RP Photonics logo
VL logo part of the
Virtual
Library

Encyclopedia of Laser Physics and Technology

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

Sellmeier formula

with the coefficients Aj and Bj. For example, the refractive index of fused silica can be calculated as [2]

Sellmeier formula for the refractive index of fused silica

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

Category: general optics


cover of print encyclopedia

Since October 2008, the Encyclopedia of Laser Physics and Technology is also available in the form of a two-volume book. Maybe you would enjoy reading it also in that form! The print version has a carefully designed layout and can be considered a must-have for any institute library, laser research group, or laser company.

You may order the print version via Wiley-VCH.

arrow
Home New articles Spotlight Feedback Advertising
Categories Search Quiz Glossary Page hits
S

This encyclopedia is provided by
RP Photonics Consulting GmbH.

You can get technical consulting from the author, Dr. Rüdiger Paschotta.

A.L.S. logo

A.L.S. GmbH

Picosecond laser diodes
<30 ps, 375 – 1600 nm, >1 Wp, single shot – 120 MHz

Onefive logo

Onefive

Low-noise
femtosecond,
picosecond,
and tunable single-frequency lasers for OEM and R&D applications.

RP Fiber Power 2.0

RP Fiber Power

This software is a powerful tool for designing fiber amplifiers and fiber lasers.
See the comprehensive description!

EKSMA logo

EKSMA Optics

Supplier of laser components, including optics, laser crystals and optomechanics.

Your Advertisement at This Place

will be seen by many thousands of visitors per month. These banners receive far over 100'000 page hits per month. Check the details.