RP Photonics logo
RP Photonics
Consulting Software Encyclopedia Buyer's Guide

Short address: rpp-con.com

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

Short address: rpp-soft.com

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

Short address: rpp-enc.com

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

Short address: rpp-bg.com

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!
VL logo part of the

Chromatic Dispersion

<<<  |  >>>  |  Feedback

Buyer's Guide

The ideal place to find suppliers for photonics products: high-quality information, simple and fast, respects your privacy!

5 suppliers for equipment for chromatic dispersion measurements are listed.

Your are not yet listed? Get your entry!

Ask RP Photonics for any kind of calculations concerning chromatic dispersion and its effects in various situations.

Definition: the frequency dependence of the phase velocity in a transparent medium

German: chromatische Dispersion

Categories: general optics, light pulses

How to cite the article; suggest additional literature

The chromatic dispersion of an optical medium is the phenomenon that the phase velocity and group velocity of light propagating in a transparent medium depend on the optical frequency. A related quantitative measure is the group velocity dispersion.

The attribute “chromatic” is used to distinguish this type of dispersion from other types, which are relevant particularly for optical fibers: intermodal dispersion and polarization mode dispersion.

Mathematical Description of Chromatic Dispersion

Chromatic dispersion of second and higher order is defined via the Taylor expansion of the wavenumber k (change in spectral phase per unit length) as a function of the angular frequency ω (around some center frequency ω0, e.g. the mean frequency of some laser pulses):

k(w) for dispersive medium

where the terms corresponding to the different orders have the following meaning:

inverse group velocity in dispersive medium
GDD for dispersive medium
TOD for dispersive medium

Second-order dispersion is often specified in units of s2/m. It is the derivative of the inverse group velocity with respect to angular frequency:

group delay dispersion and group velocity

As an example, the group delay dispersion of silica is +36 fs2/mm at 800 nm, or −22 fs2/mm at 1500 nm. Zero group delay dispersion is reached close to 1270 nm.

The dispersion of various orders for a medium can most conveniently be calculated if the refractive index is specified with a kind of Sellmeier formula. Tabulated index data are less suitable, since the numerical differentiation is sensitive to noise.

For light propagating in waveguides such as optical fibers, one considers the phase constant β instead of the wavenumber k. The second-order dispersion, for example, is then given as the second derivative of β with respect to angular frequency. This is often called β'' or β2.

Normal and Anomalous Dispersion

One distinguishes normal dispersion (for k'' > 0) and anomalous dispersion (for k'' < 0). Normal dispersion, where the group velocity decreases with increasing optical frequency, occurs for most transparent media in the visible spectral region. Anomalous dispersion sometimes occurs at longer wavelengths, e.g. in silica (the basis of most optical fibers) for wavelengths longer than the zero-dispersion wavelength of ≈ 1.3 μm.

Great care is recommended when the sign of dispersion is specified. The ultrafast optics community identifies that sign with the sign of k''. The opposite sign is usually used in optical fiber communications, where the dispersion is often specified with the dispersion parameter

dispersion of fibers

in units of picoseconds per nanometer and kilometer (ps/(nm km)). The different signs result from using a frequency derivative in one case and a wavelength derivative in the other. Note also that the conversion factor depends on the wavelength.

Conversion of Chromatic Dispersion Values

Center wavelength:
Group velocity dispersion: calc
Dispersion parameter: calc

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

Between wavelength regions with normal and anomalous dispersion, there is a zero dispersion wavelength. The region around this wavelength can be special in some respects, not only concerning weak dispersive pulse broadening.

Higher-order Dispersion

Dispersion of third and higher order is called higher-order dispersion. When dealing with very broad optical spectra, one sometimes has to consider dispersion up to the fourth or even fifth and sixth order. Ultimately, the concept of Taylor expansion loses its value in this regime, where many dispersion orders have to be considered. It is therefore often more convenient e.g. in numerical modeling to work directly with a table of frequency-dependent phase changes.

Effects of Chromatic Dispersion

Wavelength-dependent Refraction and Diffraction

A frequently encountered phenomenon is that dispersion causes wavelength-dependent refraction, which is responsible, e.g., for the occurrence of rainbows. Similarly, wavelength-dependent diffraction at a diffraction grating allows the spatial separation of different frequency components of light.

