title: Shape invariance and a universal form for the Gouy phase.
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 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.
authors.affiliation: Istituto Nazionale per la Fisica della Materia and Dipartimento di Elettronica Applicata, Università Roma Tre, Via della Vasca Navale 84, I-00146 Rome, Italy. borghi@uniroma3.it
authors.forename: Riccardo
authors.initials: R
authors.lastname: Borghi
authors.forename: Massimo
authors.initials: M
authors.lastname: Santarsiero
authors.forename: Rajiah
authors.initials: R
authors.lastname: Simon