Jones calculus

Jones calculus represents fully polarized light with complex two-component vectors and models optical elements with matrices acting on those vectors.

Jones vector: A complex two-component vector encoding the amplitude and relative phase of a fully polarized light field. It is the state representation that Jones calculus transforms.
Polarization: The orientation and time evolution of the electric-field oscillations in an electromagnetic wave. Jones vectors encode the polarization state of light.
Polarimetry: The measurement of the polarization properties of light or of materials through which it passes. Jones transformations help model polarization changes measured in optical experiments.
Partially polarized light: Light whose polarization is not fully defined by a single fixed polarization state over the measurement interval. A single Jones vector cannot fully describe this light.
Jones matrix: A complex 2×2 matrix describing a deterministic linear transformation of a fully polarized optical field. It represents each optical element as an operation on Jones vectors.
Coherence (physics): The persistence of a predictable phase relationship between waves or parts of a wave. Jones calculus requires meaningful phase relations between field components.
Ellipsometry: An optical technique that infers material properties by measuring changes in polarization upon reflection or transmission. Jones matrices model the polarization changes used to extract sample properties.
Depolarization: A reduction in the degree of polarization of light caused by averaging, scattering, or optical transformation. Jones matrices alone cannot represent transformations that produce depolarization.
Global phase: A phase factor shared by all components of a wavefunction or field, leaving its relative phases unchanged. Multiplying a Jones vector by one shared phase does not change its polarization state.
Birefringence: A material property in which refractive index depends on the light's polarization direction. It creates phase delays between components, modeled by Jones matrices.

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