Abstract

Abruptly focusing Airy beams have previously been generated using a radial cubic phase pattern that represents the Fourier transform of the Airy beam. The Fourier transform of this pattern is formed using a system length of 2f, where f is the focal length of the Fourier transform lens. In this work, we directly generate these abruptly focusing Airy beams using a 3/2 radial phase pattern encoded onto a liquid crystal display. The resulting optical system is much shorter. In addition, we can easily produce vortex patterns at the focal point of these beams. Experimental results match theoretical predictions.

© 2013 Optical Society of America

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References

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  1. G. A. Siviloglou and D. N. Christodoulides, “Accelerating finite energy Airy beams,” Opt. Lett. 32, 979–981 (2007).
    [CrossRef]
  2. G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, “Observation of accelerating Airy beams,” Phys. Rev. Lett. 99, 213901 (2007).
    [CrossRef]
  3. G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, “Ballistic dynamics of Airy beams,” Opt. Lett. 33, 207–209 (2008).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  9. D. M. Cottrell, J. A. Davis, and T. M. Hazard, “Direct generation of accelerating Airy beams using a 3/2 phase-only pattern,” Opt. Lett. 34, 2634–2636 (2009).
    [CrossRef]
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    [CrossRef]

2012 (1)

2011 (3)

2010 (1)

2009 (1)

2008 (2)

2007 (2)

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

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

Broky, J.

G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, “Ballistic dynamics of Airy beams,” Opt. Lett. 33, 207–209 (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]

Chen, Z.

Chremmos, I.

Christodoulides, D. N.

Cottrell, D. M.

Davis, J. A.

Dogariu, A.

G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, “Ballistic dynamics of Airy beams,” Opt. Lett. 33, 207–209 (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]

Efremidis, N. K.

Hazard, T. M.

Papazoglou, D.

Prakash, J.

Sand, D.

Siviloglou, G. A.

Slovick, B. A.

Tuvey, C. S.

Tzortzakis, S.

Zhang, P.

Appl. Opt. (1)

Opt. Express (1)

Opt. Lett. (7)

Phys. Rev. Lett. (1)

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

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Figures (6)

Fig. 1.
Fig. 1.

Geometrical model for abruptly focusing beam.

Fig. 2.
Fig. 2.

Radial phase patterns encoded onto LCD for (a) 3/2 radial phase pattern having an internal radius of r1 and an outer radius of r2 and (b) addition of a spiral phase to the 3/2 radial phase.

Fig. 3.
Fig. 3.

Experimental results showing how the beam forms a focus as a function of distance from the LCD. Photos taken at distances DF of (a) 35, (b) 45, (c) 55, and (d) 65 cm from the LCD.

Fig. 4.
Fig. 4.

Experimental (left) and computational results (right) showing details of the focused spot.

Fig. 5.
Fig. 5.

Experimental values of the focusing distance for the abruptly focusing Airy beam as a function of the phase shift over the intermediate region. Points show experimental data and the line show theoretical curves.

Fig. 6.
Fig. 6.

Experimental results show the vortex patterns formed at the focus point of the beam as a function of the charge (=0,3,6,±6) of the azimuthal phase encoded onto the pattern.

Equations (3)

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DF=r1a=8πr1(r2r1)3/23λΦ.
DF=8πΔ2n1(n2n1)3/23λΦ.
Φ=8πaζ3/2/3λ+2πϕ.

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