Absorption Coefficient

The absorption of light per unit length in a medium is often quantified with an absorption coefficient ($\alpha$), also called attenuation coefficient. For a short propagation length ($z$), where the overall absorption is small, the absorbed power for an incident power ($P_\textrm{in}$) is approximately ($\alpha \: z \: P_\textrm{in}$), and the total transmittance is approximately ($1 - \alpha z$). For longer propagation lengths, the transmittance is ($\exp(-\alpha z)$). (It has been assumed that other processes, leading to scattering or reflection of light, do not occur.)

Note that sometimes one uses absorption coefficients for field amplitudes instead of optical powers or intensities. These are two times smaller than the corresponding intensity absorption coefficients because the intensity is proportional to the square of a field amplitude.

In some cases, one uses a decadic absorption coefficient, which is smaller by the factor ($\ln 10$), so that the absorbance is simply that coefficient times the optical path length.

Note that an exponential decay of light intensity may not only result from absorption, but also from reflection — which is observed, for example, for metals. The exponential decay coefficient should then not be called an absorption coefficient.

If an absorption is caused by absorbing atoms or ions (for example, dopant ions in some transparent glass or crystalline material), the absorption coefficient is the product of the doping density (in units of m⁻³) and the absorption cross-section (in units of m²) at the relevant optical wavelength.