Stokes parameters
Set of values describing polarization state of electromagnetic radiation.
The Stokes parameters are four numbers that characterize the polarization of light. They were introduced by George Gabriel Stokes in 1851 as a more mathematically convenient way to describe partially polarized or incoherent light compared to using total intensity, degree of polarization, and the polarization ellipse. To find out how an optical system affects light's polarization, you can build a Stokes vector for the incoming light and use Mueller calculus to calculate the Stokes vector for the outgoing light. These parameters can be measured directly from observable effects. Stokes' original work was independently rediscovered by Francis Perrin in 1942 and by Subrahmanyan Chandrasekhar in 1947, who gave them their current name.
The parameters are usually labeled S₀, S₁, S₂, and S₃ (sometimes written as I, Q, U, and V). S₀ equals the total intensity I. The other three form a three-dimensional vector whose spherical coordinates are given by the degree of polarization p (which ranges from 0 to 1) and the angles 2ψ and 2χ. The factor of 2 in front of ψ accounts for the fact that a polarization ellipse rotated by 180° looks the same, while the factor of 2 in front of χ accounts for the fact that swapping the semi-axis lengths and rotating by 90° also yields an indistinguishable ellipse. The Stokes parameters do not record the phase of the polarized light. Given the Stokes parameters, you can recover the spherical coordinates using the equations: I = S₀, p = √(S₁² + S₂² + S₃²) / S₀, and 2ψ = arctan(S₂ / S₁).
- defined_by
- George Gabriel Stokes
- field
- Polarization of electromagnetic radiation
- known_for
- Stokes parameters, Stokes vector, Mueller calculus
Lore & Background
The Stokes parameters are a set of four values, commonly denoted I, Q, U, and V, that describe the polarization state of electromagnetic radiation. They were defined by George Gabriel Stokes in 1851. The original paper was independently rediscovered by Francis Perrin in 1942 and by Subrahamanyan Chandrasekhar in 1947, who gave them their current name. The parameters are often combined into a vector known as the Stokes vector, which can describe unpolarized, partially polarized, and fully polarized light. This is in contrast to the Jones vector, which only describes fully polarized light. The parameters can be determined from directly observable phenomena, with each parameter corresponding to a sum or difference of measurable intensities. The effect of an optical system on the polarization of light can be determined by applying Mueller calculus to the Stokes vector of the input light. There is an ambiguous sign for the V component depending on the physical convention used, either looking down the beam towards the source or away from it; a convention must be chosen and adhered to. The Stokes parameters provide a mathematically convenient alternative to describing incoherent or partially polarized radiation in terms of its total intensity, fractional degree of polarization, and the shape parameters of the polarization ellipse. The phase information of the polarized light is not recorded in the parameters.
Reader's Guide
The Stokes parameters are significant because they offer a complete and practical description of the polarization state of light, including partially polarized and unpolarized light, which is not easily handled by other methods. They are directly observable and can be used to calculate the effect of optical systems on light through Mueller calculus. The four parameters, often denoted I, Q, U, and V, correspond to total intensity and three components describing polarization. Their legacy is foundational in fields such as astronomy, remote sensing, and optics, enabling precise analysis of light from sources like stars and atmospheric particles. The parameters are constrained by the degree of polarization p, which ranges from 0 to 1, and the phase information of polarized light is not recorded in them.
Did You Know?
- The four Stokes parameters are sometimes denoted I, Q, U, and V.
- The Stokes parameters can be determined from directly observable phenomena.
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