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Absorption Length

When light is absorbed in a homogeneous medium with a certain absorption coefficient <$\alpha$>, the optical intensity decays exponentially in proportion to <$\exp(-\alpha z)$>, where <$z$> is the propagation distance. (It is assumed that the intensity is not affected by divergence or convergence of a beam.) One defines the absorption length as the inverse of the absorption coefficient. After that propagation length, the intensity decays to <$1/e$> (≈37%) of its initial value. After four absorption lengths, only ≈1.8% of the initial intensity is left.

An optically pumped laser gain medium is often made with a length which is about 2 to 3 absorption lengths at the pump wavelength, so that the pump absorption is sufficiently effective.

The term penetration depth is often used with the same meaning as absorption length, but it should be considered as a more general term because limited penetration into a material may not only result from light absorption, but also from reflection. That is a typical situation for metals, for example, where the rapid decay of intensity is mostly due to reflection.

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• absorption
• absorption coefficient