materialdispersion

Material dispersion refers to the wavelength dependence of a material's refractive index, n(λ), which causes light of different wavelengths to propagate at different speeds as it travels through the same medium. In many transparent materials across the visible and near-infrared ranges, n decreases with increasing wavelength (normal dispersion). As a result, shorter wavelengths experience greater slowing than longer wavelengths, leading to effects such as chromatic aberration in lenses and pulse broadening in broadband or ultrafast optical systems.

The propagation speed of a light pulse in a material is set by the group velocity, v_g = c / n_g, where c is the vacuum speed of light and n_g is the group index given by n_g = n(λ) − λ dn/dλ. Thus dispersion is tied to how n and its slope dn/dλ change with wavelength. A common way to model n(λ) is the Sellmeier equation, n^2(λ) = 1 + Σ (A_i λ^2)/(λ^2 − B_i^2), with material-specific coefficients A_i and B_i. This relation allows calculation of dispersion across wavelengths and identifies zero-dispersion wavelengths where dn/dλ = 0. For silica, the zero-dispersion wavelength lies near 1.3 μm, with dispersion changing sign beyond that point.

Material dispersion is distinct from waveguide dispersion, which arises from a fiber or waveguide’s geometry. In optical fibers, total dispersion is the sum of material and waveguide dispersion; controlling it is essential for high-speed communications and broadband optical systems.

Applications and relevance include lens design, prisms, spectroscopy, and fiber-optic communications, where materials with low or tailored dispersion improve performance.