Abstract

We demonstrate the generation of spectrally tunable phase-dependent wavefronts, using the 2D Airy as the primary test case, via a polymer-stabilized cholesteric liquid crystal (PSCLC) element. Specifically, we use a novel spatial light modulator (SLM) based projection system to photo-align the initial helix angle landscape of the PSCLC so that it imparts the appropriate cubic phase profile to the reflected beam. This element is spectrally selective, with a reflection bandwidth of ≈ 100 nm, and electrically tunable from λ = 530 nm to 760 nm. Under both green and red laser illumination, the element is shown to conditionally form an Airy beam depending on the position of the electrically tailored reflection band. We briefly demonstrate the generality of this approach by producing PSCLC elements which form a computer-generated hologram and a higher-order Mathieu beam.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
  30. T. Vettenburg, H. I. Dalgarno, J. Nylk, C. Coll-Lladó, D. E. Ferrier, T. Čižmár, F. J. Gunn-Moore, and K. Dholakia, “Light-sheet microscopy using an Airy beam,” Nat. Methods 11, 541 (2014).
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    [Crossref] [PubMed]
  33. H. Dai, X. Sun, D. Luo, and Y. Liu, “Airy beams generated by a binary phase element made of polymer-dispersed liquid crystals,” Opt. Express 17, 19365–19370 (2009).
    [Crossref] [PubMed]
  34. D. Luo, H. Dai, and X. Sun, “Polarization-independent electrically tunable/switchable Airy beam based on polymer-stabilized blue phase liquid crystal,” Opt. Express 21, 31318–31323 (2013).
    [Crossref]
  35. I. Moreno, J. A. Davis, T. M. Hernandez, D. M. Cottrell, and D. Sand, “Complete polarization control of light from a liquid crystal spatial light modulator,” Opt. Express 20, 364–376 (2012).
    [Crossref] [PubMed]
  36. K. M. Lee, V. P. Tondiglia, T. Lee, I. I. Smalyukh, and T. J. White, “Large range electrically-induced reflection notch tuning in polymer stabilized cholesteric liquid crystals,” J. Mater. Chem. C 3, 8788–8793 (2015).
    [Crossref]
  37. R. Hernández-Hernández, R. Terborg, I. Ricardez-Vargas, and K. Volke-Sepúlveda, “Experimental generation of mathieu–gauss beams with a phase-only spatial light modulator,” Appl. Opt. 49, 6903–6909 (2010).
    [Crossref]

2019 (2)

M. G. Nassiri and E. Brasselet, “Pure and achromatic spin-orbit shaping of light from fresnel reflection off space-variant anisotropic media,” Phys. Rev. A 99, 013836 (2019).
[Crossref]

Y. Li, Y. Liu, S. Li, P. Zhou, T. Zhan, Q. Chen, Y. Su, and S.-T. Wu, “Single-exposure fabrication of tunable pancharatnam-berry devices using a dye-doped liquid crystal,” Opt. Express 27, 9054–9060 (2019).
[Crossref] [PubMed]

2018 (4)

P. Chen, L.-L. Ma, W. Duan, J. Chen, S.-J. Ge, Z.-H. Zhu, M.-J. Tang, R. Xu, W. Gao, T. Li, W. Hu, and Y.-Q. Lu, “Digitalizing self-assembled chiral superstructures for optical vortex processing,” Adv. Mater. 30, 1705865 (2018).

B.-Y. Wei, S. Liu, P. Chen, S.-X. Qi, Y. Zhang, W. Hu, Y.-Q. Lu, and J.-L. Zhao, “Vortex Airy beams directly generated via liquid crystal q-Airy-plates,” Appl. Phys. Lett. 112, 121101 (2018).
[Crossref]

M. G. Nassiri, S. Y. Cho, H. Yoshida, M. Ozaki, and E. Brasselet, “High-order laguerre-gauss polychromatic beams from bragg-berry flat optics,” Phys. Rev. A 98, 063834 (2018).
[Crossref]

M. Rafayelyan and E. Brasselet, “Spin-to-orbital angular momentum mapping of polychromatic light,” Phys. review letters 120, 213903 (2018).
[Crossref]

