Material Dispersion (Sellmeier)
Refractive index, group index, GVD β₂ and dispersion D from published Sellmeier formulas for crystals, fused silica, IR glasses and SCHOTT glasses, with their coefficients and an n(λ) comparison.
Refractive index n
1.44402
Group index n_g
1.46260
n − λ dn/dλ
dn/dλ
-0.01198 /µm
GVD β₂
-27.95 fs²/mm
-27.95 ps²/km
Dispersion D
21.91 ps/(nm·km)
anomalous (β₂ < 0)
Zero-dispersion λ
1272.8 nm
d²n/dλ² = 0
Phase and Group Index
Material Dispersion D
Compare materials: n(λ)
Each curve covers its own fit range; the thick one is Fused silica (SiO₂).
Coefficients: Fused silica (SiO₂)
n² = A + Σ Bᵢλ²/(λ² − Cᵢ), λ in µm. Sets published with resonance wavelengths λᵢ (Cᵢ = λᵢ²) or in the pole form A′ + Σ Bᵢ′/(λ² − Cᵢ) are shown converted to this form.
| i | Bᵢ | Cᵢ (µm²) | √Cᵢ (µm) |
|---|---|---|---|
| A | 1 | ||
| 1 | 0.6961663 | 0.00467914826 | 0.0684043 |
| 2 | 0.4079426 | 0.0135120631 | 0.1162414 |
| 3 | 0.8974794 | 97.9340025 | 9.896161 |
Model
n² = A + Σ Bᵢλ²/(λ² − Cᵢ), β₂ = λ³/(2πc²) · d²n/dλ², D = −(λ/c) · d²n/dλ²
Fused silica (SiO₂): I. H. Malitson, J. Opt. Soc. Am. 55, 1205 (1965), 20 °C; fit range 210.0–6700 nm. The derivatives are analytic. Exact for the published formula within its range; the formula itself is a fit to measurements (typically ±1e-5 to ±1e-4 in n).
Model and references
Exact. The equations are exact within the stated assumptions, or are a standard's tabulated values. The results are as good as the inputs. About the tiers
Exact for the published Sellmeier formula inside its fit range, with analytic derivatives. The formula is itself a fit to measurements (typically ±1e-5 to ±1e-4 in n) at the temperature of those measurements.
- refractiveindex.info database (CC0). Sellmeier data sets for fused silica, As₂S₃ and ZBLAN glass and thirteen crystals, each with its original reference shown on the page.
- SCHOTT optical glass catalog (Zemax AGF 2017-01-20). Sellmeier coefficients of 10 glasses.
- Agrawal G. P. Nonlinear Fiber Optics, §1.2.3. Group-velocity dispersion β₂ and dispersion parameter D.
- Saleh B. E. A., Teich M. C. Fundamentals of Photonics, ch. 5. Dispersion parameter D.
- Malitson I. H. (1965). Interspecimen comparison of the refractive index of fused silica. J. Opt. Soc. Am. 55, 1205. doi:10.1364/JOSA.55.001205
- Peter F. (1923). Über Brechungsindizes und Absorptionskonstanten des Diamanten zwischen 644 und 226 mµ. Z. Phys. 15, 358. doi:10.1007/BF01330487