Sellmeier Formula | previous | next | feedback |
Definition: an equation 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 describe fairly accurately 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 equations in extreme wavelength regions; unfortunately, the validity range of available data is often not indicated.
Sellmeier data are also very useful for evaluating the chromatic dispersion of a material. This involves frequency derivatives, which can be performed analytically 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 equations 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. This can be important, for example, for calculating phase-matching configurations for nonlinear frequency conversion.
Bibliography
| [1] | W. Sellmeier, Ann. Phys. Chem. 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
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