Abstract

To controllably deflect the Airy beam in a wide range dynamic, the method of combining the classical Airy cubic phase with a diffraction blazed grating phase was adopted in this paper. By dynamically adjusting the grating parameters, the transverse self-accelerating Airy beam allows arbitrary deflection, and the deflected position can be controlled precisely. The mathematical model of the Airy beam optical field distributions generated by the combined phase patterns were proposed to explain the feasibility. Its correctness was ultimately demonstrated by the experimental results. It is significant to use this method for the Airy beam deflection control in high-precision closed-loop aiming systems.

© 2012 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef]
  3. J. Parravicini, P. Minzioni, V. Degiorgio, and E. DelRe, “Observation of nonlinear Airy-like beam evolution in lithium niobate,” Opt. Lett. 34, 3908–3910 (2009).
    [CrossRef]
  4. I. Dolev, T. Ellenbogen, and A. Arie, “Switching the acceleration direction of Airy beams by a nonlinear optical process,” Opt. Lett. 35, 1581–1583 (2010).
    [CrossRef]
  5. L. Li, T. Li, S. M. Wang, C. Zhang, and S. N. Zhu, “Plasmonic Airy beams generated by in-plane diffraction,” Phys. Rev. Lett. 107, 126804 (2011).
    [CrossRef]
  6. P. Zhang, S. Wang, Y. Liu, X. Yin, C. Lu, Z. Chen, and X. Zhang, “Plasmonic Airy beams with dynamically controlled trajectories,” Opt. Lett. 36, 3191–3193 (2011).
    [CrossRef]
  7. A. Minovich, A. E. Klein, N. Janunts, T. Pertsch, D. N. Neshev, and Y. S. Kivshar, “Generation and near-field imaging of Airy surface plasmons,” Phys. Rev. Lett. 107, 116802 (2011).
    [CrossRef]
  8. J. Broky, G. A. Siviloglou, A. Dogariu, and D. N. Christodoulides, “Self-healing properties of optical Airy beams,” Opt. Express 16, 12880–12891 (2008).
    [CrossRef]
  9. X. Chu, G. Zhou, and R. Chen, “Analytical study of the self-healing property of Airy beams,” Phys. Rev. A 85, 013815 (2012).
    [CrossRef]
  10. D. Deng, “Propagation of Airy beams through a hard-edged aperture,” Appl. Phys. B 107, 195–200 (2012).
    [CrossRef]
  11. Y. Xu and G. Zhou, “The far-field divergent properties of an Airy beam,” Opt. Laser Technol. 44, 1318–1323 (2012).
    [CrossRef]
  12. X. Chu, “Evolution of an Airy beam in turbulence,” Opt. Lett. 36, 2701–2703 (2011).
    [CrossRef]
  13. P. Zhang, J. Prakash, Z. Zhang, M. S. Mills, N. K. Efremidis, D. N. Christodoulides, and Z. Chen, “Trapping and guiding microparticles with morphing autofocusing Airy beams,” Opt. Lett. 36, 2883–2885 (2011).
    [CrossRef]
  14. R. Shi, J. Liu, J. Xu, D. Liu, Y. Pan, J. Xie, and Y. Wang, “Designing and fabricating diffractive optical elements with a complex profile by interference,” Opt. Lett. 36, 4053–4055 (2011).
    [CrossRef]
  15. Y. Hu, P. Zhang, C. Lou, S. Huang, J. Xu, and Z. Chen, “Optimal control of the ballistic motion of Airy beams,” Opt. Lett. 35, 2260–2262 (2010).
    [CrossRef]
  16. Y. Hu, G. A. Siviloglou, P. Zhang, N. K. Efremidis, D. N. Christodoulides, and Z. Chen, “Self-accelerating Airybeams: generation, control, and applications,” in Nonlinear Photonics and Novel Optical Phenomena, Z. Chen and M. Roberto, eds. (Springer, 2012), pp. 1–46.
  17. J. A. Davis, M. J. Mitry, M. A. Bandres, I. Ruiz, K. P. McAuley, and D. M. Cottrell, “Generation of accelerating Airy and accelerating parabolic beams using phase-only patterns,” Appl. Opt. 48, 3170–3176 (2009).
    [CrossRef]
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    [CrossRef]
  20. O. Vallee and M. Soares, Airy Functions and Applications to Physics (Imperial College, 2004), pp. 9–11.
  21. G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, “Observation of accelerating Airy beams,” Phys. Rev. Lett. 99, 213901 (2007).
    [CrossRef]
  22. P. F. McManamon, “A review of phased array steering for narrow-band electrooptical systems,” Proc. IEEE 97, 1078–1096 (2009).
    [CrossRef]
  23. O. K. Ersoy, Diffraction, Fourier Optics and Imaging (Wiley, 2007), pp. 44–47.
  24. T. Fujita, H. Nishihara, and J. Koyama, “Blazed gratings and Fresnel lenses fabricated by electron-beam lithography,” Opt. Lett. 7, 578–580 (1982).
    [CrossRef]
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  26. Y. C. Wang, “Fast writing of surface relief gratings based on azo dye-poly(methyl methacrylate) mixtures,” Life Sci. J. 9, 1196–1198 (2012).
  27. Y. C. Wang, “Polarization dependence of polymer surface relief gratings,” Life Sci. J. 9, 1255–1257 (2012).

