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Propagation-invariant wave fields with finite energy

2000; Optica Publishing Group; Volume: 17; Issue: 2 Linguagem: Inglês

10.1364/josaa.17.000294

1520-8532

Rafael Piestun, Yoav Y. Schechner, Joseph Shamir,

Nonlinear Photonic Systems

Propagation invariance is extended in the paraxial regime, leading to a generalized self-imaging effect. These wave fields are characterized by a finite number of transverse self-images that appear, in general, at different orientations and scales. They possess finite energy and thus can be accurately generated. Necessary and sufficient conditions are derived, and they are appropriately represented in the Gauss–Laguerre modal plane. Relations with the following phenomena are investigated: classical self-imaging, rotating beams, eigen-Fourier functions, and the recently introduced generalized propagation-invariant wave fields. In the paraxial regime they are all included within the generalized self-imaging effect that is presented. In this context we show an important relation between paraxial Bessel beams and Gauss–Laguerre beams.