2017 (2)

J. Kobashi, H. Yoshida, and M. Ozaki, “Broadband optical vortex generation from patterned cholesteric liquid crystals,” Mol. Cryst. Liq. Cryst. 646, 116–124 (2017).
[Crossref]

M. Rafayelyan, G. Agez, and E. Brasselet, “Ultrabroadband gradient-pitch bragg-berry mirrors,” Phys. Rev. A 96, 043862 (2017).
[Crossref]

2016 (8)

B.-Y. Wei, P. Chen, S.-J. Ge, W. Duan, W. Hu, and Y.-Q. Lu, “Generation of self-healing and transverse accelerating optical vortices,” Appl. Phys. Lett. 109, 121105 (2016).
[Crossref]

M. Rafayelyan, G. Tkachenko, and E. Brasselet, “Reflective spin-orbit geometric phase from chiral anisotropic optical media,” Phys. Rev. Lett. 116, 253902 (2016).
[Crossref] [PubMed]

R. Barboza, U. Bortolozzo, M. G. Clerc, and S. Residori, “Berry phase of light under bragg reflection by chiral liquid-crystal media,” Phys. Rev. Lett. 117, 053903 (2016).
[Crossref] [PubMed]

J. Kobashi, H. Yoshida, and M. Ozaki, “Planar optics with patterned chiral liquid crystals,” Nat. Photonics 10, 389 (2016).
[Crossref]

M. Rafayelyan and E. Brasselet, “Bragg-berry mirrors: reflective broadband q-plates,” Opt. Lett. 41, 3972–3975 (2016).
[Crossref] [PubMed]

J. Kobashi, H. Yoshida, and M. Ozaki, “Polychromatic optical vortex generation from patterned cholesteric liquid crystals,” Phys. Rev. Lett. 116, 253903 (2016).
[Crossref] [PubMed]

H. Yoshida and J. Kobashi, “Flat optics with cholesteric and blue phase liquid crystals,” Liq. Cryst. 43, 1909–1919 (2016).
[Crossref]

J. Nylk, K. McCluskey, S. Aggarwal, J. A. Tello, and K. Dholakia, “Enhancement of image quality and imaging depth with Airy light-sheet microscopy in cleared and non-cleared neural tissue,” Biomed. Opt. Express 7, 4021–4033 (2016).
[Crossref] [PubMed]

2015 (2)

K. M. Lee, V. P. Tondiglia, T. Lee, I. I. Smalyukh, and T. J. White, “Large range electrically-induced reflection notch tuning in polymer stabilized cholesteric liquid crystals,” J. Mater. Chem. C 3, 8788–8793 (2015).
[Crossref]

B.-Y. Wei, P. Chen, W. Hu, W. Ji, L.-Y. Zheng, S.-J. Ge, Y. Ming, V. Chigrinov, and Y.-Q. Lu, “Polarization-controllable Airy beams generated via a photoaligned director-variant liquid crystal mask,” Sci. Reports 5, 17484 (2015). Article.

2014 (2)

T. Vettenburg, H. I. Dalgarno, J. Nylk, C. Coll-Lladó, D. E. Ferrier, T. Čižmár, F. J. Gunn-Moore, and K. Dholakia, “Light-sheet microscopy using an Airy beam,” Nat. Methods 11, 541 (2014).
[Crossref] [PubMed]

W. Nelson, J. Palastro, C. Davis, and P. Sprangle, “Propagation of bessel and Airy beams through atmospheric turbulence,” J. Opt. Soc. Am. A 31, 603–609 (2014).
[Crossref]

2013 (2)

D. Luo, H. Dai, and X. Sun, “Polarization-independent electrically tunable/switchable Airy beam based on polymer-stabilized blue phase liquid crystal,” Opt. Express 21, 31318–31323 (2013).
[Crossref]

M. A. Bandres, I. Kaminer, M. Mills, B. Rodríguez-Lara, E. Greenfield, M. Segev, and D. N. Christodoulides, “Accelerating optical beams,” Opt. Photonics News 24, 30–37 (2013).
[Crossref]

2012 (3)

