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Coherence Length

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Ask RP Photonics for advice on how to measure the coherence length e.g. of a laser.

Definition: a measure of temporal coherence, expressed as the propagation distance over which the coherence significantly decays

German: Kohärenzlänge

Categories: general optics, nonlinear optics

How to cite the article; suggest additional literature

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

coherence length

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.

Calculating the Coherence Length

Center wavelength:
Bandwidth (frequency): calc
Bandwidth (wavelength): calc
Coherence length: calc

After you have modified some values, click a "calc" button to recalculate the field left of it.

interferometer setup

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.

Some 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. For monolithic semiconductor lasers, even when operating in a single-frequency mode, the coherence length is typically shorter by several orders of magnitude. The coherence length is limited by phase noise which can result from, e.g., spontaneous emission in the gain medium. The quantum noise influence is weak (allowing for a long coherence length) when the circulating power in the laser is high, the resonator losses per round trip are low, and the round-trip time is long.

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.

See also: coherence, coherence time, linewidth, speckle, Spotlight article 2006-09-22

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RP Fiber Power – the versatile Fiber Optics Software

An Amazing Tool

RP Fiber Power software

This amazing tool is extremely helpful for the development of passive and active fiber devices.

ASE

Watch our quick video tour!

Single-mode and Multi­mode Fibers

fibers

Calculate mode properties such as

  • amplitude distributions (near field and far field)
  • effective mode area
  • effective index
  • group delay and chromatic dispersion

Also calculate fiber coupling efficiencies; simulate effects of bending, nonlinear self-focusing or gain guiding on beam propagation, higher-order soliton propagation, etc.

Arbitrary Index Profiles

A fiber's index profile may be more complicated than just a circle:

special fibers

Here, we "printed" some letters, translated this into an index profile and initial optical field, propagated the light over some distance and plotted the output field – all automated with a little script code.

Fiber Couplers, Double-clad Fibers, Multicore Fibers, …

fiber devices

Simulate pump absorption in double-clad fibers, study beam propagation in fiber couplers, light propagation in tapered fibers, analyze the impact of bending, cross-saturation effects in amplifiers, leaky modes, etc.

Fiber Amplifiers

fiber amplifier

For example, calculate

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eye diagram

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fiber laser

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fiber laser

For example, study

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Apply any sequence of elements to your pulses!

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regenerative amplifier

For example, study

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RP Fiber Power is an extremely versatile tool!

Mode Solver

fiber modes

For example, calculate

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All this is calculated with high efficiency!

Beam Propagation

beam propagation

Propagate optical field with arbitrary wavefronts through fibers. These may be asymmetric, bent, tapered, exhibit random disturbances, etc.

See our demo video for numerical beam propagation.

Laser-active Ions

level scheme

Work with the standard gain model, or define your own level scheme!

Can include different ions, energy transfers, upconversion and quenching effects, complicated pumping schemes, etc.

Multiple Pump and Signal Waves, ASE

optical channels

Define multiple pump and signal waves and many ASE channels – each one with its own transverse intensity profile, loss coefficient etc.

The power calculations are highly efficient and reliable.

Simple Use and High Flexibility Combined

For simpler tasks, use convenient forms:

signal parameters

Script code is automatically generated and can then be modified by the user. A powerful script language gives you an unparalleled flexibility!

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