# In Physics, What Is Coherence Length?

Matt Hubbard

In optics, which is the branch of physics dealing with light and its properties, coherence length (CL) is the maximum distance that a beam of light or other electromagnetic phenomenon can travel while still maintaining a specified degree of temporal coherence. Temporal coherence refers to sine shape of a propagating wave and the ability to predict where in its phase a wave will be a specific moment in time. If the light is coherent, it remains in phase with itself. As a result, some texts also refer to coherence time, which is the coherence length divided by the speed of light.

Coherence length is affected by many factors: the purity and power of the light being used, the specific wavelength, the presence of potential dispersion and diffraction. Although the term "coherence length" is primarily used in optics, many of the concepts from optics have been generalized to any situation involving the propagation of waves, such as radio waves, sound waves and compression waves. It also is used in discussions of superconductivity, possibly because electrons can also be viewed as waves under certain conditions.

One significant application of coherence length is holography, the recording and recreation of three-dimensional images. Holography works by capturing the interaction between two laser beams — a reference beam and an object beam. The coherence length of the laser used is the maximum path difference that can be allowed between the beams, so it serves as a limit on the depth of the hologram that can be recorded. For a common five-milliwatt helium neon laser, this CL is limited to about 6-8 inches (15.2-20.3 cm).

Another application of coherence length is in telecommunications, the transmission of messages over an electromagnetic signal. Here the CL is the maximum distance that a message can be sent without being somehow relayed. For radio waves, the length can be approximated by dividing the speed of light through that medium by the bandwidth of the signal. Interference, dispersion and diffraction can reduce this range. For optic communications, the CL is directly proportional to the square of the source’s central wavelength and inversely proportional to the refractive index of the medium being used and the spectral width of the signal.