I. Moreno, J. A. Davis, T. M. Hernandez, D. M. Cottrell, and D. Sand, “Complete polarization control of light from a liquid crystal spatial light modulator,” Opt. Express 20, 364–376 (2012).
[Crossref] [PubMed]

I. Kaminer, R. Bekenstein, J. Nemirovsky, and M. Segev, “Nondiffracting accelerating wave packets of maxwell’s equations,” Phys. Rev. Lett. 108, 163901 (2012).
[Crossref]

P. Zhang, Y. Hu, T. Li, D. Cannan, X. Yin, R. Morandotti, Z. Chen, and X. Zhang, “Nonparaxial mathieu and weber accelerating beams,” Phys. Rev. Lett. 109, 193901 (2012).
[Crossref] [PubMed]

2011 (2)

2010 (2)

2009 (2)

H. Dai, X. Sun, D. Luo, and Y. Liu, “Airy beams generated by a binary phase element made of polymer-dispersed liquid crystals,” Opt. Express 17, 19365–19370 (2009).
[Crossref] [PubMed]

P. Polynkin, M. Kolesik, J. V. Moloney, G. A. Siviloglou, and D. N. Christodoulides, “Curved plasma channel generation using ultraintense Airy beams,” Science 324, 229–232 (2009).
[Crossref] [PubMed]

2007 (2)

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

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

2004 (1)

2002 (1)

S. Chávez-Cerda, M. Padgett, I. Allison, G. New, J. C. Gutiérrez-Vega, A. O’Neil, I. MacVicar, and J. Courtial, “Holographic generation and orbital angular momentum of high-order mathieu beams,” J. Opt. B: Quantum Semiclassical Opt. 4, S52 (2002).
[Crossref]

2000 (1)

1979 (1)

M. V. Berry and N. L. Balazs, “Nonspreading wave packets,” Am. J. Phys. 47, 264–267 (1979).
[Crossref]

Agez, G.

M. Rafayelyan, G. Agez, and E. Brasselet, “Ultrabroadband gradient-pitch bragg-berry mirrors,” Phys. Rev. A 96, 043862 (2017).
[Crossref]

Aggarwal, S.

Allison, I.

S. Chávez-Cerda, M. Padgett, I. Allison, G. New, J. C. Gutiérrez-Vega, A. O’Neil, I. MacVicar, and J. Courtial, “Holographic generation and orbital angular momentum of high-order mathieu beams,” J. Opt. B: Quantum Semiclassical Opt. 4, S52 (2002).
[Crossref]

Balazs, N. L.

M. V. Berry and N. L. Balazs, “Nonspreading wave packets,” Am. J. Phys. 47, 264–267 (1979).
[Crossref]

Bandres, M. A.

M. A. Bandres, I. Kaminer, M. Mills, B. Rodríguez-Lara, E. Greenfield, M. Segev, and D. N. Christodoulides, “Accelerating optical beams,” Opt. Photonics News 24, 30–37 (2013).
[Crossref]

M. A. Bandres, J. C. Gutiérrez-Vega, and S. Chávez-Cerda, “Parabolic nondiffracting optical wave fields,” Opt. Lett. 29, 44–46 (2004).
[Crossref] [PubMed]

Barboza, R.

R. Barboza, U. Bortolozzo, M. G. Clerc, and S. Residori, “Berry phase of light under bragg reflection by chiral liquid-crystal media,” Phys. Rev. Lett. 117, 053903 (2016).
[Crossref] [PubMed]

Bekenstein, R.

I. Kaminer, R. Bekenstein, J. Nemirovsky, and M. Segev, “Nondiffracting accelerating wave packets of maxwell’s equations,” Phys. Rev. Lett. 108, 163901 (2012).
[Crossref]

Berry, M. V.

M. V. Berry and N. L. Balazs, “Nonspreading wave packets,” Am. J. Phys. 47, 264–267 (1979).
[Crossref]

Bortolozzo, U.

R. Barboza, U. Bortolozzo, M. G. Clerc, and S. Residori, “Berry phase of light under bragg reflection by chiral liquid-crystal media,” Phys. Rev. Lett. 117, 053903 (2016).
[Crossref] [PubMed]

Brasselet, E.

