Refractive index n is the parameter that characterizes as optical properties of materials and media. Its value is equal to the ratio of the velocity of electromagnetic wave propagation in a vacuum c to the velocity u of its propagation in the medium considered:
The refractive index depends on frequency, temperature and, for an anisotropic medium, on the direction of radiation transfer.
For dielectrics and semiconductors in a high transparency region, and in the absence of absorption, the refractive index may be defined in accordance with the Snell refraction law as the ratio of sine of the angle (θ1) between the direction of radiation incident from vacuum onto the medium surface and the normal to this surface to the sine of the angle (θ2) between the direction of radiation propagation inside medium and the same normal:
In reality, all media in the spectral range of thermal radiation absorbs it to a certain degree. Therefore, a more general parametric description of optical properties is the complex refractive index N:
where n is the real part of a complex refractive index (proper refractive index), defined by expression (l), and χ is the absorption index. The properties n and χ may be related to the complex dielectric constant of a substance, or to the real dielectric permeability and electrical conductivity. Due to the presence of a sufficient quantity of conducting electrons (free electrons), the metals and other good electric conductors have a high absorption index χ over practically the whole spectral region of thermal radiation. The value of χ usually increases from 2–3 to 10 when the wavelength λ increases from the visible region to the middle infrared region. The refractive index n is more than unity in the whole spectral region and as a rule increases with increasing λ though more slowly than χ.
Dielectrics and semiconductors (including many solid substances, all gases at moderate temperatures and nearly all liquids) have a high transparency region where χ is equal to only 10–7 to 10–5. This occurs between the long wave edge of the electron absorption band and the short wavelength edge of the first lattice absorption band, the maximum being usually located in the ultraviolet region. This value cannot be considered in the complex refractive index. Its real part n in this wavelength region is more than unity and it monotonically decreases with increasing wavelength. Near the maximum absorption bands, the values n and χ are much more. In the band maximum, n may be increased twice or three times, and χ may be increased by orders of magnitude and may reach several units. Along the edge of absorption band there is a wavelength region where n < 1.
Born, M., Wolf, E. (1980) Principles of Optics, 6th edn. Pergamon Press, Oxford.
Handbook of Optical Constants of Solids (1985) E. D. Palik, Ed., Academic Press, New York.
Siegel, R. Howell, J. R. (1992) Thermal Radiation Heat Transfer, 3rd edn., Hemisphere, Washington D. C.