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The Sellmeier Formula in Optics

Overview

The Sellmeier formula, named after Wolfgang von Sellmeier, is a widely used equation to describe the wavelength-dependent refractive index of optical materials such as glass. It is a valuable tool in optics for predicting refractive index over a range of wavelengths.

Formula

The Sellmeier formula is typically expressed as:

n²(λ) = 1 + B₁λ²/(λ² – C₁) + B₂λ²/(λ² – C₂) + …

where n is the refractive index, λ is the wavelength, and B and C are coefficients.

Applications

The Sellmeier equation is used to accurately determine the refractive index of materials across various wavelengths with only a few coefficients. This data is crucial for applications such as evaluating chromatic dispersion and calculating phase-matching configurations for nonlinear frequency conversion.

Modified Equations

There are numerous modified versions of the Sellmeier equation that extend its validity range or incorporate temperature dependencies. These modifications are essential for precise calculations in different optical scenarios.

Alternatives

While the Sellmeier formula is widely used, there are other equations like the Cauchy formula and those by authors such as Schott and Hartmann. These alternatives offer different levels of simplicity and accuracy depending on the material and wavelength range.

Further Research

Researchers continue to explore and develop equations for refractive indices to improve accuracy and applicability in various optical systems. Understanding these formulas is essential for advancements in optics and photonics.

Source: Wikipedia
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