Abstract

We introduce a technique to generate arbitrary nondiffracting beams. Using a genetic algorithm that uses a Gaussian weight function merged with spatial spectrum engineering techniques, we show that it is possible to obtain the angular spectrum representation of arbitrary light patterns, thus demonstrating their nondiffracting properties.

© 2012 Optical Society of America

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2012

2011

2010

M. Mazilu, D. J. Stevenson, F. Gunn-Moore, and K. Dholakia, Laser Photon. Rev. 4, 529 (2010).
[CrossRef]

S. López-Aguayo, Y. V. Kartashov, V. A. Vysloukh, and L. Torner, Phys. Rev. Lett. 105, 013902 (2010).
[CrossRef]

2009

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, Prog. Opt. 52, 63 (2009).
[CrossRef]

2008

C. López-Mariscal and J. C. Gutiérrez-Vega, J. Opt. A: Pure Appl. Opt. 10, 015009 (2008).
[CrossRef]

2007

2005

2004

2000

1998

1996

1987

J. Durnin, J. J. Miceli, and J. H. Eberly, Phys. Rev. Lett. 58, 1499 (1987).
[CrossRef]

1982

Bandres, M. A.

Chávez-Cerda, S.

Cižmár, T.

K. Dholakia and T. Čižmár, Nat. Photonics 5, 335 (2011).
[CrossRef]

Collaro, A.

Cottrell, D. M.

Craven, J. M.

Davis, J. A.

Dholakia, K.

K. Dholakia and T. Čižmár, Nat. Photonics 5, 335 (2011).
[CrossRef]

M. Mazilu, D. J. Stevenson, F. Gunn-Moore, and K. Dholakia, Laser Photon. Rev. 4, 529 (2010).
[CrossRef]

Durnin, J.

J. Durnin, J. J. Miceli, and J. H. Eberly, Phys. Rev. Lett. 58, 1499 (1987).
[CrossRef]

Eberly, J. H.

J. Durnin, J. J. Miceli, and J. H. Eberly, Phys. Rev. Lett. 58, 1499 (1987).
[CrossRef]

Ferreiro, M. S.

Fienup, J. R.

Franceschetti, G.

Gunn-Moore, F.

M. Mazilu, D. J. Stevenson, F. Gunn-Moore, and K. Dholakia, Laser Photon. Rev. 4, 529 (2010).
[CrossRef]

Gutiérrez-Vega, J. C.

Iturbe-Castillo, M. D.

Jia, W.

Jiang, L.

Kartashov, Y. V.

Y. V. Kartashov, S. López-Aguayo, V. A. Vysloukh, and L. Torner, Opt. Express 19, 9505 (2011).
[CrossRef]

S. López-Aguayo, Y. V. Kartashov, V. A. Vysloukh, and L. Torner, Phys. Rev. Lett. 105, 013902 (2010).
[CrossRef]

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, Prog. Opt. 52, 63 (2009).
[CrossRef]

Kihm, K. D.

Li, X.

López-Aguayo, S.

Y. V. Kartashov, S. López-Aguayo, V. A. Vysloukh, and L. Torner, Opt. Express 19, 9505 (2011).
[CrossRef]

S. López-Aguayo, Y. V. Kartashov, V. A. Vysloukh, and L. Torner, Phys. Rev. Lett. 105, 013902 (2010).
[CrossRef]

López-Mariscal, C.

C. López-Mariscal and J. C. Gutiérrez-Vega, J. Opt. A: Pure Appl. Opt. 10, 015009 (2008).
[CrossRef]

Lyons, D. P.

Mazilu, M.

M. Mazilu, D. J. Stevenson, F. Gunn-Moore, and K. Dholakia, Laser Photon. Rev. 4, 529 (2010).
[CrossRef]

Miceli, J. J.

J. Durnin, J. J. Miceli, and J. H. Eberly, Phys. Rev. Lett. 58, 1499 (1987).
[CrossRef]

Michalewicz, Z.

Z. Michalewicz, Genetic Algorithms+Data Structures=Evolution Programs (Springer, 1996), p. 111.

Palmieri, F.

Stevenson, D. J.

