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# Transmissivity

Definition: the ratio of transmitted optical power to the incident optical power at a surface

German: Transmissivität

Formula symbol: <$T$>

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The transmissivity of a surface (e.g. an interface between two optical media) is defined as the ratio of transmitted optical power to the incident optical power, as e.g. measured with a light beam. Usually, it is applied to cases with exactly flat unstructured surfaces, i.e., not to cases with extended objects or light scattering.

Strictly speaking, the term transmissivity should be used only for transmission through one particular surface – not for example for transmission through extended objects, such as glass plates or optical resonators; in such cases, the term transmittance is appropriate. However, it is common, for example, to specify transmissivities of laser mirrors, although these are usually dielectric mirrors, involving interferences between reflections from many different optical interfaces. One may actually consider a whole thin-film structure, usually having an overall thickness far below 1 mm, as one surface. A more questionable case is a fiber Bragg grating, which can be far more extended.

Note that for non-normal incidence the ratio of transmitted and incident optical intensity does generally not match the transmissivity. This is essentially because the change of propagation direction due to refraction is also associated with a change in beam area.

## Relation to Transmission Coefficients

The transmission through an optical surface is also often described with a complex transmission coefficient. Its squared modulus is the transmissivity, and it also carries a complex phase according to the optical phase change associated with the transmission.

## Fresnel Equations

Complex transmission coefficients and transmissivity for optical interfaces can be calculated with Fresnel equations. They depend only on the refractive indexes of both optical materials.

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