Dispersive Pulse Broadening and Chirping

Dispersion has an important impact on the propagation of pulses, because a pulse always has a finite spectral width (bandwidth), so that dispersion can cause its frequency components to propagate with different velocities. Normal dispersion, for example, leads to a lower group velocity of higher-frequency components, and thus to a positive chirp, whereas anomalous dispersion creates negative chirps.

The frequency dependence of the group velocity also has an effect on the pulse duration. If the pulse is initially unchirped, dispersion in a medium will always increase its duration (dispersive pulse broadening). For an originally unchirped Gaussian pulse with the duration τ0, the pulse duration is increased according to

dispersive broadening

if second-order group delay dispersion D2 is applied. The approximation holds for the case of strong broadening, i.e., for D2 >> τ02. In that regime, shorter input pulses lead to longer output pulses. This is an effect of the increased pulse bandwidth.

As a numerical example, an initially unchirped 30-fs pulse at 800 nm becomes stretched to 45 fs after 10 mm of propagation in silica (with +360 fs2). After 10 cm, the pulse duration would increase to 334 fs.

Dispersive Pulse Broadening

Unchirped pulse duration:
Group delay dispersion:
Pulse duration: calc

After you have modified some inputs, click the "calc" button to recalculate the output.

Dispersion of the opposite sign can be used later to recompress the pulse (dispersive pulse compression). This is important, e.g., in the context of chirped-pulse amplification. Depending on the sign and amount of required dispersion, and also on other factors such as the optical peak power, different devices are used as dispersive compressors. Examples are prism pairs, pairs of diffraction gratings, chirped mirrors, chirped Bragg gratings, and dispersive glass fibers.

dispersive pulse broadening

Figure 1: Output pulse duration versus initial pulse duration for dispersive pulse broadening with different levels of group delay dispersion (GDD). Note that shorter pulses are increasingly sensitive to dispersion. Substantial broadening occurs when the square of the pulse duration is smaller than the group delay dispersion.

Higher-order dispersion causes more complicated changes of the pulse shape. A challenge in dispersion compensation is often to compensate not only the lowest (second) order of dispersion, but also higher orders for approaching the transform limit.

Soliton Effects

Although dispersion alone leads to pulse broadening, dispersion combined with the Kerr nonlinearity can give rise to the formation of solitons and in this way assist the generation of extremely short pulses of light with a soliton mode-locked laser. However, this usually requires the careful management of dispersion over a wide wavelength range, i.e., taking care also of higher-order terms.

Dispersion in Nonlinear Optics

In nonlinear optics, particularly concerning nonlinear frequency conversion, chromatic dispersion has manifold influences, which can be grouped into three categories:

  • It determines the options for phase matching of parametric nonlinear processes.
  • It limits the effective interaction length for short pulses via the group velocity mismatch (→ temporal walk-off, limited phase-matching bandwidth).
  • It can also limit the nonlinear interaction length via dispersive pulse broadening: eventually, the pulses become so long that their peak power is too low for efficient nonlinear interactions. However, the group velocity mismatch normally introduces the more stringent limitation.

Chromatic Dispersion of Optical Components

Dispersion can also be defined for optical components rather than media. In that case, one performs the Taylor expansion as shown above for the total phase delay of the component (rather than for the wavenumber, i.e., the phase delay per unit length), and obtains the total group delay dispersion (in units of seconds squared) rather than the dispersion per unit length.

The chromatic dispersion of an optical component may simply result from the dispersion of its parts, but in some cases large amounts of dispersion can arise from interference effects. For example, a Gires–Tournois interferometer generates dispersion by interference effects in an optical resonator, and not primarily via material dispersion. The same happens in other types of interferometers. The amount of dispersion arising from such effects can be huge when large differences in propagation lengths are involved.

Chromatic dispersion can also result from geometric effects. An important example is that of a prism pair as is often used for dispersion compensation in mode-locked lasers. Here, chromatic dispersion arises from wavelength-dependent path lengths, caused by wavelength-dependent refraction at prism surfaces. Similar effects occur in laser resonators containing Brewster-angled optical components, and in Bragg grating pairs as used for dispersive pulse compression.

