# Coherence length

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Coherence length

In physics, coherence length is the propagation distance from a coherent source to a point where an electromagnetic wave (or wave_packet, wave_function, etc.) 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

$L={c \over n\, \Delta f},$

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

$L={2 \ln(2) \over \pi n} {\lambda^2 \over \Delta\lambda},$

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 laser beam which corresponds to a 1 / e = 37% fringe visibility,[1] where the fringe visibility is defined as

$V = {I_\max - I_\min \over I_\max + I_\min} ,\,$

where I is the fringe intensity.

Multimode helium-neon lasers have a typical coherence length of 20 cm, while the coherence length of singlemode ones can exceed 100 m. Semiconductor lasers reach some 100 m. Singlemode fiber lasers with linewidths of a few kHz can have coherence lengths exceeding 100 km. Similar coherence lengths can be reached with optical frequency combs due to the narrow linewidth of each tooth. Non-zero visibility is present only for short intervals of pulses repeated after cavity length distances up to this long coherence length.

## References

1. ^ Ackermann, Gerhard K. (2007). Holography: A Practical Approach. Wiley-VCH. ISBN 3527406638.

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