Optical Dispersion Models

The , n (dimensionless) may be expressed as a function of wavelength using an optical dispersion model. 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 () 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.

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 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,

The model, described in Ref. 2, used to calculated the refractive index of air is

where T = Tref and P = Pref and nair,STP is the refractive index of air at standard temperature and pressure. By definition, the standard temperature is Tstd = 15 °C and the standard pressure is Pstd = 101,325 Pa and then (with a CO2 concentration of 0.03%) nair,STP is given by

The built-in optical dispersion models are listed in Table 3-3.

Table 3-3: List of Optical dispersion models
name	expression
Cauchy
Conrady
Herzberger
Schott
Schott extended
Sellmeier
Sellmeier modified, type 1
Sellmeier modified, type 2
Temperature- dependent Sellmeier	, ,

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, μm2, μm3, and so on. The input wavelength can still have any unit; the normalization to microns is done automatically.