SellmeierCauchy

Sellmeier-Cauchy is a dispersion model used in optics to describe how the refractive index of a transparent material varies with wavelength. It combines elements of the Sellmeier equation, which uses resonant terms of the form (S_i λ^2)/(λ^2 − λ_i^2), with a Cauchy-like polynomial that adds extra flexibility through terms in powers of 1/λ^2. The resulting formula provides a practical balance between physical motivation and empirical accuracy, allowing reliable fits over broad spectral ranges.

A common representation is n^2(λ) = 1 + sum over i of (S_i λ^2)/(λ^2 − λ_i^2) plus a sum over k of P_k / λ^{2k}, where λ is the wavelength in micrometers, λ_i are resonance wavelengths, S_i are oscillator strengths, and P_k are coefficients akin to a Cauchy expansion. Other variants may apply the Cauchy-like terms directly to n(λ). Coefficients are material-specific and determined by fitting to measured refractive-index data.

Applications include optical design and simulation for glasses and crystals used in lenses, prisms, coatings, and waveguides. The model is valued for its accuracy in the visible and near-infrared, and for providing smooth, differentiable dispersion curves needed in ray tracing and optimization.

Limitations include potential loss of accuracy outside the fitted wavelength range and dependence on environmental factors such as temperature and pressure. For precise work, temperature-dependent or state-specific fits may be required. See also Sellmeier equation, Cauchy equation, refractive index, and dispersion data in optical handbooks.