M. G. Nassiri and E. Brasselet, “Pure and achromatic spin-orbit shaping of light from fresnel reflection off space-variant anisotropic media,” Phys. Rev. A 99, 013836 (2019).
[Crossref]

M. G. Nassiri, S. Y. Cho, H. Yoshida, M. Ozaki, and E. Brasselet, “High-order laguerre-gauss polychromatic beams from bragg-berry flat optics,” Phys. Rev. A 98, 063834 (2018).
[Crossref]

M. Rafayelyan and E. Brasselet, “Spin-to-orbital angular momentum mapping of polychromatic light,” Phys. review letters 120, 213903 (2018).
[Crossref]

M. Rafayelyan, G. Agez, and E. Brasselet, “Ultrabroadband gradient-pitch bragg-berry mirrors,” Phys. Rev. A 96, 043862 (2017).
[Crossref]

M. Rafayelyan, G. Tkachenko, and E. Brasselet, “Reflective spin-orbit geometric phase from chiral anisotropic optical media,” Phys. Rev. Lett. 116, 253902 (2016).
[Crossref] [PubMed]

M. Rafayelyan and E. Brasselet, “Bragg-berry mirrors: reflective broadband q-plates,” Opt. Lett. 41, 3972–3975 (2016).
[Crossref] [PubMed]

Broky, J.

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

Cannan, D.

P. Zhang, Y. Hu, T. Li, D. Cannan, X. Yin, R. Morandotti, Z. Chen, and X. Zhang, “Nonparaxial mathieu and weber accelerating beams,” Phys. Rev. Lett. 109, 193901 (2012).
[Crossref] [PubMed]

Chávez-Cerda, S.

M. A. Bandres, J. C. Gutiérrez-Vega, and S. Chávez-Cerda, “Parabolic nondiffracting optical wave fields,” Opt. Lett. 29, 44–46 (2004).
[Crossref] [PubMed]

S. Chávez-Cerda, M. Padgett, I. Allison, G. New, J. C. Gutiérrez-Vega, A. O’Neil, I. MacVicar, and J. Courtial, “Holographic generation and orbital angular momentum of high-order mathieu beams,” J. Opt. B: Quantum Semiclassical Opt. 4, S52 (2002).
[Crossref]

J. C. Gutiérrez-Vega, M. Iturbe-Castillo, and S. Chávez-Cerda, “Alternative formulation for invariant optical fields: Mathieu beams,” Opt. Lett. 25, 1493–1495 (2000).
[Crossref]

Chen, H.

Chen, J.

P. Chen, L.-L. Ma, W. Duan, J. Chen, S.-J. Ge, Z.-H. Zhu, M.-J. Tang, R. Xu, W. Gao, T. Li, W. Hu, and Y.-Q. Lu, “Digitalizing self-assembled chiral superstructures for optical vortex processing,” Adv. Mater. 30, 1705865 (2018).

Chen, P.

P. Chen, L.-L. Ma, W. Duan, J. Chen, S.-J. Ge, Z.-H. Zhu, M.-J. Tang, R. Xu, W. Gao, T. Li, W. Hu, and Y.-Q. Lu, “Digitalizing self-assembled chiral superstructures for optical vortex processing,” Adv. Mater. 30, 1705865 (2018).

B.-Y. Wei, S. Liu, P. Chen, S.-X. Qi, Y. Zhang, W. Hu, Y.-Q. Lu, and J.-L. Zhao, “Vortex Airy beams directly generated via liquid crystal q-Airy-plates,” Appl. Phys. Lett. 112, 121101 (2018).
[Crossref]

B.-Y. Wei, P. Chen, S.-J. Ge, W. Duan, W. Hu, and Y.-Q. Lu, “Generation of self-healing and transverse accelerating optical vortices,” Appl. Phys. Lett. 109, 121105 (2016).
[Crossref]

B.-Y. Wei, P. Chen, W. Hu, W. Ji, L.-Y. Zheng, S.-J. Ge, Y. Ming, V. Chigrinov, and Y.-Q. Lu, “Polarization-controllable Airy beams generated via a photoaligned director-variant liquid crystal mask,” Sci. Reports 5, 17484 (2015). Article.

