Abstract

We present an attenuation-corrected “nondiffracting” Airy beam. The correction factor can be adjusted to deliver a beam that exhibits an adjustable exponential intensity increase or decrease over a finite distance. A digital micromirror device that shapes both amplitude and phase is used to experimentally verify the propagation of these beams through air and partially absorbing media.

© 2014 Optical Society of America

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  19. R. Floyd and L. Steinberg, Proc. Soc. Inf. Disp. 17, 75 (1976).

2014

T. Vettenburg, H. I. C. Dalgarno, J. Nylk, C. Coll-Llado, D. E. K. Ferrier, T. Cizmar, F. J. Gunn-Moore, and K. Dholakia, Nat. Methods 11, 541 (2014).
[CrossRef]

S. Jia, J. C. Vaughan, and X. Zhuang, Nat. Photonics 8, 302 (2014).
[CrossRef]

2013

2012

2011

H. Ryoo, D. W. Kang, and J. W. Hahn, Microelectron. Eng. 88, 235 (2011).
[CrossRef]

2010

A. Chong, W. H. Renninger, D. N. Christodoulides, and F. W. Wise, Nat. Photonics 4, 103 (2010).
[CrossRef]

D. Abdollahpour, S. Suntsov, D. G. Papazoglou, and S. Tzortzakis, Phys. Rev. Lett. 105, 253901 (2010).
[CrossRef]

Y.-X. Ren, M. Li, K. Huang, J.-G. Wu, H.-F. Gao, Z.-Q. Wang, and Y.-M. Li, Appl. Opt. 49, 1838 (2010).
[CrossRef]

A. Salandrino and D. N. Christodoulides, Opt. Lett. 35, 2082 (2010).
[CrossRef]

2009

P. Polynkin, M. Kolesik, and J. Moloney, Phys. Rev. Lett. 103, 123902 (2009).
[CrossRef]

2008

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

2007

G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, Phys. Rev. Lett. 99, 213901 (2007).
[CrossRef]

1994

B. Kolner, IEEE J. Quantum Electron. 30, 1951 (1994).
[CrossRef]

1979

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

1976

R. Floyd and L. Steinberg, Proc. Soc. Inf. Disp. 17, 75 (1976).

1969

B. R. Brown and A. W. Lohmann, IBM J. Res. Dev. 13, 160 (1969).
[CrossRef]

Abdollahpour, D.

D. Abdollahpour, S. Suntsov, D. G. Papazoglou, and S. Tzortzakis, Phys. Rev. Lett. 105, 253901 (2010).
[CrossRef]

Balazs, N.

M. Berry and N. 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.

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

Boyd, R. W.

Broky, J.

G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, Phys. Rev. Lett. 99, 213901 (2007).
[CrossRef]

Brown, B. R.

B. R. Brown and A. W. Lohmann, IBM J. Res. Dev. 13, 160 (1969).
[CrossRef]

Chen, C.

Chong, A.

A. Chong, W. H. Renninger, D. N. Christodoulides, and F. W. Wise, Nat. Photonics 4, 103 (2010).
[CrossRef]

Christodoulides, D. N.

A. Chong, W. H. Renninger, D. N. Christodoulides, and F. W. Wise, Nat. Photonics 4, 103 (2010).
[CrossRef]

A. Salandrino and D. N. Christodoulides, Opt. Lett. 35, 2082 (2010).
[CrossRef]

G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, Phys. Rev. Lett. 99, 213901 (2007).
[CrossRef]

Cizmar, T.

T. Vettenburg, H. I. C. Dalgarno, J. Nylk, C. Coll-Llado, D. E. K. Ferrier, T. Cizmar, F. J. Gunn-Moore, and K. Dholakia, Nat. Methods 11, 541 (2014).
[CrossRef]

Coll-Llado, C.

T. Vettenburg, H. I. C. Dalgarno, J. Nylk, C. Coll-Llado, D. E. K. Ferrier, T. Cizmar, F. J. Gunn-Moore, and K. Dholakia, Nat. Methods 11, 541 (2014).
[CrossRef]

Dalgarno, H. I. C.

T. Vettenburg, H. I. C. Dalgarno, J. Nylk, C. Coll-Llado, D. E. K. Ferrier, T. Cizmar, F. J. Gunn-Moore, and K. Dholakia, Nat. Methods 11, 541 (2014).
[CrossRef]

Dholakia, K.

T. Vettenburg, H. I. C. Dalgarno, J. Nylk, C. Coll-Llado, D. E. K. Ferrier, T. Cizmar, F. J. Gunn-Moore, and K. Dholakia, Nat. Methods 11, 541 (2014).
[CrossRef]

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

Dogariu, A.

G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, Phys. Rev. Lett. 99, 213901 (2007).
[CrossRef]

Drori, Y.

Ferrier, D. E. K.

T. Vettenburg, H. I. C. Dalgarno, J. Nylk, C. Coll-Llado, D. E. K. Ferrier, T. Cizmar, F. J. Gunn-Moore, and K. Dholakia, Nat. Methods 11, 541 (2014).
[CrossRef]

Floyd, R.

