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

<math>L={c \over \Delta f}</math>,

where <math> c</math> is the speed of light in a vacuum, <math>n</math> is the refractive index of the medium, and <math>\Delta f</math> is the bandwidth of the source.

In optical communications, the coherence length <math>L</math> is given approximately by

<math>L={\lambda^2 \over n \Delta\lambda}</math>,

where <math>\lambda</math> is the central wavelength of the source, <math>n</math> is the refractive index of the medium, and <math>\Delta\lambda</math> 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^{[citation needed]}:

The coherence length is the optical path length difference of a self-interfering laserbeam which corresponds to a 50% fringe visibility, where the fringe visibility is defined as

<math>V = {I_{max} - I_{min} \over I_{max} + I_{min}}</math>,

where <math>I</math> is the fringe intensity.

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.