of the three-dimensional vector of cartesian coordinates ( S 1 , S 2 , S 3 ) {displaystyle (S_{1},S_{2},S_{3})} . I {displaystyle I} is the total intensity of the beam, and p {displaystyle p} is the degree of polarization, constrained by 0 ≤ p ≤ 1 {displaystyle 0leq pleq 1} . The factor of two before ψ {displaystyle psi } represents the fact that any polarization ellipse is indistinguishable from one rotated by 180°, while the factor of two before χ {displaystyle chi } indicates that an ellipse is indistinguishable from one with the semi-axis lengths swapped accompanied by a 90° rotation. The phase information of the polarized light is not recorded in the Stokes parameters. The four Stokes parameters are sometimes denoted I, Q, U and V, respectively. If given the Stokes parameters one can solve for the spherical coordinates with the following equations: The Stokes parameters are often combined into a vector, known as the Stokes vector: The Stokes vector spans the space of unpolarized, partially polarized, and fully polarized light. For comparison, the Jones vector only spans the space of fully polarized light, but is more useful for problems involving coherent light. The four Stokes parameters are not a preferred coordinate system of the space, but rather were chosen because they can be easily measured or calculated. Note that there is an ambiguous sign for the V {displaystyle V} component depending on the physical convention used. In practice, there are two separate conventions used, either defining the Stokes parameters when looking down the beam towards the source (opposite the direction of light propagation) or looking down the beam away from the source (coincident with the direction of light propagation). These two conventions result in different signs for V {displaystyle V} , and a convention must be chosen and adhered to.