Chen, Q.

Chen, Z.

P. Zhang, Y. Hu, T. Li, D. Cannan, X. Yin, R. Morandotti, Z. Chen, and X. Zhang, “Nonparaxial mathieu and weber accelerating beams,” Phys. Rev. Lett. 109, 193901 (2012).
[Crossref] [PubMed]

Chigrinov, V.

B.-Y. Wei, P. Chen, W. Hu, W. Ji, L.-Y. Zheng, S.-J. Ge, Y. Ming, V. Chigrinov, and Y.-Q. Lu, “Polarization-controllable Airy beams generated via a photoaligned director-variant liquid crystal mask,” Sci. Reports 5, 17484 (2015). Article.

Cho, S. Y.

M. G. Nassiri, S. Y. Cho, H. Yoshida, M. Ozaki, and E. Brasselet, “High-order laguerre-gauss polychromatic beams from bragg-berry flat optics,” Phys. Rev. A 98, 063834 (2018).
[Crossref]

Christodoulides, D.

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

Christodoulides, D. N.

M. A. Bandres, I. Kaminer, M. Mills, B. Rodríguez-Lara, E. Greenfield, M. Segev, and D. N. Christodoulides, “Accelerating optical beams,” Opt. Photonics News 24, 30–37 (2013).
[Crossref]

D. G. Papazoglou, N. K. Efremidis, D. N. Christodoulides, and S. Tzortzakis, “Observation of abruptly autofocusing waves,” Opt. Lett. 36, 1842–1844 (2011).
[Crossref] [PubMed]

N. K. Efremidis and D. N. Christodoulides, “Abruptly autofocusing waves,” Opt. Lett. 35, 4045–4047 (2010).
[Crossref] [PubMed]

P. Polynkin, M. Kolesik, J. V. Moloney, G. A. Siviloglou, and D. N. Christodoulides, “Curved plasma channel generation using ultraintense Airy beams,” Science 324, 229–232 (2009).
[Crossref] [PubMed]

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

Cižmár, T.

T. Vettenburg, H. I. Dalgarno, J. Nylk, C. Coll-Lladó, D. E. Ferrier, T. Čižmár, F. J. Gunn-Moore, and K. Dholakia, “Light-sheet microscopy using an Airy beam,” Nat. Methods 11, 541 (2014).
[Crossref] [PubMed]

Clerc, M. G.

R. Barboza, U. Bortolozzo, M. G. Clerc, and S. Residori, “Berry phase of light under bragg reflection by chiral liquid-crystal media,” Phys. Rev. Lett. 117, 053903 (2016).
[Crossref] [PubMed]

Coll-Lladó, C.

T. Vettenburg, H. I. Dalgarno, J. Nylk, C. Coll-Lladó, D. E. Ferrier, T. Čižmár, F. J. Gunn-Moore, and K. Dholakia, “Light-sheet microscopy using an Airy beam,” Nat. Methods 11, 541 (2014).
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T. Vettenburg, H. I. Dalgarno, J. Nylk, C. Coll-Lladó, D. E. Ferrier, T. Čižmár, F. J. Gunn-Moore, and K. Dholakia, “Light-sheet microscopy using an Airy beam,” Nat. Methods 11, 541 (2014).
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Davis, J. A.

Dholakia, K.

J. Nylk, K. McCluskey, S. Aggarwal, J. A. Tello, and K. Dholakia, “Enhancement of image quality and imaging depth with Airy light-sheet microscopy in cleared and non-cleared neural tissue,” Biomed. Opt. Express 7, 4021–4033 (2016).
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T. Vettenburg, H. I. Dalgarno, J. Nylk, C. Coll-Lladó, D. E. Ferrier, T. Čižmár, F. J. Gunn-Moore, and K. Dholakia, “Light-sheet microscopy using an Airy beam,” Nat. Methods 11, 541 (2014).
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G. Siviloglou, J. Broky, A. Dogariu, and D. Christodoulides, “Observation of accelerating Airy beams,” Phys. Rev. Lett. 99, 213901 (2007).
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P. Chen, L.-L. Ma, W. Duan, J. Chen, S.-J. Ge, Z.-H. Zhu, M.-J. Tang, R. Xu, W. Gao, T. Li, W. Hu, and Y.-Q. Lu, “Digitalizing self-assembled chiral superstructures for optical vortex processing,” Adv. Mater. 30, 1705865 (2018).

