## Propagation-invariant wave fields with finite energy

JOSA A, Vol. 17, Issue 2, pp. 294-303 (2000)

http://dx.doi.org/10.1364/JOSAA.17.000294

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### Abstract

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.

© 2000 Optical Society of America

**OCIS Codes**

(030.4070) Coherence and statistical optics : Modes

(050.1960) Diffraction and gratings : Diffraction theory

(110.6760) Imaging systems : Talbot and self-imaging effects

(140.3300) Lasers and laser optics : Laser beam shaping

(350.5030) Other areas of optics : Phase

(350.5500) Other areas of optics : Propagation

(350.7420) Other areas of optics : Waves

**History**

Original Manuscript: May 6, 1999

Revised Manuscript: October 5, 1999

Manuscript Accepted: October 8, 1999

Published: February 1, 2000

**Citation**

Rafael Piestun, Yoav Y. Schechner, and Joseph Shamir, "Propagation-invariant wave fields with finite energy," J. Opt. Soc. Am. A **17**, 294-303 (2000)

http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-17-2-294

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### References

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