Abstract

We report the first experimental observation of parabolic non-diffracting beams, the fourth fundamental family of propagation-invariant optical fields of the Helmholtz equation. We generate the even and odd stationary parabolic beam and with them we are able to produce traveling parabolic beams. It is observed that these fields exhibit a number of unitary in-line vortices that do not interact on propagation. The experimental transverse patterns show an inherent parabolic structure in good agreement with the theoretical predictions. Our results exhibit a transverse energy flow of traveling beams never observed before.

© 2005 Optical Society of America

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References

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Appl Phys. B

C. O. Weiss, M. Vaupel, K. Staliunas, G. Slekys and V. B. Taranenko, �?? Solitons and vortices in lasers,�?? Appl Phys. B 68, 151�??168 (1999).
[CrossRef]

J. Mod. Opt.

S. Chávez-Cerda, �??A new approach to Bessel beams,�?? J. Mod. Opt. 46, 923�??942 (1999).

J. Opt. B: Quantum Semiclass.

K. Volke-Sepúlveda, V. Garcés-Chávez, S. Chávez-Cerda, J. Arlt, and K. Dholakia, �??Orbital angular momentum of a high-order Bessel light beam,�?? J. Opt. B: Quantum Semiclass. Opt. 4, S82�??S89 (2002).
[CrossRef]

J. Opt. B: Quantum Semiclass. Opt.

S. Chávez-Cerda, M. J. Padgett, I. Allison, G. H. C. New, J. C. Gutiérrez-Vega, A. T. O�??Neil, I. MacVicar, and J. Courtial, �??Holographic generation and orbital angular momentum of high-order Mathieu beams,�?? J. Opt. B: Quantum Semiclass. Opt. 4, S52�??S57 (2002).
[CrossRef]

J. Opt. Soc. Am. A

J. Vac. Sci. Technol. B

M. Erdélyi, Z. L. Horváth, G. Szabó, S. Bor, F. K. Tittel, J. R. Cavallaro, and M. C. Smayling, �??Generation of diffraction-free beams for applications in optical microlithography,�?? J. Vac. Sci. Technol. B 15, 287�??292 (1997).
[CrossRef]

Nature

V. Garcés-Chávez, D. McGloin, H. Melville, W. Sibbett, and K. Dholakia, �??Simultaneous micromanipulation in multiple planes using a self-reconstructing light beam,�?? Nature 419, 145�??147 (2002).
[CrossRef] [PubMed]

Opt. Commun

J. C. Gutiérrez-Vega, M. D. Iturbe-Castillo, G. A. Ramírez, E. Tepichín, R. M. Rodríguez-Dagnino, S. Chávez-Cerda, and G.H.C. New, �??Experimental demonstration of optical Mathieu beams,�?? Opt. Commun. 195, 35�??40 (2001).
[CrossRef]

Opt. Commun.

J. Y. Lu and S. He, �??Optical X wave communications,�?? Opt. Commun. 161, 187�??192 (1999).
[CrossRef]

Opt. Lett.

Opt. Soc. Am. A

G. Indebetouw, �??Nondiffractiing optical fields: some remarks on their analysis and synthesis,�?? J. Opt. Soc. Am. A 6, 150�??152 (1989).
[CrossRef]

Phys. Rev. Lett.

D. L. Feder, A. A. Svidzinsky, A. L. Fetter and C. W. Clark, �??Anomalous Modes Drive Vortex Dynamics in Confined Bose-Einstein Condensates,�?? Phys. Rev. Lett. 86, 564�??567 (2001).
[CrossRef] [PubMed]

I. S. Aranson, A. R. Bishop, I. Daruka and V. M. Vinokur, �??Ginzburg-Landau Theory of Spiral Surface Growth,�?? Phys. Rev. Lett. 80, 1770�??1773 (1998).
[CrossRef]

J. Durnin, J. J. Micely Jr., and J. H. Eberly, �??Diffraction-Free Beams,�?? Phys. Rev. Lett. 58, 1499�??1501 (1987).
[CrossRef] [PubMed]

Proc. R. Soc. Lond

J. F. Nye and M. V. Berry, �??Dislocations in wave trains, �?? Proc. R. Soc. Lond. A 336, 165�??190 (1974).
[CrossRef]

Other

H. I. Bjelkhagen, Silver-halide recording materials (Springer, Berlin, 1993) Ch. 5.

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Figures (4)

Fig. 1.
Fig. 1.

Experimental transverse intensity profiles of the (a) even and (b) odd PBs for α=0. For the even beam f=30 cm and R=4.5 cm, whereas for the odd beam f=15 cm, R=2.5 cm and z is the distance from the lens.

Fig. 2.
Fig. 2.

Experimental transverse intensity profiles of the even (a) and odd (b) high-order PBs for α=4.0 at different distances along the propagation axis.

Fig. 3.
Fig. 3.

a) Photographic sequence of the propagation of a bounded traveling PB TU-(η,ξ ;α=4). (b) Computer simulated propagation.

Fig. 4.
Fig. 4.

Interference pattern between the generated traveling beam TU-(η,ξ ;α=4) and a reference plane wave. A number of in-line vortices lying along the positive x axis are observed.

Equations (6)

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u ( r t ) = π π A ( φ ) exp [ i k t ( x cos φ + y sin φ ) ] d φ ,
u e ( r t ; a ) = Γ 1 2 π 2 P e ( σ ξ ; a ) P e ( σ η ; a ) ,
u o ( r t ; a ) = 2 Γ 3 2 π 2 P o ( σ ξ ; a ) P o ( σ η ; a ) ,
A e ( φ ; a ) = 1 2 ( π sin φ ) 1 2 exp ( i a ln tan φ 2 ) ,
A o ( φ ; a ) = 1 i { A e ( φ ; a ) , φ ( π , 0 ) A e ( φ ; a ) , φ ( 0 , π ) ,
T U ± ( r ; a ) = [ u e ( r t ; a ) ± i u o ( r t ; a ) ] exp ( i k z z ) ,

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