Coherence length

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In physics, coherence length is the propagation distance from a coherent source to a point where an electromagnetic wave maintains a specified degree of coherence. The significance is that interference will be strong within a coherence length of the source, but not beyond it. This concept is also commonly used in telecommunication engineering.

In long-distance transmission systems, the coherence length may be reduced by propagation factors such as dispersion, scattering, and diffraction.

In radio-band systems, the coherence length is approximated by

where c is the speed of light in a vacuum, n is the refractive index of the medium, and Δf is the bandwidth of the source.

In optical communications, the coherence length L is given by

where λ is the central wavelength of the source, n is the refractive index of the medium, and Δλ is the spectral width of the source.

Coherence length is usually applied to the optical regime.

The expression above is a frequently used approximation. Due to ambiguities in the definition of spectral width of a source, however, the following definition of coherence length has been suggested:

The coherence length can be measured using a Michelson interferometer and is the optical path length difference of a self-interfering laserbeam which corresponds to a 1 / e = 37% fringe visibility[1], where the fringe visibility is defined as

where I is the fringe intensity.

Multimode helium-neon lasers have a typical coherence length of 20 cm, while semiconductor lasers reach some 100 m. Fiber lasers can have coherence lengths exceeding 100 km.

See also


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