The Refractive index, real part,
n (dimensionless) may be expressed as a function of wavelength using an optical dispersion model. The
Optical dispersion model for domains outside the selection can be specified in the
Geometrical Optics interface. Domains that are included in the Geometrical Optics interface selection have dispersion models that are specified in the
Medium Properties feature.
where T is the temperature (SI unit: K) and
P is the pressure (SI unit: Pa). The refractive index of air at standard temperature and pressure,
nair,STP, is given by
where, by definition, the standard temperature is Tstd = 15
°C and the standard pressure is
Pstd = 101,325 Pa (and with a CO
2 concentration of 0.03%).
It is important to appreciate that the refractive indices given by manufacturers are often relative to air at a certain temperature and pressure. Therefore, each of the optical dispersion models (except Temperature-dependent Sellmeier) require a reference temperature
Tref (SI unit: K) and pressure
Pref (SI unit: Pa) to be specified. This is interpreted to be the temperature and pressure of the air in which the refractive indices used to generate the model were measured. The reference pressure is absolute. If the reference pressure
Pref ≠ 0, then it is assumed that the dispersion model will give relative refractive indices
nrel (dimensionless). The conversion of refractive index from relative (
nrel) to absolute (
n) is made using a model for the refractive index of air (
nair). That is,
Each model requires a set of coefficients to be specified. These can be determined, for example, by making a least squares fit to a set of refractive index measurements at discrete wavelengths. At least one optical dispersion model (Temperature-dependent Sellmeier) allows the refractive index to be expressed as a function of both wavelength and temperature. All other optical dispersion models may be used together with a thermo-optic dispersion model to calculate temperature-dependent indices. This is discussed in
Thermo-Optic Dispersion Models.
All optical dispersion models assume that coefficients have been determined with expressions where the wavelengths have units of μm. For example, in the Schott model, the coefficients have units
1,
μm,
μm
2,
μm
3, and so on. The input wavelength can still have any unit; the normalization to microns is done automatically.
The Temperature-dependent Sellmeier model (
Ref. 3,
Ref. 4) assumes coefficients based on absolute temperature specified in Kelvin (K).