R. Floyd and L. Steinberg, Proc. Soc. Inf. Disp. 17, 75 (1976).

Gao, H.-F.

Gong, L.

Gunn-Moore, F. J.

T. Vettenburg, H. I. C. Dalgarno, J. Nylk, C. Coll-Llado, D. E. K. Ferrier, T. Cizmar, F. J. Gunn-Moore, and K. Dholakia, Nat. Methods 11, 541 (2014).
[CrossRef]

Hahn, J. W.

H. Ryoo, D. W. Kang, and J. W. Hahn, Microelectron. Eng. 88, 235 (2011).
[CrossRef]

Huang, K.

Jia, S.

S. Jia, J. C. Vaughan, and X. Zhuang, Nat. Photonics 8, 302 (2014).
[CrossRef]

Kang, D. W.

H. Ryoo, D. W. Kang, and J. W. Hahn, Microelectron. Eng. 88, 235 (2011).
[CrossRef]

Katz, N.

Kolesik, M.

P. Polynkin, M. Kolesik, and J. Moloney, Phys. Rev. Lett. 103, 123902 (2009).
[CrossRef]

Kolner, B.

B. Kolner, IEEE J. Quantum Electron. 30, 1951 (1994).
[CrossRef]

Lerner, V.

Li, M.

Li, Y.-M.

Lin, J.

Q. Xu, Y. Wang, S. Siew, J. Lin, and Y. Zhang, “Generating self-accelerating Airy beams using a digital micromirror device,” Appl. Phys. B, doi:10.1007/s00340-014-5813-2 (2014).
[CrossRef]

Lohmann, A. W.

B. R. Brown and A. W. Lohmann, IBM J. Res. Dev. 13, 160 (1969).
[CrossRef]

Malik, M.

Mazilu, M.

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

Mirhosseini, M.

Moloney, J.

P. Polynkin, M. Kolesik, and J. Moloney, Phys. Rev. Lett. 103, 123902 (2009).
[CrossRef]

na Loaiza, O. S. M.

Nylk, J.

T. Vettenburg, H. I. C. Dalgarno, J. Nylk, C. Coll-Llado, D. E. K. Ferrier, T. Cizmar, F. J. Gunn-Moore, and K. Dholakia, Nat. Methods 11, 541 (2014).
[CrossRef]

Papazoglou, D. G.

D. Abdollahpour, S. Suntsov, D. G. Papazoglou, and S. Tzortzakis, Phys. Rev. Lett. 105, 253901 (2010).
[CrossRef]

Polynkin, P.

P. Polynkin, M. Kolesik, and J. Moloney, Phys. Rev. Lett. 103, 123902 (2009).
[CrossRef]

Preciado, M. A.

Ren, Y.-X.

Renninger, W. H.

A. Chong, W. H. Renninger, D. N. Christodoulides, and F. W. Wise, Nat. Photonics 4, 103 (2010).
[CrossRef]

Rodenburg, B.

Ryoo, H.

H. Ryoo, D. W. Kang, and J. W. Hahn, Microelectron. Eng. 88, 235 (2011).
[CrossRef]

Salandrino, A.

Shwa, D.

Siew, S.

Q. Xu, Y. Wang, S. Siew, J. Lin, and Y. Zhang, “Generating self-accelerating Airy beams using a digital micromirror device,” Appl. Phys. B, doi:10.1007/s00340-014-5813-2 (2014).
[CrossRef]

Siviloglou, G. A.

G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, Phys. Rev. Lett. 99, 213901 (2007).
[CrossRef]

Steinberg, L.

R. Floyd and L. Steinberg, Proc. Soc. Inf. Disp. 17, 75 (1976).

Sugden, K.

Suntsov, S.

D. Abdollahpour, S. Suntsov, D. G. Papazoglou, and S. Tzortzakis, Phys. Rev. Lett. 105, 253901 (2010).
[CrossRef]

Tzortzakis, S.

D. Abdollahpour, S. Suntsov, D. G. Papazoglou, and S. Tzortzakis, Phys. Rev. Lett. 105, 253901 (2010).
[CrossRef]

Vaughan, J. C.

S. Jia, J. C. Vaughan, and X. Zhuang, Nat. Photonics 8, 302 (2014).
[CrossRef]

Vettenburg, T.

T. Vettenburg, H. I. C. Dalgarno, J. Nylk, C. Coll-Llado, D. E. K. Ferrier, T. Cizmar, F. J. Gunn-Moore, and K. Dholakia, Nat. Methods 11, 541 (2014).
[CrossRef]

Wang, Q.-C.

Wang, Y.

Q. Xu, Y. Wang, S. Siew, J. Lin, and Y. Zhang, “Generating self-accelerating Airy beams using a digital micromirror device,” Appl. Phys. B, doi:10.1007/s00340-014-5813-2 (2014).
[CrossRef]

Wang, Z.-Q.

Wise, F. W.

A. Chong, W. H. Renninger, D. N. Christodoulides, and F. W. Wise, Nat. Photonics 4, 103 (2010).
[CrossRef]

Wu, J.-G.

Xu, Q.

