JonesVektor

Jonesvektor, commonly known as the Jones vector, is a two-component complex vector used in polarization optics to describe the polarization state of completely polarized light. It is written in a chosen orthonormal basis of orthogonal electric-field components, typically horizontal x and vertical y, as [E_x; E_y], where E_x and E_y are complex amplitudes that encode both magnitude and relative phase. The physical electric field can be expressed as E(t) = Re{ (E_x x_hat + E_y y_hat) e^{i ω t} }. Since an overall complex factor is not observable, the Jones vector is defined up to a global phase and scale.

Optical elements act on polarization through Jones matrices, 2x2 complex matrices, so that the output Jones vector is J times the input vector. The representation depends on the chosen basis, and basis changes are accomplished by corresponding unitary transformations. The Jones formalism, or Jones calculus, is particularly convenient for analyzing and designing polarization devices such as waveplates, polarizers, and fiber-optic components when the light is completely polarized.

Jones vectors cannot describe partially polarized or depolarized light; they convey state information only for pure polarization. For partially polarized light, Stokes parameters and Muller calculus are typically used. The development of Jones calculus is attributed to R. C. Jones, whose work in the mid-20th century established a foundational framework for polarization analysis in optics and photonics.