2012 (5)

X. Chu, G. Zhou, and R. Chen, “Analytical study of the self-healing property of Airy beams,” Phys. Rev. A 85, 013815 (2012).
[CrossRef]

D. Deng, “Propagation of Airy beams through a hard-edged aperture,” Appl. Phys. B 107, 195–200 (2012).
[CrossRef]

Y. Xu and G. Zhou, “The far-field divergent properties of an Airy beam,” Opt. Laser Technol. 44, 1318–1323 (2012).
[CrossRef]

Y. C. Wang, “Fast writing of surface relief gratings based on azo dye-poly(methyl methacrylate) mixtures,” Life Sci. J. 9, 1196–1198 (2012).

Y. C. Wang, “Polarization dependence of polymer surface relief gratings,” Life Sci. J. 9, 1255–1257 (2012).

2011 (7)

2010 (2)

2009 (3)

2008 (1)

2007 (3)

1987 (1)

1982 (1)

1978 (1)

Arie, A.

Bandres, M. A.

Broky, J.

J. Broky, G. A. Siviloglou, A. Dogariu, and D. N. Christodoulides, “Self-healing properties of optical Airy beams,” Opt. Express 16, 12880–12891 (2008).
[CrossRef]

G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, “Observation of accelerating Airy beams,” Phys. Rev. Lett. 99, 213901 (2007).
[CrossRef]

Bu, J.

Chen, R.

X. Chu, G. Zhou, and R. Chen, “Analytical study of the self-healing property of Airy beams,” Phys. Rev. A 85, 013815 (2012).
[CrossRef]

Chen, Z.

Christodoulides, D. N.

P. Zhang, J. Prakash, Z. Zhang, M. S. Mills, N. K. Efremidis, D. N. Christodoulides, and Z. Chen, “Trapping and guiding microparticles with morphing autofocusing Airy beams,” Opt. Lett. 36, 2883–2885 (2011).
[CrossRef]

J. Broky, G. A. Siviloglou, A. Dogariu, and D. N. Christodoulides, “Self-healing properties of optical Airy beams,” Opt. Express 16, 12880–12891 (2008).
[CrossRef]

G. A. Siviloglou and D. N. Christodoulides, “Accelerating finite energy Airy beams,” Opt. Lett. 32, 979–981 (2007).
[CrossRef]

G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, “Observation of accelerating Airy beams,” Phys. Rev. Lett. 99, 213901 (2007).
[CrossRef]

Y. Hu, G. A. Siviloglou, P. Zhang, N. K. Efremidis, D. N. Christodoulides, and Z. Chen, “Self-accelerating Airybeams: generation, control, and applications,” in Nonlinear Photonics and Novel Optical Phenomena, Z. Chen and M. Roberto, eds. (Springer, 2012), pp. 1–46.

Chu, X.

X. Chu, G. Zhou, and R. Chen, “Analytical study of the self-healing property of Airy beams,” Phys. Rev. A 85, 013815 (2012).
[CrossRef]

X. Chu, “Evolution of an Airy beam in turbulence,” Opt. Lett. 36, 2701–2703 (2011).
[CrossRef]

Cottrell, D. M.

Davis, J. A.

Degiorgio, V.

DelRe, E.

Deng, D.

D. Deng, “Propagation of Airy beams through a hard-edged aperture,” Appl. Phys. B 107, 195–200 (2012).
[CrossRef]

Dogariu, A.

J. Broky, G. A. Siviloglou, A. Dogariu, and D. N. Christodoulides, “Self-healing properties of optical Airy beams,” Opt. Express 16, 12880–12891 (2008).
[CrossRef]

G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, “Observation of accelerating Airy beams,” Phys. Rev. Lett. 99, 213901 (2007).
[CrossRef]

Dolev, I.

Durnin, J.