Q. Xu, Y. Wang, S. Siew, J. Lin, and Y. Zhang, “Generating self-accelerating Airy beams using a digital micromirror device,” Appl. Phys. B, doi:10.1007/s00340-014-5813-2 (2014).
[CrossRef]

Xue, G.-S.

Zhang, Y.

Q. Xu, Y. Wang, S. Siew, J. Lin, and Y. Zhang, “Generating self-accelerating Airy beams using a digital micromirror device,” Appl. Phys. B, doi:10.1007/s00340-014-5813-2 (2014).
[CrossRef]

Zhong, M.-C.

Zhou, J.-H.

Zhuang, X.

S. Jia, J. C. Vaughan, and X. Zhuang, Nat. Photonics 8, 302 (2014).
[CrossRef]

Am. J. Phys.

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

Appl. Opt.

IBM J. Res. Dev.

B. R. Brown and A. W. Lohmann, IBM J. Res. Dev. 13, 160 (1969).
[CrossRef]

IEEE J. Quantum Electron.

B. Kolner, IEEE J. Quantum Electron. 30, 1951 (1994).
[CrossRef]

Microelectron. Eng.

H. Ryoo, D. W. Kang, and J. W. Hahn, Microelectron. Eng. 88, 235 (2011).
[CrossRef]

Nat. Methods

T. Vettenburg, H. I. C. Dalgarno, J. Nylk, C. Coll-Llado, D. E. K. Ferrier, T. Cizmar, F. J. Gunn-Moore, and K. Dholakia, Nat. Methods 11, 541 (2014).
[CrossRef]

Nat. Photonics

S. Jia, J. C. Vaughan, and X. Zhuang, Nat. Photonics 8, 302 (2014).
[CrossRef]

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

A. Chong, W. H. Renninger, D. N. Christodoulides, and F. W. Wise, Nat. Photonics 4, 103 (2010).
[CrossRef]

Opt. Express

Opt. Lett.

Phys. Rev. Lett.

D. Abdollahpour, S. Suntsov, D. G. Papazoglou, and S. Tzortzakis, Phys. Rev. Lett. 105, 253901 (2010).
[CrossRef]

P. Polynkin, M. Kolesik, and J. Moloney, Phys. Rev. Lett. 103, 123902 (2009).
[CrossRef]

G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, Phys. Rev. Lett. 99, 213901 (2007).
[CrossRef]

Proc. Soc. Inf. Disp.

R. Floyd and L. Steinberg, Proc. Soc. Inf. Disp. 17, 75 (1976).

Other

Q. Xu, Y. Wang, S. Siew, J. Lin, and Y. Zhang, “Generating self-accelerating Airy beams using a digital micromirror device,” Appl. Phys. B, doi:10.1007/s00340-014-5813-2 (2014).
[CrossRef]

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Figures (5)

Fig. 1.
Fig. 1.

Intensity profile of the attenuation-compensating Airy beam as it propagates through a losses medium with x0=1, z0=1, α=0, and b0=0.2; (a) xz intensity density plot; and (b) cross section in the apex plane z=0.

Fig. 2.
Fig. 2.

Setup for (a) lossless (air) and (b) lossy (Rhodamine B solution) Airy beam propagation experiments. LS, laser source; BE, beam expander; M, mirror; CV, cuvette with solution; L1, L2, and L3, lenses; CCD, charge-coupled device camera; DMD, digital micromirror device; PH, pinhole.

Fig. 3.
Fig. 3.

Beam intensity function captured with the CCD after 11 cm of lossless propagation. (a)–(c) First, second, and third example, where beam axes “1” and “2” are showed in a white dotted and dashed–dotted line, respectively. (d)–(i) Measured (solid) and numerically simulated (dashed) beam intensity across beam axes [(d), (e), and (f)] “1” and [(g), (h), and (i)] “2” for the first, second, and third beam example, respectively.

Fig. 4.
Fig. 4.

Beam peak intensity during the lossless propagation from numerical simulation (solid) and experimental measurements (circle-dashed) for the (a) first, (b) second, and (c) third beam example, designed to exhibit an exponential growth of 0, 1.29, and 2.48 dB/cm, respectively.

Fig. 5.
Fig. 5.

Peak intensity along a path of lossy medium propagation inside the cuvette containing the Rhodamine B water solution, obtained from experimental measurements (crosses) and linear fit (solid), compared to the theoretically expected peak intensity evolution (dashed) for the (a) first, (b) second, and (c) third beam example, respectively.

Equations (5)

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

u^0(kx)=x0exp(ix03kx3/3),
u^(kx,z)=exp(ikx2z2kikz)u^0(kx)exp(b0kx),
u^(kx,z)exp(ikx2z2n0k0ikz)u^0(kx)exp(b0kx).
u(x,z)=Ai(xx0z24z02+ib0x0)exp(αz2+zb02z0x0)exp(iz312z03iz0zx02izx2z0x0),
f(x,y)=f0(x,y)+f+1(x,y)+f1(x,y)=|ψ(x,y)|+Re(ψ(x,y)ei(kxx+kyy)),

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