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Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Editor: Stephen A. Burns
  • Vol. 22, Iss. 11 — Nov. 1, 2005
  • pp: 2465–2475

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

Michel Zamboni-Rached, Erasmo Recami, and Hugo E. Hernández-Figueroa  »View Author Affiliations

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

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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 0 z L of the propagation axis z. Their intensity envelope remains static, i.e., with velocity v = 0 , so we have named “frozen waves” (FWs) these new solutions to the wave equations (and, in particular, to the Maxwell equation). Inside the envelope of a FW, only the carrier wave propagates. The longitudinal shape, within the interval 0 z L , can be chosen in such a way that no nonnegligible field exists outside the predetermined region (consisting, e.g., in one or more high-intensity peaks). Our solutions are notable also for the different and interesting applications they can have—especially in electromagnetism and acoustics—such as optical tweezers, atom guides, optical or acoustic bistouries, and various important medical apparatuses.

© 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

Original Manuscript: March 7, 2005
Manuscript Accepted: April 13, 2005
Published: November 1, 2005

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)

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  36. 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.
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  38. 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.
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