RP Photonics
Encyclopedia

Dr. Paschotta, the founder of RP Photonics, supports your R & D with his deep expertise. Save time and money with efficient support!

Powerful simulation software for fiber lasers and amplifiers, resonator design, pulse propagation and multilayer coating design.

The famous Encyclopedia of Laser Physics and Technology provides a wealth of high-quality scientific and technical information.

In the RP Photonics Buyer's Guide, you easily find suppliers for photo­nics products. As a supp­lier, you can profit from enhanced entries!

Learn on lasers and photonics every day!
 part of theVirtualLibrary

# Coherence Length

Use the RP Photonics Buyer's Guide to find suppliers for photonics products! You will hardly find a more convenient resource.

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

Formula symbol: Lcoh

Units: m

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.

## 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.

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.

 Your general impression: don't know poor satisfactory good excellent Technical quality: don't know poor satisfactory good excellent Usefulness: don't know poor satisfactory good excellent Readability: don't know poor satisfactory good excellent Comments: Found any errors? Suggestions for improvements? Do you know a better web page on this topic? Spam protection: (enter the value of 5 + 8 in this field!)

If you want a response, you may leave your e-mail address in the comments field, or directly send an e-mail.

If you like our website, you may also want to get our newsletters!

Dr. Paschotta, author of this encyclopedia, has also published three books in the SPIE Field Guide series:

You can order these books on the SPIE website – just click on one of the images.

# RP Fiber Power – the versatile Fiber Optics Software

## An Amazing Tool

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

Watch our quick video tour!

## Single-mode and Multi­mode 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:

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, …

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

For example, calculate

• gain and saturation characteristics (for continuous or pulsed operation)
• energy transfers in erbium-ytterbium-doped amplifier fibers
• influence of quenching effects, amplified spontaneous emission etc.

in single amplifier stages or in multi-stage amplifier systems, with double-clad fibers, etc.

## Fiber-optic Telecom Systems

For example,

• analyze dispersive and nonlinear signal distortions
• investigate the impact of amplifier noise
• optimize nonlinear management and the placement of amplifiers

Find out in detail what is going on in such a system!

## Fiber Lasers

For example, analyze and optimize the

• power conversion efficiency
• wavelength tuning range
• Q switching dynamics
• femtosecond pulse generation with mode locking

for lasers based on double-clad fiber, with linear or ring resonator, etc.

## Ultrafast Fiber Lasers and Amplifiers

For example, study

• pulse formation mechanisms
• impact of nonlinearities and chromatic dispersion
• parabolic pulse amplification
• feedback sensitivity
• supercontinuum generation

Apply any sequence of elements to your pulses!

## … and even Bulk Devices

For example, study

• Q switching dynamics
• mode-locking behavior
• impact of nonlinearities and chromatic dispersion
• influence of a saturable absorber
• chirped-pulse amplification
• regenerative amplification

RP Fiber Power is an extremely versatile tool!

## Mode Solver

For example, calculate

• amplitude and intensity profiles
• effective mode areas
• cut-off wavelengths
• propagation constants
• group velocities
• chromatic dispersion

All this is calculated with high efficiency!

## Beam Propagation

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

## Laser-active Ions

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

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:

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

## High-quality Documentation and Competent Support

The carefully prepared comprehensive documentation includes a PDF manual and an interactive online help system.

Competent technical support is provided: the developer himself will help you and make sure that any problem is solved!

Our support is like included technical consulting.

## Boost your competence, efficiency and creativity!

• Stop fishing in the dark! Develop a clear quantitative understanding of your devices.
• Explore the effects of possible design changes on your desk.
• That way, get most efficient in the lab.
• Find optimized solutions efficiently, minimizing time to market.
• Get new ideas by playing with your models.

Efficiency and success of
R & D are not a matter of chance.

See our detailed description with many case studies!