M. Mazilu, D. J. Stevenson, F. Gunn-Moore, and K. Dholakia, Laser Photon. Rev. 4, 529 (2010).
[CrossRef]

Torner, L.

Y. V. Kartashov, S. López-Aguayo, V. A. Vysloukh, and L. Torner, Opt. Express 19, 9505 (2011).
[CrossRef]

S. López-Aguayo, Y. V. Kartashov, V. A. Vysloukh, and L. Torner, Phys. Rev. Lett. 105, 013902 (2010).
[CrossRef]

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, Prog. Opt. 52, 63 (2009).
[CrossRef]

Vysloukh, V. A.

Y. V. Kartashov, S. López-Aguayo, V. A. Vysloukh, and L. Torner, Opt. Express 19, 9505 (2011).
[CrossRef]

S. López-Aguayo, Y. V. Kartashov, V. A. Vysloukh, and L. Torner, Phys. Rev. Lett. 105, 013902 (2010).
[CrossRef]

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, Prog. Opt. 52, 63 (2009).
[CrossRef]

Zheng, G.

Appl. Opt.

J. Opt. A: Pure Appl. Opt.

C. López-Mariscal and J. C. Gutiérrez-Vega, J. Opt. A: Pure Appl. Opt. 10, 015009 (2008).
[CrossRef]

J. Opt. Soc. Am. A

Laser Photon. Rev.

M. Mazilu, D. J. Stevenson, F. Gunn-Moore, and K. Dholakia, Laser Photon. Rev. 4, 529 (2010).
[CrossRef]

Nat. Photonics

K. Dholakia and T. Čižmár, Nat. Photonics 5, 335 (2011).
[CrossRef]

Opt. Express

Opt. Lett.

Phys. Rev. Lett.

J. Durnin, J. J. Miceli, and J. H. Eberly, Phys. Rev. Lett. 58, 1499 (1987).
[CrossRef]

S. López-Aguayo, Y. V. Kartashov, V. A. Vysloukh, and L. Torner, Phys. Rev. Lett. 105, 013902 (2010).
[CrossRef]

Prog. Opt.

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, Prog. Opt. 52, 63 (2009).
[CrossRef]

Other

Z. Michalewicz, Genetic Algorithms+Data Structures=Evolution Programs (Springer, 1996), p. 111.

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Figures (3)

Fig. 1.
Fig. 1.

(a) Objective intensity pattern of a third order modulated Bessel beam and (b) intensity pattern obtained, using the genetic algorithm and (c) its phase distribution. All profiles are shown in a xy box of 12×12 with kt=4. (d) Evolution of the error function. (e) Amplitude and (f) phase angular spectrum obtained with the genetic algorithm.

Fig. 2.
Fig. 2.

(a) Objective intensity pattern of a fourth even order Mathieu beam. (b) Intensity obtained pattern and (c) phase distribution using the GA. (d) Amplitude and (e) phase angular spectrum obtained using the GA. (f) Evolution of the error function. (g) Objective intensity pattern of a traveling parabolic beam. (h) Obtained intensity and (i) phase distributions using the GA. (j) Amplitude and (k) phase angular spectrum obtained using the GA. (l) Evolution of the error function. All profiles are shown in a xy box of 12×12 with kt=4.

Fig. 3.
Fig. 3.

(a) Intensity, (b) phase, and (c) amplitude and (d) phase angular spectrum of unusual NBs that corresponds to an asymmetric Bessel beam, a zigzag cosine like beam and a spiral nondiffracting beam. All profiles are shown in a xy box of 12×12 with kt=3 for the zigzag case, and kt=4 for the rest.

Equations (5)

Equations on this page are rendered with MathJax. Learn more.

Ψ(r)=02πA(ϕ)exp[iktrcos(ϕθ)]dϕ.
A(ϕ)=n=1Nαnexp(iβn)δ(ϕϕn),
Ψ(r)=n=1Nαnexp(iβn)exp[iktrcos(ϕnθ)].
γ=jNxkNywjk|ΨΨ*ΨobjΨobj*|,
w(r)=σr12/πexp(r2/2σr2),

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