Efremidis, N. K.

P. Zhang, J. Prakash, Z. Zhang, M. S. Mills, N. K. Efremidis, D. N. Christodoulides, and Z. Chen, “Trapping and guiding microparticles with morphing autofocusing Airy beams,” Opt. Lett. 36, 2883–2885 (2011).
[CrossRef]

Y. Hu, G. A. Siviloglou, P. Zhang, N. K. Efremidis, D. N. Christodoulides, and Z. Chen, “Self-accelerating Airybeams: generation, control, and applications,” in Nonlinear Photonics and Novel Optical Phenomena, Z. Chen and M. Roberto, eds. (Springer, 2012), pp. 1–46.

Ellenbogen, T.

Ersoy, O. K.

O. K. Ersoy, Diffraction, Fourier Optics and Imaging (Wiley, 2007), pp. 44–47.

Fujita, T.

Gaylord, T. K.

Gutierrez-Vega, J. C.

Hu, Y.

Y. Hu, P. Zhang, C. Lou, S. Huang, J. Xu, and Z. Chen, “Optimal control of the ballistic motion of Airy beams,” Opt. Lett. 35, 2260–2262 (2010).
[CrossRef]

Y. Hu, G. A. Siviloglou, P. Zhang, N. K. Efremidis, D. N. Christodoulides, and Z. Chen, “Self-accelerating Airybeams: generation, control, and applications,” in Nonlinear Photonics and Novel Optical Phenomena, Z. Chen and M. Roberto, eds. (Springer, 2012), pp. 1–46.

Huang, S.

Janunts, N.

A. Minovich, A. E. Klein, N. Janunts, T. Pertsch, D. N. Neshev, and Y. S. Kivshar, “Generation and near-field imaging of Airy surface plasmons,” Phys. Rev. Lett. 107, 116802 (2011).
[CrossRef]

Kivshar, Y. S.

A. Minovich, A. E. Klein, N. Janunts, T. Pertsch, D. N. Neshev, and Y. S. Kivshar, “Generation and near-field imaging of Airy surface plasmons,” Phys. Rev. Lett. 107, 116802 (2011).
[CrossRef]

Klein, A. E.

A. Minovich, A. E. Klein, N. Janunts, T. Pertsch, D. N. Neshev, and Y. S. Kivshar, “Generation and near-field imaging of Airy surface plasmons,” Phys. Rev. Lett. 107, 116802 (2011).
[CrossRef]

Koyama, J.

Li, L.

L. Li, T. Li, S. M. Wang, C. Zhang, and S. N. Zhu, “Plasmonic Airy beams generated by in-plane diffraction,” Phys. Rev. Lett. 107, 126804 (2011).
[CrossRef]

Li, T.

L. Li, T. Li, S. M. Wang, C. Zhang, and S. N. Zhu, “Plasmonic Airy beams generated by in-plane diffraction,” Phys. Rev. Lett. 107, 126804 (2011).
[CrossRef]

Liu, D.

Liu, J.

Liu, Y.

Lou, C.

Lu, C.

Magnusson, R.

McAuley, K. P.

McManamon, P. F.

P. F. McManamon, “A review of phased array steering for narrow-band electrooptical systems,” Proc. IEEE 97, 1078–1096 (2009).
[CrossRef]

Mills, M. S.

Minovich, A.

A. Minovich, A. E. Klein, N. Janunts, T. Pertsch, D. N. Neshev, and Y. S. Kivshar, “Generation and near-field imaging of Airy surface plasmons,” Phys. Rev. Lett. 107, 116802 (2011).
[CrossRef]

Minzioni, P.

Mitry, M. J.

Neshev, D. N.

A. Minovich, A. E. Klein, N. Janunts, T. Pertsch, D. N. Neshev, and Y. S. Kivshar, “Generation and near-field imaging of Airy surface plasmons,” Phys. Rev. Lett. 107, 116802 (2011).
[CrossRef]

Nishihara, H.

Pan, Y.

Parravicini, J.

Pertsch, T.

A. Minovich, A. E. Klein, N. Janunts, T. Pertsch, D. N. Neshev, and Y. S. Kivshar, “Generation and near-field imaging of Airy surface plasmons,” Phys. Rev. Lett. 107, 116802 (2011).
[CrossRef]

Prakash, J.

Ruiz, I.

Shi, R.

Siviloglou, G. A.