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P. Chen, L.-L. Ma, W. Duan, J. Chen, S.-J. Ge, Z.-H. Zhu, M.-J. Tang, R. Xu, W. Gao, T. Li, W. Hu, and Y.-Q. Lu, “Digitalizing self-assembled chiral superstructures for optical vortex processing,” Adv. Mater. 30, 1705865 (2018).

B.-Y. Wei, P. Chen, S.-J. Ge, W. Duan, W. Hu, and Y.-Q. Lu, “Generation of self-healing and transverse accelerating optical vortices,” Appl. Phys. Lett. 109, 121105 (2016).
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M. A. Bandres, I. Kaminer, M. Mills, B. Rodríguez-Lara, E. Greenfield, M. Segev, and D. N. Christodoulides, “Accelerating optical beams,” Opt. Photonics News 24, 30–37 (2013).
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T. Vettenburg, H. I. Dalgarno, J. Nylk, C. Coll-Lladó, D. E. Ferrier, T. Čižmár, F. J. Gunn-Moore, and K. Dholakia, “Light-sheet microscopy using an Airy beam,” Nat. Methods 11, 541 (2014).
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P. Chen, L.-L. Ma, W. Duan, J. Chen, S.-J. Ge, Z.-H. Zhu, M.-J. Tang, R. Xu, W. Gao, T. Li, W. Hu, and Y.-Q. Lu, “Digitalizing self-assembled chiral superstructures for optical vortex processing,” Adv. Mater. 30, 1705865 (2018).

B.-Y. Wei, P. Chen, S.-J. Ge, W. Duan, W. Hu, and Y.-Q. Lu, “Generation of self-healing and transverse accelerating optical vortices,” Appl. Phys. Lett. 109, 121105 (2016).
[Crossref]

B.-Y. Wei, P. Chen, W. Hu, W. Ji, L.-Y. Zheng, S.-J. Ge, Y. Ming, V. Chigrinov, and Y.-Q. Lu, “Polarization-controllable Airy beams generated via a photoaligned director-variant liquid crystal mask,” Sci. Reports 5, 17484 (2015). Article.

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P. Zhang, Y. Hu, T. Li, D. Cannan, X. Yin, R. Morandotti, Z. Chen, and X. Zhang, “Nonparaxial mathieu and weber accelerating beams,” Phys. Rev. Lett. 109, 193901 (2012).
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Ji, W.

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M. A. Bandres, I. Kaminer, M. Mills, B. Rodríguez-Lara, E. Greenfield, M. Segev, and D. N. Christodoulides, “Accelerating optical beams,” Opt. Photonics News 24, 30–37 (2013).
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I. Kaminer, R. Bekenstein, J. Nemirovsky, and M. Segev, “Nondiffracting accelerating wave packets of maxwell’s equations,” Phys. Rev. Lett. 108, 163901 (2012).
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J. Kobashi, H. Yoshida, and M. Ozaki, “Broadband optical vortex generation from patterned cholesteric liquid crystals,” Mol. Cryst. Liq. Cryst. 646, 116–124 (2017).
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H. Yoshida and J. Kobashi, “Flat optics with cholesteric and blue phase liquid crystals,” Liq. Cryst. 43, 1909–1919 (2016).
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J. Kobashi, H. Yoshida, and M. Ozaki, “Planar optics with patterned chiral liquid crystals,” Nat. Photonics 10, 389 (2016).
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J. Kobashi, H. Yoshida, and M. Ozaki, “Polychromatic optical vortex generation from patterned cholesteric liquid crystals,” Phys. Rev. Lett. 116, 253903 (2016).
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P. Polynkin, M. Kolesik, J. V. Moloney, G. A. Siviloglou, and D. N. Christodoulides, “Curved plasma channel generation using ultraintense Airy beams,” Science 324, 229–232 (2009).
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K. M. Lee, V. P. Tondiglia, T. Lee, I. I. Smalyukh, and T. J. White, “Large range electrically-induced reflection notch tuning in polymer stabilized cholesteric liquid crystals,” J. Mater. Chem. C 3, 8788–8793 (2015).
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Lee, T.

