Shape invariance and a Universal form for the Gouy phase

Borghi, Riccardo ; Santarsiero, Massimo ; Simon, Rajiah (2004) Shape invariance and a Universal form for the Gouy phase Journal of the Optical Society of America A: Optics, Image Science, and Vision, 21 (4). pp. 572-579. ISSN 1084-7529

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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 arctan(z/zR) form, with quantized values for the prefactor 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.

Item Type:Article
Source:Copyright of this article belongs to Optical Society of America.
ID Code:87694
Deposited On:20 Mar 2012 15:10
Last Modified:20 Mar 2012 15:10

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