In this work, in terms of suitable superpositions of equal-frequency Bessel beams, we develop a theoretical method to obtain localized stationary wave fields, in absorbing media, capable to assume, approximately, any desired longitudinal intensity pattern within a chosen interval 0 ≤ zL of the propagation axis z. As a particular case, we obtain new nondiffractive beams that can resist the loss effects for long distances. These new solutions can have different and interesting applications, such as optical tweezers, optical or acoustic bistouries, various important medical apparatuses, etc..

© 2006 Optical Society of America

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  1. 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); and references therein.
    [CrossRef] [PubMed]
  2. M. Zamboni-Rached, E. Recami, H. Figueroa, "Theory of Frozen Waves: Modelling the Shape of Stationary Wave Fields," J. Opt. Soc. Am. A 22, 2465-2475 (2005); and references therein.
  3. This paper did first appear as e-print arXiv:physics/0506067, 8 Jun 2005.

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Figures (2)

Fig. 1.
Fig. 1.

(a) Three-dimensional field-intensity of the resulting beam. (b) The resulting beam, in an orthogonal projection and in logaritmic scale.

Fig. 2.
Fig. 2.

Three-dimensional field-intensity of the resulting beam, in the absorbing medium, with a growing longitudinal field intensity.

Equations (9)

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Ψ ρ z t = m = N N A m J 0 ( ( k ρ R m + i k ρ I m ) ρ ) e i β R m z e iωt e β I m z ,
k ρ m 2 = n 2 ω 2 c 2 β m 2
β R m β I m = n R n I
β R m = Q + 2 πm L
0 Q + 2 πm L n R ω c
Ψ ρ z t = e iωt e iQz m = N N A m J 0 ( ( k ρ R m + i k ρ I m ) ρ ) e i 2 πm L z e β I m z ,
A m = 1 L 0 L F ( z ) e β ¯ I z e i 2 πm L z dz
F ( z ) = { 1 for 0 z Z 0 elsewhere ,
F ( z ) = { exp ( z Z ) for 0 z Z 0 elsewhere ,