MuellerJoneskalkulus

MuellerJoneskalkulus is a theoretical framework in polarization optics that seeks to unify Mueller calculus, which uses Stokes parameters and 4x4 Mueller matrices, with Jones calculus, which uses 2x2 complex Jones vectors for fully polarized light. The goal is to provide a single algebraic language for describing how optical elements transform polarization states across the entire range from fully polarized to partially depolarized light.

In practice, the framework introduces a joint state representation that couples the Jones vector with a corresponding Stokes-like descriptor, enabling direct translation between the Jones and Mueller formalisms. Transformation rules are defined so that pure Jones matrices reduce to standard Jones transformations, while depolarizing effects are captured through additional mixed-state operators.

Benefits include a more seamless modeling of devices that exhibit both diattenuation and depolarization, and the ability to propagate mixed states through multi-layer systems without switching representations. Applications appear in ellipsometry, polarization microscopy, remote sensing, and optical communications.

Limitations include that not all Mueller matrices admit a Jones decomposition, and the hybrid algebra can be more complex to implement. The approach is not yet standardized and remains mainly theoretical.

Origin and status: the term appears in theoretical discussions and is not widely adopted; some researchers reference it as a conceptual bridge rather than a fully established formalism.