Sellmeier Equation Calculator

Enter the wavelength (λ) and the three pairs of Sellmeier coefficients (B1, B2, B3, C1, C2, C3) to compute the refractive index of a transparent optical medium. The Sellmeier Equation Calculator applies the empirical dispersion formula n² = 1 + ΣBᵢλ²/(λ²−Cᵢ) and returns both n² and the refractive index n. Pre-loaded with standard fused silica (quartz) coefficients so you see results right away.

Select a preset to auto-fill coefficients, or choose Custom to enter your own.

μm

Wavelength of light in micrometres (μm). Visible range: 0.38–0.78 μm.

First oscillator strength coefficient (dimensionless).

Second oscillator strength coefficient (dimensionless).

Third oscillator strength coefficient (dimensionless).

μm²

First resonance wavelength squared (μm²).

μm²

Second resonance wavelength squared (μm²).

μm²

Third resonance wavelength squared (μm²).

Results

Refractive Index (n)

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n² (Refractive Index Squared)

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Term 1 Contribution (B1λ²/(λ²−C1))

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Term 2 Contribution (B2λ²/(λ²−C2))

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Term 3 Contribution (B3λ²/(λ²−C3))

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Sellmeier Term Contributions to n²

Frequently Asked Questions

What is the Sellmeier equation?

The Sellmeier equation is an empirical relationship between the refractive index and wavelength of light for a transparent optical medium. It is expressed as n²(λ) = 1 + Σ Bᵢλ²/(λ²−Cᵢ), where B and C are material-specific Sellmeier coefficients determined experimentally. It accurately models chromatic dispersion across a wide wavelength range.

What are B and C coefficients in the Sellmeier equation?

The B coefficients (B1, B2, B3) are dimensionless oscillator strengths related to the electronic resonances of the material. The C coefficients (C1, C2, C3) have units of μm² and represent the squared resonance wavelengths. Together they characterise how a specific material disperses light.

What units should I use for wavelength in this calculator?

This calculator uses micrometres (μm) for wavelength. The visible light spectrum spans approximately 0.38–0.78 μm. Ensure your C coefficients are also expressed in μm² so the units remain consistent throughout the Sellmeier formula.

What are the Sellmeier coefficients for fused silica (quartz)?

For fused silica, the standard Sellmeier coefficients are B1 = 0.6961663, B2 = 0.4079426, B3 = 0.8974794, C1 = 0.0684043 μm², C2 = 0.1162414 μm², and C3 = 9.896161 μm². These values are pre-loaded as the default preset in this calculator.

What are the Sellmeier coefficients for silicon?

Silicon's Sellmeier coefficients for the infrared range are approximately B1 = 10.6684293, B2 = 0.0030434748, B3 = 1.54133408, C1 = 0.301516485 μm², C2 = 1.13475115 μm², and C3 = 1104 μm². Note that silicon is not transparent in the visible spectrum, so the equation applies in the near- and mid-infrared.

What is the Sellmeier equation used for in optics?

The Sellmeier equation is widely used in optics and photonics to model chromatic dispersion, design optical fibres, lenses, and laser crystals, and to calculate group velocity dispersion (GVD). It is fundamental for predicting how different wavelengths of light travel through a material at different speeds.

Why does the Sellmeier equation use three terms?

Three terms are typically sufficient to accurately model the dispersion of most optical glasses and crystals across their transparency window. Each term corresponds to a different absorption resonance (electronic or vibrational). More or fewer terms can be used depending on the material and the required accuracy.

What happens if λ² equals one of the C coefficients?

If λ² equals Cᵢ, the denominator of that term becomes zero, causing a singularity. This corresponds to a resonance absorption wavelength of the material — light at that wavelength is strongly absorbed rather than transmitted. Physical Sellmeier models are only valid in regions away from these absorption resonances.

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