Abstract

In this work, we theoretically and experimentally study the physical process of Airy beams induced by binary phase patterns combined with a slope factor. Theoretical simulations show that the binary phase patterns generate a pair of symmetrically inverted twin Airy beams. The slope factor can regulate the spacing between the two Airy beam peaks, decrease the error induced by the binarization process, and adjust the position of the focus formed by the twin Airy beams. The experimental results are consistent with the theoretical ones.

© 2013 Optical Society of America

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References

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  1. M. V. Berry and N. L. Balazs, Am. J. Phys. 47, 264 (1979).
    [CrossRef]
  2. G. A. Siviloglou and D. N. Christodoulides, Opt. Lett. 32, 979 (2007).
    [CrossRef]
  3. G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, Opt. Lett. 33, 207 (2008).
    [CrossRef]
  4. J. Baumgartl, M. Mazilu, and K. Dholakia, Nat. Photonics 2, 675 (2008).
    [CrossRef]
  5. I. M. Besieris and A. M. Shaarawi, Opt. Lett. 32, 2447 (2007).
    [CrossRef]
  6. A. V. Novitsky and D. V. Novitsky, Opt. Lett. 34, 3430 (2009).
    [CrossRef]
  7. J. Broky, G. A. Siviloglou, A. Dogariu, and D. N. Christodoulides, Opt. Express 16, 12880 (2008).
    [CrossRef]
  8. H. I. Sztul and R. R. Alfano, Opt. Express 16, 9411 (2008).
    [CrossRef]
  9. G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, Phys. Rev. Lett. 99, 213901 (2007).
    [CrossRef]
  10. H. T. Dai, X. W. Sun, D. Luo, and Y. J. Liu, Opt. Express 17, 19365 (2009).
    [CrossRef]

2009

2008

2007

1979

M. V. Berry and N. L. Balazs, Am. J. Phys. 47, 264 (1979).
[CrossRef]

Alfano, R. R.

Balazs, N. L.

M. V. Berry and N. L. Balazs, Am. J. Phys. 47, 264 (1979).
[CrossRef]

Baumgartl, J.

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

Berry, M. V.

M. V. Berry and N. L. Balazs, Am. J. Phys. 47, 264 (1979).
[CrossRef]

Besieris, I. M.

Broky, J.

Christodoulides, D. N.

Dai, H. T.

Dholakia, K.

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

Dogariu, A.

Liu, Y. J.

Luo, D.

Mazilu, M.

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

Novitsky, A. V.

Novitsky, D. V.

Shaarawi, A. M.

Siviloglou, G. A.

Sun, X. W.

Sztul, H. I.

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Figures (6)

Fig. 1.
Fig. 1.

Phase profiles and corresponding frequency spectra. (a) Gray cubic phase and (b) corresponding frequency spectrum. (c) Binary phase and (d) corresponding frequency spectrum.

Fig. 2.
Fig. 2.

Two-dimensional phase patterns and corresponding frequency spectra: (a) cubic phase pattern of f2a, (b) slope phase pattern of f2g, (c) combined phase pattern of f2ag, and (d) binary phase pattern of fbin(2ag). (A)–(D) are the corresponding frequency spectra of (a)–(d), respectively.

Fig. 3.
Fig. 3.

Slope factor-induced binary phase patterns and Airy beams: binary phase patterns at (a) g=5, (b) g=3, (c) g=0, (d) g=3, and (e) g=5, respectively. (A)–(E) are the corresponding twin Airy beams.

Fig. 4.
Fig. 4.

Dependence of frequency spectrum error on slope factor.

Fig. 5.
Fig. 5.

Experimental setup for generating twin Airy beams using binary phase patterns. Inset is typical results at g=5rad/mm.

Fig. 6.
Fig. 6.

Propagating properties of the twin Airy beams generated using binary phase patterns. Twin Airy beams captured by CCD at (a) z=0mm, (b) z=140mm, (c) z=283.5mm, and (d) z=350mm. (e) Simulation results of the experimental results of (a)–(d).

Equations (9)

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f1B(k)=+π2atf1(k)[2nπ,(2n+1)π]f1B(k)=π2atf1(k)[(2n1)π,2nπ),
F1B(x)=exp[if1B(k)]exp(2πikx)dkF1B*(x)=exp[if1B(k)]exp(2πikx)dkF1B(x)=exp[if1B(k)]exp(2πikx)dk.
F1B(x)F1B*(x)=F1B(x)F1B*(x).
f2a(kx,ky)=kx3+ky33,
f2g(kx,ky)=g·(kx+ky).
f2ag(kx,ky)=f2a(kx,ky)+f2g(kx,ky).
F2ag(x,y)=F{exp[if2ag(kx,ky)]}=F{exp[if2a(kx,ky)]·exp[if2g(kx,ky)]}=F{exp[if2a(kx,ky)]}F{exp[if2g(kx,ky)]}=F{exp[if2a(kx,ky)]}F{exp[ig(kx,ky)]}=A(x,y)δ(xg/2π,yg/2π)=A(xg/2π,yg/2π),
fbin(2ag)(kx,ky)=+π/2atf2ag(kx,ky)[2nπ,(2n+1)π]fbin(2ag)(kx,ky)=π/2atf2ag(kx,ky)[(2n1)π,2nπ).
eF=(F2agF2ag*2Fbin(2ag)Fbin(2ag)*)2(F2agF2ag*)2,

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