Coherence Length | previous | next | feedback |
Definition: a measure of temporal coherence, expressed as the propagation distance over which the coherence significantly decays
The coherence length can be used for quantifying the degree of temporal (not spatial!) coherence as the propagation length (and thus propagation time) over which coherence degrades significantly. It is defined as the coherence time times the vacuum velocity of light.
For light with a Lorentzian optical spectrum, the coherence length can be calculated as
where Δν is the (full width at half-maximum) linewidth (optical bandwidth). However, such relations are not valid in cases where the coherence function has a more complicated shape, as is the case for, e.g., a frequency comb.
Figure 1: Setup of an interferometer, where the coherence length of light is important.
The reason for often using the term coherence length instead of coherence time is that the optical time delays involved in some experiment are often determined by optical path lengths. For example, the interferometer in Figure 1 shows pronounced interference fringes only if the coherence length of the laser light is at least as long as the path-length difference of the two arms. Also, in a setup for making holographic recordings, coherence between two beams with a somewhat different optical path length is required, so that the coherence length of the light source should be longer than the maximum occurring path-length difference. In addition to holography, a number of other applications may require a certain coherence length; see the article on coherence.
Lasers, particularly single-frequency solid-state lasers, can have very long coherence lengths, e.g. 9.5 km for a Lorentzian spectrum with a linewidth of 10 kHz. The coherence length is limited by phase noise which can result from, e.g., spontaneous emission in the gain medium.
Coherence Length in Nonlinear Optics
An unfortunate use of the term coherence length is common in nonlinear optics: for example, in second-harmonic generation, the coherence length is often understood as the length over which fundamental and harmonic wave get out of phase (more precisely, the phase difference accumulated over this length is π). This is inconsistent with the general notion of coherence, because a predictable phase relationship (strong phase correlation) is definitely maintained over more than this length, although there is a systematic evolution of the relative phase.
Dear user of this encyclopedia,
Trying to constantly improve this resource, RP Photonics would greatly appreciate your feedback. You may be able to indicate points of insufficient clarity, to report errors, or to suggest additions – concerning new articles, helpful equations, links to useful references, etc. The simplest way to deliver feedback is the feedback form. A link to this form is found to the right of each article heading. You may stay anonymous, if you wish so.
See also: coherence, coherence time, linewidth, speckle, Spotlight article 2006-09-22
Categories: general optics, nonlinear optics
Since October 2008, the Encyclopedia of Laser Physics and Technology is also available in the form of a two-volume book. Maybe you would enjoy reading it also in that form! The print version has a carefully designed layout and can be considered a must-have for any institute library, laser research group, or laser company.
You may order the print version via Wiley-VCH.
