Coherence length

From Wikipedia, the free encyclopedia
Jump to navigation Jump to search

In physics, coherence length is the propagation distance over which a coherent wave (e.g. an electromagnetic wave) maintains a specified degree of coherence. Wave interference is strong when the paths taken by all of the interfering waves differ by less than the coherence length. A wave with a longer coherence length is closer to a perfect sinusoidal wave. Coherence length is important in holography and telecommunications engineering.

This article focuses on the coherence of classical electromagnetic fields. In quantum mechanics, there is a mathematically analogous concept of the quantum coherence length of a wave function.


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 is the bandwidth of the source.

In optical communications, assuming that the source has a Gaussian emission spectrum, the coherence length is given by [1]

where is the central wavelength of the source, is the refractive index of the medium, and is the (FWHM) spectral width of the source. If the source has a Gaussian spectrum with FWHM spectral width , then a path offset of ± will reduce the fringe visibility to 50%.

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 fringe visibility,[2] where the fringe visibility is defined as

where is the fringe intensity.

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


Multimode helium–neon lasers have a typical coherence length of 20 cm, while the coherence length of single-mode lasers can exceed 100 m. Semiconductor lasers reach some 100 m, but small, inexpensive semiconductor lasers have shorter lengths, with one source[3] claiming 20 cm. 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.

Other light sources[edit]

The coherence length of a mercury-vapor lamp is 0.03 cm.[4]

See also[edit]


  1. ^ Akcay, C., Parrein. P., and Rolland, J. P. (2002). Estimation of longitudinal resolution in optical coherence imaging. Applied Optics 41 (25), 5256–5262, equation 9.
  2. ^ Ackermann, Gerhard K. (2007). Holography: A Practical Approach. Wiley-VCH. ISBN 3-527-40663-8.
  3. ^ "Sam's Laser FAQ - Diode Lasers". Retrieved 2017-02-06.
  4. ^ Hecht, Eugene (2002). Optics (4th ed.). San Francisco ; Montreal: Pearson/Addison-Wesley. ISBN 978-0805385663.