Snellschem

Snellschem is a theoretical framework in optics and materials science that describes how electromagnetic waves propagate through engineered media with spatially varying refractive indices. It generalizes Snell's law to inhomogeneous and anisotropic materials by incorporating gradient-index profiles, dispersion, and boundary conditions into a unified modelling approach.

The framework emphasizes the role of spatial variation in the optical properties n(r) and the tensorial character of permittivity and permeability. It combines principles from Fermat's principle and Maxwell's equations to predict refraction, refraction-induced focusing, and wavefront shaping in complex media. Snellschem also incorporates losses and bandwidth limitations that arise in real materials.

In practice, Snellschem informs the design of metamaterials, gradient-index lenses, and transformation-optics inspired devices. It is used in simulations to optimize beam steering, flat optics, cloaking concepts, and compact waveguides, where local refractive-index engineering governs wave propagation.

Relationship to related fields: Snellschem intersects with metamaterials, gradient-index optics, transformation optics, and acoustic-wave analogues. While the precise formulations vary among researchers, the core aim is to predict and exploit how spatially tailored media bend and guide waves.

See also: Snell's law; metamaterials; gradient-index optics; transformation optics.