K. M. Lee, V. P. Tondiglia, T. Lee, I. I. Smalyukh, and T. J. White, “Large range electrically-induced reflection notch tuning in polymer stabilized cholesteric liquid crystals,” J. Mater. Chem. C 3, 8788–8793 (2015).
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Li, T.

P. Chen, L.-L. Ma, W. Duan, J. Chen, S.-J. Ge, Z.-H. Zhu, M.-J. Tang, R. Xu, W. Gao, T. Li, W. Hu, and Y.-Q. Lu, “Digitalizing self-assembled chiral superstructures for optical vortex processing,” Adv. Mater. 30, 1705865 (2018).

P. Zhang, Y. Hu, T. Li, D. Cannan, X. Yin, R. Morandotti, Z. Chen, and X. Zhang, “Nonparaxial mathieu and weber accelerating beams,” Phys. Rev. Lett. 109, 193901 (2012).
[Crossref] [PubMed]

Li, Y.

Liu, S.

B.-Y. Wei, S. Liu, P. Chen, S.-X. Qi, Y. Zhang, W. Hu, Y.-Q. Lu, and J.-L. Zhao, “Vortex Airy beams directly generated via liquid crystal q-Airy-plates,” Appl. Phys. Lett. 112, 121101 (2018).
[Crossref]

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Lu, Y.-Q.

B.-Y. Wei, S. Liu, P. Chen, S.-X. Qi, Y. Zhang, W. Hu, Y.-Q. Lu, and J.-L. Zhao, “Vortex Airy beams directly generated via liquid crystal q-Airy-plates,” Appl. Phys. Lett. 112, 121101 (2018).
[Crossref]

P. Chen, L.-L. Ma, W. Duan, J. Chen, S.-J. Ge, Z.-H. Zhu, M.-J. Tang, R. Xu, W. Gao, T. Li, W. Hu, and Y.-Q. Lu, “Digitalizing self-assembled chiral superstructures for optical vortex processing,” Adv. Mater. 30, 1705865 (2018).

B.-Y. Wei, P. Chen, S.-J. Ge, W. Duan, W. Hu, and Y.-Q. Lu, “Generation of self-healing and transverse accelerating optical vortices,” Appl. Phys. Lett. 109, 121105 (2016).
[Crossref]

B.-Y. Wei, P. Chen, W. Hu, W. Ji, L.-Y. Zheng, S.-J. Ge, Y. Ming, V. Chigrinov, and Y.-Q. Lu, “Polarization-controllable Airy beams generated via a photoaligned director-variant liquid crystal mask,” Sci. Reports 5, 17484 (2015). Article.

Luo, D.

Ma, L.-L.

P. Chen, L.-L. Ma, W. Duan, J. Chen, S.-J. Ge, Z.-H. Zhu, M.-J. Tang, R. Xu, W. Gao, T. Li, W. Hu, and Y.-Q. Lu, “Digitalizing self-assembled chiral superstructures for optical vortex processing,” Adv. Mater. 30, 1705865 (2018).

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S. Chávez-Cerda, M. Padgett, I. Allison, G. New, J. C. Gutiérrez-Vega, A. O’Neil, I. MacVicar, and J. Courtial, “Holographic generation and orbital angular momentum of high-order mathieu beams,” J. Opt. B: Quantum Semiclassical Opt. 4, S52 (2002).
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Mills, M.

M. A. Bandres, I. Kaminer, M. Mills, B. Rodríguez-Lara, E. Greenfield, M. Segev, and D. N. Christodoulides, “Accelerating optical beams,” Opt. Photonics News 24, 30–37 (2013).
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B.-Y. Wei, P. Chen, W. Hu, W. Ji, L.-Y. Zheng, S.-J. Ge, Y. Ming, V. Chigrinov, and Y.-Q. Lu, “Polarization-controllable Airy beams generated via a photoaligned director-variant liquid crystal mask,” Sci. Reports 5, 17484 (2015). Article.

