JonesVektorModell

JonesVektorModell, also known in English literature as the Jones calculus or Jones vector formalism, is a mathematical framework used in classical optics to describe the polarization state of fully coherent light. It represents the transverse electric field as a two-component complex vector, relative to a chosen orthonormal basis such as horizontal and vertical directions. A Jones vector has the form [E_x; E_y], where E_x and E_y are complex amplitudes that encode both magnitude and relative phase. Global phase is not observable; only relative phase and amplitude determine the polarization state.

Optical elements are represented by 2x2 complex Jones matrices, transforming input vectors via E_out = J E_in. Common elements include linear polarizers, waveplates, and rotators; their action is described by specific matrices in the chosen basis. The framework assumes monochromatic, coherent light propagating along a fixed direction, and is valid only for completely polarized light. It cannot describe partially polarized or unpolarized light, nor depolarizing or scattering processes; for those cases Stokes parameters and Mueller calculus are used.

The model is basis-dependent; polarization states such as linear, circular, and elliptical are represented by appropriate Jones vectors, and rotations between bases are accomplished by unitary rotation matrices. It is named after R. Clark Jones, who developed the formalism in the 1940s, and remains widely used in optics and photonics for the analysis and design of polarization optics, fiber optics, and related instrumentation. In German-language contexts it is often referred to as Jones-Vektor-Modell.