absorption coefficient (original) (raw)

Definition: a logarithmic measure for the distributed absorption in a medium

Alternative terms: attenuation coefficient, extinction coefficient

Category: article belongs to category general optics general optics

Related: absorptionabsorbancetransition cross-sections

Units: m−1, cm−1

Formula symbol: α

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DOI: 10.61835/y25 Cite the article: BibTex BibLaTex plain textHTML Link to this page! LinkedIn

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Contents

Definition of 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.

Relation to Microscopic Properties

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.

Frequently Asked Questions

What is an absorption coefficient?

The absorption coefficient ($\alpha$) is a measure of how strongly a medium absorbs light per unit of distance. For a path length ($z$), the transmittance through the medium is given by ($\exp(-\alpha z)$), assuming no other losses.

For a medium containing absorbing atoms or ions, the absorption coefficient ($\alpha$) is the product of the density of these absorbers and the absorption cross-section of a single absorber.

What is the difference between an intensity absorption coefficient and an amplitude absorption coefficient?

The absorption coefficient for optical intensity is twice the value of the absorption coefficient for the field amplitude. This factor of two arises because the intensity is proportional to the square of the field amplitude.

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