Abstract

We generate both accelerated Airy and accelerated parabolic beams using phase-only patterns encoded onto a liquid crystal display (LCD). The usual system length is 2f, where f is the focal length of the Fourier transform lens. We develop a compact optical system having a total system length of f. However, the mask must now incorporate the Fresnel diffraction that is not provided by the reduced optical system length. Finally we incorporate the Fourier transform lens onto the mask. We obtain excellent experimental results with a phase-only pattern and a shorter optical system. This approach makes these beams much easier to implement.

© 2009 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] [PubMed]
  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] [PubMed]
  4. M. A. Bandres and J. C. Gutiérrez-Vega, “Airy-Gauss beams and their transformation by paraxial optical systems,” Opt. Express 15, 16719-16728 (2007).
    [CrossRef] [PubMed]
  5. M. A. Bandres, “Accelerating parabolic beams,” Opt. Lett. 33, 1678-1680 (2008).
    [CrossRef] [PubMed]
  6. J. A. Davis, M. J. Mitry, M. A. Bandres, and D. M. Cottrell, “Observation of accelerating parabolic beams,” Opt. Express 16, 12866-12871 (2008).
    [CrossRef] [PubMed]
  7. J. Baumgartl, M. Mazilu, and K. Dholakia, “Optically mediated particle clearing using Airy wavepackets,” Nat. Photon. 2, 675-678 (2008).
    [CrossRef]
  8. J. Baumgartl, G. M. Hannappel, D. J. Stevenson, D. Day, M. Gu, and K. Dholakia, “Optical redistribution of microparticles and cells between microwells,” Lab Chip 9, 1334-1336(2009).
    [CrossRef] [PubMed]
  9. J. A. Davis, D. M. Cottrell, J. Campos, M. J. Yzuel, and I. Moreno, “Encoding amplitude information onto phase-only filters,” Appl. Opt. 38, 5004-5013 (1999).
    [CrossRef]
  10. J. B. Bentley, J. A. Davis, M. A. Bandres, and J. C. Gutiérrez-Vega, “Generation of helical Ince-Gaussian beams with a liquid-crystal display,” Opt. Lett. 31, 649-651 (2006).
    [CrossRef] [PubMed]
  11. J. A. Davis, P. Tsai, D. M. Cottrell, T. Sonehara, and J. Amako, “Transmission variations in liquid crystal spatial light modulators caused by interference and diffraction effects,” Opt. Eng. 38, 1051-1057 (1999).
    [CrossRef]
  12. D. M. Cottrell, J. A. Davis, T. R. Hedman, and R. A. Lilly, “Multiple imaging phase-encoded optical elements written on programmable spatial light modulators,” Appl. Opt. 29, 2505-2509 (1990).
    [CrossRef] [PubMed]

2009 (1)

J. Baumgartl, G. M. Hannappel, D. J. Stevenson, D. Day, M. Gu, and K. Dholakia, “Optical redistribution of microparticles and cells between microwells,” Lab Chip 9, 1334-1336(2009).
[CrossRef] [PubMed]

2008 (4)

2007 (3)

2006 (1)

1999 (2)

J. A. Davis, P. Tsai, D. M. Cottrell, T. Sonehara, and J. Amako, “Transmission variations in liquid crystal spatial light modulators caused by interference and diffraction effects,” Opt. Eng. 38, 1051-1057 (1999).
[CrossRef]

J. A. Davis, D. M. Cottrell, J. Campos, M. J. Yzuel, and I. Moreno, “Encoding amplitude information onto phase-only filters,” Appl. Opt. 38, 5004-5013 (1999).
[CrossRef]

1990 (1)

Amako, J.

J. A. Davis, P. Tsai, D. M. Cottrell, T. Sonehara, and J. Amako, “Transmission variations in liquid crystal spatial light modulators caused by interference and diffraction effects,” Opt. Eng. 38, 1051-1057 (1999).
[CrossRef]

Bandres, M. A.

Baumgartl, J.

J. Baumgartl, G. M. Hannappel, D. J. Stevenson, D. Day, M. Gu, and K. Dholakia, “Optical redistribution of microparticles and cells between microwells,” Lab Chip 9, 1334-1336(2009).
[CrossRef] [PubMed]

J. Baumgartl, M. Mazilu, and K. Dholakia, “Optically mediated particle clearing using Airy wavepackets,” Nat. Photon. 2, 675-678 (2008).
[CrossRef]

Bentley, J. B.

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] [PubMed]

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

Campos, J.

Christodoulides, D. N.

Cottrell, D. M.

Davis, J. A.

Day, D.

J. Baumgartl, G. M. Hannappel, D. J. Stevenson, D. Day, M. Gu, and K. Dholakia, “Optical redistribution of microparticles and cells between microwells,” Lab Chip 9, 1334-1336(2009).
[CrossRef] [PubMed]

Dholakia, K.

J. Baumgartl, G. M. Hannappel, D. J. Stevenson, D. Day, M. Gu, and K. Dholakia, “Optical redistribution of microparticles and cells between microwells,” Lab Chip 9, 1334-1336(2009).
[CrossRef] [PubMed]

J. Baumgartl, M. Mazilu, and K. Dholakia, “Optically mediated particle clearing using Airy wavepackets,” Nat. Photon. 2, 675-678 (2008).
[CrossRef]

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] [PubMed]

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

Gu, M.

