## Theory of “frozen waves”: modeling the shape of stationary wave fields

JOSA A, Vol. 22, Issue 11, pp. 2465-2475 (2005)

http://dx.doi.org/10.1364/JOSAA.22.002465

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### Abstract

In this work, starting by suitable superpositions of equal-frequency Bessel beams, we develop a theoretical and experimental methodology to obtain localized *stationary* wave fields (with high transverse localization) whose longitudinal intensity pattern can approximately assume any desired shape within a chosen interval *z*. Their intensity envelope remains static, i.e., with velocity

© 2005 Optical Society of America

**OCIS Codes**

(070.2580) Fourier optics and signal processing : Paraxial wave optics

(140.3300) Lasers and laser optics : Laser beam shaping

(170.4520) Medical optics and biotechnology : Optical confinement and manipulation

(230.0230) Optical devices : Optical devices

(260.1960) Physical optics : Diffraction theory

(350.7420) Other areas of optics : Waves

**ToC Category:**

Lasers and Laser Optics

**History**

Original Manuscript: March 7, 2005

Manuscript Accepted: April 13, 2005

Published: November 1, 2005

**Citation**

Michel Zamboni-Rached, Erasmo Recami, and Hugo E. Hernández-Figueroa, "Theory of “frozen waves”: modeling the shape of stationary wave fields," J. Opt. Soc. Am. A **22**, 2465-2475 (2005)

http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-22-11-2465

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### References

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- However, when we get complete control over the longitudinal shape, we cannot have total control also over the transverse localization, since our stationary fields are of course constrained to obey the wave equation.
- M. Zamboni-Rached, “Stationary optical wave fields with arbitrary longitudinal shape by superposing equal frequency Bessel beams: Frozen Waves,” Opt. Express 12, 4001–4006 (2004). [CrossRef] [PubMed]
- Such a choice of the longitudinal intensity pattern does imply an interesting freedom, since we can consider more generally any expansion ∑m=−∞∞Bmexp(i2πmz∕L)=F(z)exp[iϕ(z)], quantity ϕ(z) being an arbitrary function of the coordinate z.
- The same apparatus could also be used to generate higher-order FWs, when the zero-order Bessel beams in superposition (23) are replaced with higher-order Bessel functions. Experimentally, higher-order Bessel beams can be produced by angular modulation of the slits.
- C. A. Dartora, M. Zamboni-Rached, K. Z. Nóbrega, E. Recami, H. E. Hernández Figueroa, “General formulation for the analysis of scalar diffraction-free beams using angular modulation: Mathieu and Bessel beams,” Opt. Commun. 222, 75–80 (2003). [CrossRef]

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