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A. R. Forouhi and I. Bloomer deduced dispersion equations for the refractive index, n, and extinction coefficient, k, which were published in 1986 [1] and 1988. [2] The 1986 publication relates to amorphous materials, while the 1988 publication relates to crystalline.
Extinction coefficient refers to several different measures of the absorption of light in a medium: Attenuation coefficient , sometimes called "extinction coefficient" in meteorology or climatology Mass extinction coefficient , how strongly a substance absorbs light at a given wavelength, per mass density
ε is the molar absorption coefficient of that material; c is the molar concentration of those species; ℓ is the path length. Different disciplines have different conventions as to whether absorbance is decadic (10-based) or Napierian (e-based), i.e., defined with respect to the transmission via common logarithm (log 10) or a natural ...
Most commonly, the quantity measures the exponential decay of intensity, that is, the value of downward e-folding distance of the original intensity as the energy of the intensity passes through a unit (e.g. one meter) thickness of material, so that an attenuation coefficient of 1 m −1 means that after passing through 1 metre, the radiation ...
[1]: 128 It is related to the absorption coefficient, , through: [39]: 41 = These values depend upon the frequency of the light used in the measurement. That κ corresponds to absorption can be seen by inserting this refractive index into the expression for electric field of a plane electromagnetic wave traveling in the x -direction.
There are also weaker dependencies on temperature, pressure/stress, etc., as well on precise material compositions (presence of dopants, etc.); for many materials and typical conditions, however, these variations are at the percent level or less. Thus, it's especially important to cite the source for an index measurement if precision is required.
The scattering and reflection spectra of a material are influenced by both its refractive index and its absorption spectrum. In an optical context, the absorption spectrum is typically quantified by the extinction coefficient, and the extinction and index coefficients are quantitatively related through the Kramers–Kronig relations. Therefore ...
where n is the refractive index, λ is the wavelength, A, B, C, etc., are coefficients that can be determined for a material by fitting the equation to measured refractive indices at known wavelengths. The coefficients are usually quoted for λ as the vacuum wavelength in micrometres. Usually, it is sufficient to use a two-term form of the ...