J. Broky, G. A. Siviloglou, A. Dogariu, and D. N. Christodoulides, “Self-healing properties of optical Airy beams,” Opt. Express 16, 12880–12891 (2008).
[CrossRef]

G. A. Siviloglou and D. N. Christodoulides, “Accelerating finite energy Airy beams,” Opt. Lett. 32, 979–981 (2007).
[CrossRef]

G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, “Observation of accelerating Airy beams,” Phys. Rev. Lett. 99, 213901 (2007).
[CrossRef]

Y. Hu, G. A. Siviloglou, P. Zhang, N. K. Efremidis, D. N. Christodoulides, and Z. Chen, “Self-accelerating Airybeams: generation, control, and applications,” in Nonlinear Photonics and Novel Optical Phenomena, Z. Chen and M. Roberto, eds. (Springer, 2012), pp. 1–46.

Soares, M.

O. Vallee and M. Soares, Airy Functions and Applications to Physics (Imperial College, 2004), pp. 9–11.

Vallee, O.

O. Vallee and M. Soares, Airy Functions and Applications to Physics (Imperial College, 2004), pp. 9–11.

Wang, J.

Wang, M.

Wang, S.

Wang, S. M.

L. Li, T. Li, S. M. Wang, C. Zhang, and S. N. Zhu, “Plasmonic Airy beams generated by in-plane diffraction,” Phys. Rev. Lett. 107, 126804 (2011).
[CrossRef]

Wang, Y.

Wang, Y. C.

Y. C. Wang, “Fast writing of surface relief gratings based on azo dye-poly(methyl methacrylate) mixtures,” Life Sci. J. 9, 1196–1198 (2012).

Y. C. Wang, “Polarization dependence of polymer surface relief gratings,” Life Sci. J. 9, 1255–1257 (2012).

Xie, J.

Xu, J.

Xu, Y.

Y. Xu and G. Zhou, “The far-field divergent properties of an Airy beam,” Opt. Laser Technol. 44, 1318–1323 (2012).
[CrossRef]

Yang, Y.

Yin, X.

Yuan, X.

Zhang, C.

L. Li, T. Li, S. M. Wang, C. Zhang, and S. N. Zhu, “Plasmonic Airy beams generated by in-plane diffraction,” Phys. Rev. Lett. 107, 126804 (2011).
[CrossRef]

Zhang, P.

Zhang, X.

Zhang, Z.

Zhou, G.

X. Chu, G. Zhou, and R. Chen, “Analytical study of the self-healing property of Airy beams,” Phys. Rev. A 85, 013815 (2012).
[CrossRef]

Y. Xu and G. Zhou, “The far-field divergent properties of an Airy beam,” Opt. Laser Technol. 44, 1318–1323 (2012).
[CrossRef]

Zhu, S. N.

L. Li, T. Li, S. M. Wang, C. Zhang, and S. N. Zhu, “Plasmonic Airy beams generated by in-plane diffraction,” Phys. Rev. Lett. 107, 126804 (2011).
[CrossRef]

Appl. Opt. (2)

Appl. Phys. B (1)

D. Deng, “Propagation of Airy beams through a hard-edged aperture,” Appl. Phys. B 107, 195–200 (2012).
[CrossRef]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (1)

Life Sci. J. (2)

Y. C. Wang, “Fast writing of surface relief gratings based on azo dye-poly(methyl methacrylate) mixtures,” Life Sci. J. 9, 1196–1198 (2012).

Y. C. Wang, “Polarization dependence of polymer surface relief gratings,” Life Sci. J. 9, 1255–1257 (2012).

Opt. Express (2)

Opt. Laser Technol. (1)

Y. Xu and G. Zhou, “The far-field divergent properties of an Airy beam,” Opt. Laser Technol. 44, 1318–1323 (2012).
[CrossRef]

Opt. Lett. (9)

X. Chu, “Evolution of an Airy beam in turbulence,” Opt. Lett. 36, 2701–2703 (2011).
[CrossRef]

P. Zhang, J. Prakash, Z. Zhang, M. S. Mills, N. K. Efremidis, D. N. Christodoulides, and Z. Chen, “Trapping and guiding microparticles with morphing autofocusing Airy beams,” Opt. Lett. 36, 2883–2885 (2011).
[CrossRef]

R. Shi, J. Liu, J. Xu, D. Liu, Y. Pan, J. Xie, and Y. Wang, “Designing and fabricating diffractive optical elements with a complex profile by interference,” Opt. Lett. 36, 4053–4055 (2011).
[CrossRef]

Y. Hu, P. Zhang, C. Lou, S. Huang, J. Xu, and Z. Chen, “Optimal control of the ballistic motion of Airy beams,” Opt. Lett. 35, 2260–2262 (2010).
[CrossRef]

