Sellmeier Formula | previous | next | feedback |
Definition: formula for calculating the wavelength-dependent refractive index
For the specification of a wavelength-dependent refractive index of a transparent optical material, it is common to use a so-called Sellmeier formula [1] (also called Sellmeier equation or Sellmeier dispersion formula, after W. Sellmeier). This is typically of the form
with the coefficients Aj and Bj. For example, the refractive index of fused silica can be calculated as [2]
where the wavelength in micrometers has to be inserted.
Such equations are very useful, as they make it possible to quite accurately describe the refractive index in a wide wavelength range with only a few so-called Sellmeier coefficients, which are usually obtained from measured data with some least-square fitting algorithm. Sellmeier coefficients for many optical materials are available in databases. Some caution is advisable when applying Sellmeier formulae in extreme wavelength regions; unfortunately, the validity range of available data is often not indicated.
Sellmeier data are also very useful to evaluate the chromatic dispersion of a material. This involves frequency derivatives, which can be performed analytically or numerically, and are unproblematic with Sellmeier data even for high orders of dispersion, whereas numerical differentiation on the basis of tabulated index data is sensitive to noise.
The literature contains a great variety of modified formulae which are also often called Sellmeier formulae. Extensions to the simple form give above can enlarge the wavelength range of validity, or make it possible to include the temperature dependence of refractive indices.
Bibliography
| [1] | W. Sellmeier, Annalen der Physik und Chemie 143, 271 (1871) |
| [2] | I. H. Malitson, "Interspecimen comparison of the refractive index of fused silica", J. Opt. Soc. Am. 55 (10), 1205 (1965) |
| [3] | D. H. Jundt, "Temperature-dependent Sellmeier equation for the index of refraction, ne, in congruent lithium niobate", Opt. Lett. 22 (20), 1553 (1997) |
See also: refractive index, dispersion
