RP Photonics logo
RP Photonics
Technical consulting services on lasers, nonlinear optics, fiber optics etc.
Profit from the knowledge and experience of a top expert!
Powerful simulation and design software.
Make computer models in order to get a comprehensive understanding of your devices!
Success comes from understanding – be it in science or in industrial development.
The famous Encyclopedia of Laser Physics and Technology – available online for free!
The ideal place for finding suppliers for many photonics products.
Advertisers: Make sure to have your products displayed here!
… combined with a great Buyer's Guide!
VLib part of the

Gouy Phase Shift

<<<  |  >>>  |  Feedback

Buyer's Guide

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

Definition: an additional phase shift occurring in the propagation of focused Gaussian beams

German: Gouy-Phasenverschiebung

Category: general optics

How to cite the article; suggest additional literature

(Widespread wrong spelling: “Guoy phase shift”)

Along its propagation direction, a Gaussian beam acquires a phase shift which differs from that for a plane wave with the same optical frequency. This difference is called the Gouy phase shift [1]:

Gouy phase shift

where zR is the Rayleigh length and z = 0 corresponds to the position of the beam waist. It results in a slightly increased distance between wavefronts, compared with the wavelength as defined for a plane wave of the same frequency. This also means that the phase fronts have to propagate somewhat faster, leading to an effectively increased local phase velocity.

Overall, the Gouy phase shift of a Gaussian beam for going through a focus (from the far field to the far field on the other side of the focus) is π.

Gouy phase shift

Figure 1: Beam radius and Gouy phase shift along the propagation direction for a beam in air with 1064 nm wavelength and 100 μm radius at the waist. The positions at plus and minus the Rayleigh length are marked.

It is actually not surprising that the phase shift of a Gaussian beam is not exactly the same as for a plane wave. A Gaussian beam can be considered as a superposition of plane waves with different propagation directions. Those plane wave components with propagation directions different from the beam axis experience smaller phase shifts in z direction; the overall phase shift arises from a superposition of all these components.

For higher-order transverse modes, the Gouy phase shift is stronger. For TEMnm modes, for example, it is stronger by the factor 1 + n + m. This causes the resonance frequencies of higher-order modes in optical resonators to be somewhat higher. By lifting the frequency degeneracy of resonator modes, the Gouy phase shift also has an important impact on the beam quality achieved in a laser resonator under the influence of aberrations [5].


[1]L. G. Gouy, “Sur une propriete nouvelle des ondes lumineuses”, C. R. Acad. Sci. Paris 110, 1251 (1890)
[2]A. Rubinowicz, “On the anomalous propagation of phase in the focus”, Phys. Rev. 54 (11), 931 (1938)
[3]L. G. Gouy, “Sur la propagation anomale des ondes”, Compt. Rendue Acad. Sci. Paris 111, 33 (1890)
[4]R. W. Boyd, “Intuitive explanation of the phase anomaly of focused light beams”, J. Opt. Soc. Am. 70 (7), 877 (1980)
[5]R. Paschotta, “Beam quality deterioration of lasers caused by intracavity beam distortions”, Opt. Express 14 (13), 6069 (2006) (explaining the important impact of the Gouy phase on the laser beam quality)

(Suggest additional literature!)

See also: Gaussian beams, Spotlight article 2008-11-25

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:


Fiber Optics Software
with Further Improved
User Interface

In RP Fiber Power V6, one can use nice custom forms, which can be
tailored to specific applications.

custom form in RP Fiber Power

Users can make such forms themselves, or get them from RP Photonics within the technical support. The latter is like buying a custom software for every purpose – but without spending a lot of money every time!

Beginners can now get started very easily, even if they need quite special calculations!

– Show all banners –

– Get your own banner! –