The window crystals

CaF2, MgF2, BaF2 and sapphire (Al2O3) are the window and substrate crystals of ultrafast optics, and N-BK7 its commonest glass. Each recommended model is the Sellmeier formula of its source, made absolute (TC-545, TC-546, TC-651). This page explains the reference-medium corrections, source agreement and temperature limits. Read Solids: conventions and models for the common interface and Quick start for a first calculation.

from optmat.solid.models.registry import default_model, default_reason, models

caf2 = default_model("CaF2")  # daimon_2002/sellmeier_20C, absolute
mgf2_o = default_model("MgF2", "o")  # a uniaxial crystal needs its axis
n = caf2.refractive_index(1030e-9)
beta2 = mgf2_o.gvd(800e-9)  # s^2/m
default_reason("CaF2")  # why this model
models("CaF2")  # every model of CaF2, by name

The recommended models

Material	Axis	Model	Range (nm)	Sample	Index relative to	n at 500 nm	n at 1 µm
CaF2		daimon_2002/sellmeier_20C	138-2326	20 °C	nitrogen, 1013.25 hPa	1.43690	1.42931
MgF2	o	dodge_1984/sellmeier_o	203-7042	19 °C	room air (inferred)	1.38016	1.37396
MgF2	e	dodge_1984/sellmeier_e	203-7042	19 °C	room air (inferred)	1.39207	1.38557
BaF2		malitson_1964/sellmeier	265-10349	25 °C	room air (inferred)	1.47824	1.46895
Al2O3	o	weber_2003/sellmeier_o	220-5001	20 °C	room air (inferred)	1.77475	1.75616
Al2O3	e	weber_2003/sellmeier_e	220-5001	20 °C	room air (inferred)	1.76655	1.74828
N-BK7		schott_2023/sellmeier	313-2326	20 °C, catalogue	air, 1013.3 hPa	1.52184	1.50791

Relative to a gas, made absolute. A prism refractometer measures the index relative to the gas around the prism.

• Daimon & Masumura measured CaF2 in nitrogen at 1013.25 hPa and state it.

• SCHOTT’s catalogue indices are relative to air at 20 °C and 1013.3 hPa, as its Technical Information TIE-29 states.

• The NBS papers (Malitson’s CaF2, BaF2 and sapphire; Dodge’s MgF2; Malitson & Dodge’s sapphire of 1972) measured in room air and do not say so. The reading is supported by CaF2: made absolute, Malitson’s formula agrees with Daimon’s within 3.3e-5 at one temperature, and read as absolute it would be 3.9e-4 low.

Each model multiplies by the index of its gas:

• nitrogen: optmat’s fit/N2 at the ideal-gas density;

• air: Edlén’s dry air.

Treating coefficients measured relative to a gas as absolute indices omits this reference-medium correction (TC-545, TC-546).

Sapphire and N-BK7 come from reprints.

• Sapphire. Malitson & Dodge’s 1972 formulas of both rays appeared only as a talk abstract and in handbooks. optmat reads them in Weber’s Handbook of Optical Materials (2003).

  • They are recommended as a pair, so that the birefringence (0.0091 at 0.3 µm to 0.0056 at 5 µm) comes from one determination, and they reach 220 nm.

  • Malitson’s 1962 formula, fitted to 46 measured ordinary indices at 24 °C, is the check (malitson_1962/sellmeier_o). It lies 5-8e-5 above the ordinary ray at 0.4-2 µm, about what the 4 K difference in temperature gives.

• N-BK7. SCHOTT’s data sheet gives the catalogue formula of a melt of nominal nd and vd. A given melt departs from it by up to its tolerance grade (±5e-4 in the widest). The data sheet’s internal transmittance and dn/dT are curated (schott_2023), but the model is lossless: its index has no imaginary part, and a propagation code that needs the glass’s absorption takes it from the curated transmittance. BK7 (the older catalogue glass) and N-BK7 are distinct materials.

How well each formula holds its paper. With its reference gas removed, each formula reproduces its paper’s table (tests/solid/test_crystals.py):

• Daimon’s reproduces the 69 measured indices within 1.9e-6 (rms 6e-7).

• Dodge’s and Malitson’s reproduce their computed columns to the printed digit, apart from a few printed values their authors do not explain (TC-546).

The papers state their accuracy as follows:

• Daimon: 6e-7 (rms of the fit), with a stated uncertainty per wavelength;

• Dodge: “better than 2e-5”;

• Malitson: 2e-5 to 3e-5.

Temperature. Each model is at its paper’s temperature, between 19 and 25 °C. For CaF2 near room temperature, dn/dT is about −1.1e-5 per K: 4 K moves n by 4e-5, more than the formulas’ uncertainty. daimon_2002/sellmeier_25C gives CaF2 at 25 °C, and Daimon’s measured dn/dT is daimon_2002/dndt.

Not yet recommended: CaF2 beyond 2.33 µm. Use malitson_1963/sellmeier (to 9.7 µm); Daimon’s infrared term is weakly determined.