## Shape invariance and a universal form for the Gouy phase

JOSA A, Vol. 21, Issue 4, pp. 572-579 (2004)

http://dx.doi.org/10.1364/JOSAA.21.000572

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### Abstract

It is shown that Hermite–Gaussian beams, Laguerre–Gaussian beams, and certain linear combinations thereof are the only finite-energy coherent beams that propagate, on free propagation, in a shape-invariant manner. All shape-invariant beams have Gouy phase of the universal *c*. It is also shown that, as limiting cases, even two- and three-dimensional nondiffracting beams belong to this class when the Rayleigh distance goes to infinity. The results are deduced from the transport-of-intensity equations, by elementary means as well as by use of the Iwasawa decomposition. A pivotal role in the analysis is the finding that the only possible change in the phase front of a shape-invariant beam from one transverse plane to another is quadratic.

© 2004 Optical Society of America

**OCIS Codes**

(030.4070) Coherence and statistical optics : Modes

**History**

Original Manuscript: September 9, 2003

Revised Manuscript: September 9, 2003

Manuscript Accepted: December 2, 2003

Published: April 1, 2004

**Citation**

Riccardo Borghi, Massimo Santarsiero, and Rajiah Simon, "Shape invariance and a universal form for the Gouy phase," J. Opt. Soc. Am. A **21**, 572-579 (2004)

http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-21-4-572

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