November 24, 2014, Monday, 327

Absorption vs Index

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Materials which absorb light have a complex refractive index. Since absorption (and the related quantity attenuation) can be expressed in various units, we list some of the standard conversions here:

Assuming that the complex refractive index is expressed as <math>n+/-i*kappa</math>, where "i" is the square root of -1, and where the sign is chosen by the convention established by the definition of wave propagation. For the present purposes, we use "kappa", which should be understood to be always positive. The following conversions are therefore known, for a layer that has thickness <math>d</math>:

  • Attenuation coefficient [units of 1/length]: <math>\alpha = 4*pi*\kappa/\lambda</math>, where the intensity through a film follows <math>I=I_0 \exp(-\alpha d)</math>
  • Transmittance [-]: <math>T = \exp(-\alpha d)</math>
  • Absorbance, Optical Density [units of log]: <math>O.D. = -log_{10}(\exp(-\alpha d))</math>