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Spectral Phase

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Ask RP Photonics for advice on possible methods to measure the spectral phase of the pulses from your laser, and how to correct it.

Definition: the phase of the electric field in the frequency domain

German: spektrale Phase

Categories: optical metrology, light pulses

Formula symbol: φ

Units: rad

How to cite the article; suggest additional literature

The electric field of an optical pulse may be described in the time domain or in the frequency domain. In the frequency domain, it can be of interest to know not only the power spectral density (i.e., the intensity spectrum) but also the spectral phase. This is defined as the phase of the electric field in the frequency domain, i.e., the complex phase of the function

Fourier transform

Complete pulse characterization includes measuring not only the optical spectrum, i.e. the squared modulus of E(ν), but also the spectral phase, which contains additional information. This is possible e.g. with the methods of frequency-resolved optical gating (FROG) and spectral phase interferometry for direct electric-field reconstruction (SPIDER, → spectral interferometry).

Food for Thought

Can you find out without doing a calculation, what the effect of a weak Kerr nonlinearity on the spectral phase of a sech2-shaped pulse is? As a hint, use the fact that the effects of group delay dispersion and Kerr nonlinearity can cancel each other in a fundamental soliton pulse, apart from a remaining constant phase shift.

Spectral Phase and Group Delay

The group delay can be defined as the derivative of the spectral phase with respect to angular frequency. This means e.g. that the group delay of all spectral components is zero if the spectral phase is constant. If this is not the case, the group delay may be frequency dependent: different frequency components can then be considered to arrive at different times. However, this kind of interpretation is somewhat problematic, as becomes apparent e.g. when considering that the instantaneous frequency may acquire a certain value more than once within the pulse duration, whereas the group delay for a particular frequency can have only one value. For simple pulse shapes, however, the group delay can be used to describe the position of the pulse maximum of the whole pulse, or of the pulse obtained after a bandpass filter.


It is instructive to consider the changes of spectral phase associated with certain operations:

When the spectral phase is constant or depends linearly on the frequency, the pulse is unchirped, which implies that it is at the transform limit. A chirp in the time domain is associated with a nonlinear frequency dependence of the spectral phase. A dispersive pulse compressor basically has the task of applying spectral phase shifts so that the resulting spectral phase is constant (or changes only linearly with frequency). The deviations from a flat spectral phase are more informative measure of the quality of pulse compression than e.g. just the pulse duration achieved.

The spectral phase can be useful for understanding the phenomenon of spectral interference. For example, consider two identical pulses with a relative time delay T. The difference in spectral phase, which is linear in frequency (see above), causes a spectral modulation. See the article on spectral interferometry for more details.

Modifying the Spectral Phase

There are pulse shapers which can be used to modify the spectral phase of pulses. Such a setup consists of, e.g., a first diffraction grating to separate different frequency components spatially, a liquid crystal modulator for applying position-dependent phase shifts, and a second diffraction grating to recombine the frequency components.

By properly adjusting all the phase values, it is possible e.g. to obtain transform-limited pulses, being as short as the given spectral width allows, or to form longer pulses with complicated temporal shapes. Conditions for such capabilities are that the full optical bandwidth can be processed, and that the spectral resolution (related to the maximum occurring group delay) is sufficiently high. On the other hand, a fast optical modulator is not required.


[1]J. P. Heritage et al., “Picosecond pulse shaping by spectral phase and amplitude manipulation”, Opt. Lett. 10 (12), 609 (1985)
[2]I. A. Walmsley and V. Wong, “Characterization of the electric field of ultrashort optical pulses”, J. Opt. Soc. Am. B 13 (11), 2453 (1996)
[3]C. Iaconis and I. A. Walmsley, “Spectral phase interferometry for direct electric-field reconstruction of ultrashort optical pulses”, Opt. Lett. 23 (10), 792 (1998)

(Suggest additional literature!)

See also: chirp, transform limit, pulse characterization, spectral interferometry, pulse compression, double pulses

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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.


Watch our quick video tour!

Single-mode and Multi­mode Fibers


Calculate mode properties such as

  • amplitude distributions (near field and far field)
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  • 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,

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

Fiber Lasers

fiber laser

For example, analyze and optimize the

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

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fiber laser

For example, study

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Apply any sequence of elements to your pulses!

… and even Bulk Devices

regenerative amplifier

For example, study

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RP Fiber Power is an extremely versatile tool!

Mode Solver

fiber modes

For example, calculate

  • amplitude and intensity profiles
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  • 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.

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