J. Baumgartl, G. M. Hannappel, D. J. Stevenson, D. Day, M. Gu, and K. Dholakia, “Optical redistribution of microparticles and cells between microwells,” Lab Chip 9, 1334-1336(2009).
[CrossRef] [PubMed]

Gutiérrez-Vega, J. C.

Hannappel, G. M.

J. Baumgartl, G. M. Hannappel, D. J. Stevenson, D. Day, M. Gu, and K. Dholakia, “Optical redistribution of microparticles and cells between microwells,” Lab Chip 9, 1334-1336(2009).
[CrossRef] [PubMed]

Hedman, T. R.

Lilly, R. A.

Mazilu, M.

J. Baumgartl, M. Mazilu, and K. Dholakia, “Optically mediated particle clearing using Airy wavepackets,” Nat. Photon. 2, 675-678 (2008).
[CrossRef]

Mitry, M. J.

Moreno, I.

Siviloglou, G. A.

Sonehara, T.

J. A. Davis, P. Tsai, D. M. Cottrell, T. Sonehara, and J. Amako, “Transmission variations in liquid crystal spatial light modulators caused by interference and diffraction effects,” Opt. Eng. 38, 1051-1057 (1999).
[CrossRef]

Stevenson, D. J.

J. Baumgartl, G. M. Hannappel, D. J. Stevenson, D. Day, M. Gu, and K. Dholakia, “Optical redistribution of microparticles and cells between microwells,” Lab Chip 9, 1334-1336(2009).
[CrossRef] [PubMed]

Tsai, P.

J. A. Davis, P. Tsai, D. M. Cottrell, T. Sonehara, and J. Amako, “Transmission variations in liquid crystal spatial light modulators caused by interference and diffraction effects,” Opt. Eng. 38, 1051-1057 (1999).
[CrossRef]

Yzuel, M. J.

Appl. Opt. (2)

Lab Chip (1)

J. Baumgartl, G. M. Hannappel, D. J. Stevenson, D. Day, M. Gu, and K. Dholakia, “Optical redistribution of microparticles and cells between microwells,” Lab Chip 9, 1334-1336(2009).
[CrossRef] [PubMed]

Nat. Photon. (1)

J. Baumgartl, M. Mazilu, and K. Dholakia, “Optically mediated particle clearing using Airy wavepackets,” Nat. Photon. 2, 675-678 (2008).
[CrossRef]

Opt. Eng. (1)

J. A. Davis, P. Tsai, D. M. Cottrell, T. Sonehara, and J. Amako, “Transmission variations in liquid crystal spatial light modulators caused by interference and diffraction effects,” Opt. Eng. 38, 1051-1057 (1999).
[CrossRef]

Opt. Express (2)

Opt. Lett. (4)

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 (10)

Fig. 1
Fig. 1

Amplitude (first row) and phase (second row) Fourier spectral masks for the AiB beam (left column), and for the ApB beams for n = 0 (middle column) and n = 6 (right column) with a = 0.02 .

Fig. 2
Fig. 2

Experimental results for AiB and for ApB beams with n = 0 and n = 6 at distances of z = { 0 , 15 , 30 , 45 } cm using amplitude and phase masks.

Fig. 3
Fig. 3

Experimental results for AiB and for ApB beams with n = 0 and n = 6 at distances of z = { 0 , 15 , 30 , 45 } cm using phase-only masks.

Fig. 4
Fig. 4

Experimental results at a fixed propagation distance for ApB beam with n = 0 using phase-only mask with different binary vertical slit widths.

Fig. 5
Fig. 5

Experimental results for AiB and for ApB beams with n = 0 and n = 6 at distances of z = { 0 , 15 , 30 , 45 } cm using phase masks with properly chosen binary slit width.

Fig. 6
Fig. 6

(a) Conventional optical Fourier system; (b) shortened optical Fourier system.

Fig. 7
Fig. 7

Experimental results for AiB and for ApB beams with n = 0 and n = 6 at distances of z = { 0 , 15 , 30 , 45 } cm using amplitude and phase masks and with a shortened optical system.

Fig. 8
Fig. 8

Amplitude (a) and phase (b) spectral masks for ApB beam with n = 6 . Amplitude (c) and phase (d) spectral masks incorporating Fresnel diffraction through a distance of 1 m for an ApB beam with n = 6 .

Fig. 9
Fig. 9

Experimental results for AiB and for ApB beams with n = 0 and n = 6 at distances of z = { 0 , 15 , 30 , 45 } cm using phase-only masks that encode both the generating spectral mask and the effects of Fresnel diffraction with the shorter optical system.

Fig. 10
Fig. 10

Experimental results for AiB and for ApB beams with n = 0 and n = 6 at distances of z = { 0 , 15 , 30 , 45 } cm using phase-only masks that encode the generating spectral mask, the effects of Fresnel diffraction, and the Fourier transform lens, with the shorter optical system.

Equations (3)

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I [ ϕ ] ( k x , k y ) exp [ i x 0 3 ( k x 3 / 3 + k y 3 / 3 ) ] exp [ a x 0 2 ( k x 2 + k y 2 ) ] .
I [ ϕ n ] ( k x , k y ) exp [ i κ 3 ( k x 3 / 3 a 2 k x / κ 2 + k x k y 2 ) ] exp [ a κ 2 ( k x 2 + k y 2 ) ] Θ m ( 2 k y κ ) .
y = ( z 2 / 4 k 2 x 0 3 ) ( 1 z R ) = ( z 2 / 4 k 2 x 0 3 ) ( 1 z ( 1 d 1 / f ) f ) .

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