Abstract

The primary interest in the finite-energy Airy beam derives from the special properties possessed by the maximum intensity at its central lobe. However, the defining spatial dependence, the Airy function, is an oscillatory function that consists of decaying side lobes. For some applications these side lobes may create deleterious effects. Fortunately, a nonsymmetric apodization of the beam in Fourier space is shown to enhance the central lobe as the side lobes are reduced and clipped. The properties of the central lobe are unaffected over a large proportion of the propagation path.

© 2011 Optical Society of America

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References

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2010 (4)

2009 (2)

T. Ellenbogen, N. Voloch-Bloch, A. Ganany-Padowicz, and A. Arie, Nat. Photon. 3, 395 (2009).
[CrossRef]

P. Polynkin, M. Kolisik, J. Moloney, G. Siviloglou, and D. Christodoulides, Science 324, 229 (2009).
[CrossRef] [PubMed]

2008 (2)

2007 (1)

Arie, A.

T. Ellenbogen, N. Voloch-Bloch, A. Ganany-Padowicz, and A. Arie, Nat. Photon. 3, 395 (2009).
[CrossRef]

Baumgartl, J.

J. Baumgartl, M. Mazilu, and K. Dholakia, Nat. Photon. 2, 675 (2008).
[CrossRef]

Broky, J.

Carvalho, M.

Cheng, H.

Christodoulides, D.

Dholakia, K.

J. Baumgartl, M. Mazilu, and K. Dholakia, Nat. Photon. 2, 675 (2008).
[CrossRef]

Dogariu, A.

Ellenbogen, T.

T. Ellenbogen, N. Voloch-Bloch, A. Ganany-Padowicz, and A. Arie, Nat. Photon. 3, 395 (2009).
[CrossRef]

Facao, M.

Ganany-Padowicz, A.

T. Ellenbogen, N. Voloch-Bloch, A. Ganany-Padowicz, and A. Arie, Nat. Photon. 3, 395 (2009).
[CrossRef]

Gbur, G.

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1968).

Gu, Y.

Heyman, E.

Kaganovsky, Y.

Kolisik, M.

P. Polynkin, M. Kolisik, J. Moloney, G. Siviloglou, and D. Christodoulides, Science 324, 229 (2009).
[CrossRef] [PubMed]

Mazilu, M.

J. Baumgartl, M. Mazilu, and K. Dholakia, Nat. Photon. 2, 675 (2008).
[CrossRef]

Moloney, J.

P. Polynkin, M. Kolisik, J. Moloney, G. Siviloglou, and D. Christodoulides, Science 324, 229 (2009).
[CrossRef] [PubMed]

Polynkin, P.

P. Polynkin, M. Kolisik, J. Moloney, G. Siviloglou, and D. Christodoulides, Science 324, 229 (2009).
[CrossRef] [PubMed]

Siviloglou, G.

Tian, J.

Voloch-Bloch, N.

T. Ellenbogen, N. Voloch-Bloch, A. Ganany-Padowicz, and A. Arie, Nat. Photon. 3, 395 (2009).
[CrossRef]

Zang, W.

Zhuo, W.

Nat. Photon. (2)

T. Ellenbogen, N. Voloch-Bloch, A. Ganany-Padowicz, and A. Arie, Nat. Photon. 3, 395 (2009).
[CrossRef]

J. Baumgartl, M. Mazilu, and K. Dholakia, Nat. Photon. 2, 675 (2008).
[CrossRef]

Opt. Express (4)

Opt. Lett. (2)

Science (1)

P. Polynkin, M. Kolisik, J. Moloney, G. Siviloglou, and D. Christodoulides, Science 324, 229 (2009).
[CrossRef] [PubMed]

Other (1)

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1968).

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Figures (6)

Fig. 1
Fig. 1

Ray optics caustics of (a) the finite- energy Airy beam and (b) the same beam generated with pupil apodization.

Fig. 2
Fig. 2

Normalized transverse intensity distributions H at various z values versus x for (a) a finite-energy Airy beam and (b) the same beam generated with pupil apodization. The corresponding values of z are (i)  0.2 , (ii) 0, (iii) 0.2, (iv) 0.4, and (v)  0.6 cm .

Fig. 3
Fig. 3

Ratio of the intensity at the central lobe to the intensity at the second lobe versus z for various apodi zation parameters. Units of c and β are centimeters and cm 1 , respectively.

Fig. 4
Fig. 4

Transverse position of the central lobe versus z (blue solid curve) with and (red dashed curve) without apodization.

Fig. 5
Fig. 5

Normalized intensities of the central lobe and first two side lobes versus z for apodization param eters c = 0.1 cm and β = 3.0 cm 1 .

Fig. 6
Fig. 6

Peak intensity of the central lobe relative to the peak intensity with no apodization at constant beam power versus c for (blue solid curve) β = 3.0 cm 1 ; total transmission of the pupil (red dotted curve) versus c.

Equations (2)

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H ( x , z ) = A λ ( f + z ) | e ( i k ( m u 3 W 20 u 2 x f + z u ) α u 2 ) d u | 2 ,
M ( u ) = 1 / ( 1 + e β ( u + c ) ) ,

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