P. Zhang, S. Wang, Y. Liu, X. Yin, C. Lu, Z. Chen, and X. Zhang, “Plasmonic Airy beams with dynamically controlled trajectories,” Opt. Lett. 36, 3191–3193 (2011).
[CrossRef]

G. A. Siviloglou and D. N. Christodoulides, “Accelerating finite energy Airy beams,” Opt. Lett. 32, 979–981 (2007).
[CrossRef]

J. Parravicini, P. Minzioni, V. Degiorgio, and E. DelRe, “Observation of nonlinear Airy-like beam evolution in lithium niobate,” Opt. Lett. 34, 3908–3910 (2009).
[CrossRef]

I. Dolev, T. Ellenbogen, and A. Arie, “Switching the acceleration direction of Airy beams by a nonlinear optical process,” Opt. Lett. 35, 1581–1583 (2010).
[CrossRef]

T. Fujita, H. Nishihara, and J. Koyama, “Blazed gratings and Fresnel lenses fabricated by electron-beam lithography,” Opt. Lett. 7, 578–580 (1982).
[CrossRef]

Phys. Rev. A (1)

X. Chu, G. Zhou, and R. Chen, “Analytical study of the self-healing property of Airy beams,” Phys. Rev. A 85, 013815 (2012).
[CrossRef]

Phys. Rev. Lett. (3)

A. Minovich, A. E. Klein, N. Janunts, T. Pertsch, D. N. Neshev, and Y. S. Kivshar, “Generation and near-field imaging of Airy surface plasmons,” Phys. Rev. Lett. 107, 116802 (2011).
[CrossRef]

L. Li, T. Li, S. M. Wang, C. Zhang, and S. N. Zhu, “Plasmonic Airy beams generated by in-plane diffraction,” Phys. Rev. Lett. 107, 126804 (2011).
[CrossRef]

G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, “Observation of accelerating Airy beams,” Phys. Rev. Lett. 99, 213901 (2007).
[CrossRef]

Proc. IEEE (1)

P. F. McManamon, “A review of phased array steering for narrow-band electrooptical systems,” Proc. IEEE 97, 1078–1096 (2009).
[CrossRef]

Other (3)

O. K. Ersoy, Diffraction, Fourier Optics and Imaging (Wiley, 2007), pp. 44–47.

Y. Hu, G. A. Siviloglou, P. Zhang, N. K. Efremidis, D. N. Christodoulides, and Z. Chen, “Self-accelerating Airybeams: generation, control, and applications,” in Nonlinear Photonics and Novel Optical Phenomena, Z. Chen and M. Roberto, eds. (Springer, 2012), pp. 1–46.

O. Vallee and M. Soares, Airy Functions and Applications to Physics (Imperial College, 2004), pp. 9–11.

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Figures (5)

Fig. 1.
Fig. 1.

Experimental schematic.

Fig. 2.
Fig. 2.

Phase pattern encoded on the SLM. (a) Cubic phase pattern and (b) grating phase pattern.

Fig. 3.
Fig. 3.

Results of simulation. (a1)–(a4) combined phase patterns by the cubic phase and grating, (b1)–(b4) Airy beams field distribution at z=0, and (c1)–(c4) propagation of the Airy beams along the z direction.

Fig. 4.
Fig. 4.

Airy beams optical field distribution of the nine positions in the range of 11mm.

Fig. 5.
Fig. 5.

Arbitrary deflection of the Airy beams in XY 2D plane.

Equations (10)

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

iϕz+122ϕs2=0,
ϕ(s,z=0)=Ai(s),
ϕ(s,z=0)=Ai(s)exp(as),
A0(kx,z=0)exp(akx2)exp(i3(kx33a2kxia3)),
A(kx,z=0)=A0(kx,z=0)·exp(ipkx).
A(kx,z)=A(kx,z=0)·exp(iμz),
ϕ(s,z)=A(kx,z)·exp(ikxs)dkx.
ϕ(s,z)=A0(kx,z=0)·exp(ipkx)·exp(iμz)·exp(ikxs)dkx.
ϕ(s,ξ)=Ai[p+s(ξ2)2+iaξ]·exp[a(p+s)+i(p+s+a2)ξ2aξ22iξ312+iξz02],
ϕ(sx,sy,ξ)=Ai[px+sx(ξ2)2+iaξ]·Ai[py+sy(ξ2)2+iaξ]×exp[a(px+sx)+i(px+sx+a2)ξ2aξ22iξ312+iξz02]×exp[a(py+sy)+i(py+sy+a2)ξ2aξ22iξ312+iξz02].

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