Waveguide Dispersion

The discussion above is based on the assumption of plane waves. In practice, significant deviations from this situation can occur, in particular in the context of waveguides. Here, the quantity of interest is usually not the magnitude of the wave vector (k vector) (which anyway is no longer well defined), but rather the value β (the imaginary part of the propagation constant), which specifies the phase change per unit length in the propagation direction. As β is influenced by the waveguide (particularly for mode diameters of only a few wavelengths or even less), the dispersion is also affected (→ waveguide dispersion). This is important e.g. in optical fibers, and particularly in photonic crystal fibers with very small effective mode areas. In some cases, waveguide dispersion makes the overall dispersion anomalous even in the visible wavelength region, where the material dispersion of silica alone is clearly in the normal dispersion regime. For telecom applications, fiber designs are often made for tailored dispersion properties, resulting in, e.g., dispersion-shifted fibers.

Chromatic Dispersion from Polarization Effects

A special type of chromatic dispersion can result from polarization mode dispersion e.g. in optical fibers. For a certain fiber span and a given wavelength, two input principal polarization states can be determined, which exhibit somewhat different values of the group delay. Besides this differential group delay, there are contributions to the group delay dispersion with opposite signs for the two principal polarization states. Such effects can be relevant for optical fiber communications at very high bit rates.

Measurement of Chromatic Dispersion

There are several techniques for measuring chromatic dispersion:


[1]L. G. Cohen and C. Lin, “Pulse delay measurements in the zero material dispersion wavelength region for optical fibers”, Appl. Opt. 16 (12), 3136 (1977)
[2]D. N. Payne and A. H. Hartog, “Determination of the wavelength of zero material dispersion in optical fibers by pulse-delay measurement”, Electron. Lett. 13 (21), 627 (1977)
[3]A. Sugimura and K. Daikoku, “Wavelength dispersion of optical fibers directly measured by ‘difference method’ in the 0.8–1.6 μm range”, Rev. Sci. Instrum. 50 (3), 434 (1979)
[4]M. Tateda et al., “Interferometric method for chromatic dispersion measurement in a single-mode optical fiber”, IEEE J. Quantum Electron. 17 (3), 404 (1981)
[5]H.-T. Shang, “Chromatic dispersion measurement by white-light interferometry on metre-length single-mode optical fibres”, Electron. Lett. 17 (17), 603 (1981)
[6]B. Costa et al., “Phase-shift technique for the measurement of chromatic dispersion in single-mode optical fibres using LED's”, Electron. Lett. 19 (25), 1074 (1982)
[7]L. Cohen, “Comparison of single-mode fiber dispersion measurement techniques”, J. Lightwave Technol. 3 (5), 958 (1985)
[8]L. Thevenaz et al., “All-fiber interferometer for chromatic dispersion measurements”, J. Lightwave Technol. 6 (1), 1 (1988)
[9]C. Dorrer, “Chromatic dispersion characterization by direct instantaneous frequency measurement”, Opt. Lett. 29 (2), 204 (2004)
[10]I. A. Walmsley et al., “The role of dispersion in ultrafast optics”, Rev. Sci. Instrum. 72 (1), 1 (2001)
[11]R. Paschotta, tutorial on "Passive Fiber Optics", Part 10: Chromatic Dispersion

(Suggest additional literature!)

See also: group velocity dispersion, group delay dispersion, zero dispersion wavelength, dispersion, waveguide dispersion, dispersion compensation, dispersion management, fibers, group velocity, refraction, refractive index, Sellmeier formula, Kramers–Kronig relations, dispersion-shifted fibers

How do you rate this article?

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

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!

If you like this article, share it with your friends and colleagues, e.g. via social media:

cover of SPIE Field Guide cover of SPIE Field Guide cover of SPIE Field Guide

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

- Field Guide to Lasers

- Field Guide to Laser Pulse Generation

- Field Guide to Optical Fiber Technology

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

RP Fiber Power software

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:

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

  • 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

eye diagram

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

fiber laser

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

fiber laser

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

regenerative amplifier

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

fiber modes

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

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!

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!

Contact us to get a quotation!

– Show all banners –

– Get your own banner! –