Moloney, J. V.

P. Polynkin, M. Kolesik, J. V. Moloney, G. A. Siviloglou, and D. N. Christodoulides, “Curved plasma channel generation using ultraintense Airy beams,” Science 324, 229–232 (2009).
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Morandotti, R.

P. Zhang, Y. Hu, T. Li, D. Cannan, X. Yin, R. Morandotti, Z. Chen, and X. Zhang, “Nonparaxial mathieu and weber accelerating beams,” Phys. Rev. Lett. 109, 193901 (2012).
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M. G. Nassiri, S. Y. Cho, H. Yoshida, M. Ozaki, and E. Brasselet, “High-order laguerre-gauss polychromatic beams from bragg-berry flat optics,” Phys. Rev. A 98, 063834 (2018).
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Nemirovsky, J.

I. Kaminer, R. Bekenstein, J. Nemirovsky, and M. Segev, “Nondiffracting accelerating wave packets of maxwell’s equations,” Phys. Rev. Lett. 108, 163901 (2012).
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S. Chávez-Cerda, M. Padgett, I. Allison, G. New, J. C. Gutiérrez-Vega, A. O’Neil, I. MacVicar, and J. Courtial, “Holographic generation and orbital angular momentum of high-order mathieu beams,” J. Opt. B: Quantum Semiclassical Opt. 4, S52 (2002).
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J. Nylk, K. McCluskey, S. Aggarwal, J. A. Tello, and K. Dholakia, “Enhancement of image quality and imaging depth with Airy light-sheet microscopy in cleared and non-cleared neural tissue,” Biomed. Opt. Express 7, 4021–4033 (2016).
[Crossref] [PubMed]

T. Vettenburg, H. I. Dalgarno, J. Nylk, C. Coll-Lladó, D. E. Ferrier, T. Čižmár, F. J. Gunn-Moore, and K. Dholakia, “Light-sheet microscopy using an Airy beam,” Nat. Methods 11, 541 (2014).
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S. Chávez-Cerda, M. Padgett, I. Allison, G. New, J. C. Gutiérrez-Vega, A. O’Neil, I. MacVicar, and J. Courtial, “Holographic generation and orbital angular momentum of high-order mathieu beams,” J. Opt. B: Quantum Semiclassical Opt. 4, S52 (2002).
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M. G. Nassiri, S. Y. Cho, H. Yoshida, M. Ozaki, and E. Brasselet, “High-order laguerre-gauss polychromatic beams from bragg-berry flat optics,” Phys. Rev. A 98, 063834 (2018).
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J. Kobashi, H. Yoshida, and M. Ozaki, “Broadband optical vortex generation from patterned cholesteric liquid crystals,” Mol. Cryst. Liq. Cryst. 646, 116–124 (2017).
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J. Kobashi, H. Yoshida, and M. Ozaki, “Polychromatic optical vortex generation from patterned cholesteric liquid crystals,” Phys. Rev. Lett. 116, 253903 (2016).
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J. Kobashi, H. Yoshida, and M. Ozaki, “Planar optics with patterned chiral liquid crystals,” Nat. Photonics 10, 389 (2016).
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S. Chávez-Cerda, M. Padgett, I. Allison, G. New, J. C. Gutiérrez-Vega, A. O’Neil, I. MacVicar, and J. Courtial, “Holographic generation and orbital angular momentum of high-order mathieu beams,” J. Opt. B: Quantum Semiclassical Opt. 4, S52 (2002).
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Papazoglou, D. G.

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P. Polynkin, M. Kolesik, J. V. Moloney, G. A. Siviloglou, and D. N. Christodoulides, “Curved plasma channel generation using ultraintense Airy beams,” Science 324, 229–232 (2009).
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B.-Y. Wei, S. Liu, P. Chen, S.-X. Qi, Y. Zhang, W. Hu, Y.-Q. Lu, and J.-L. Zhao, “Vortex Airy beams directly generated via liquid crystal q-Airy-plates,” Appl. Phys. Lett. 112, 121101 (2018).
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M. Rafayelyan and E. Brasselet, “Spin-to-orbital angular momentum mapping of polychromatic light,” Phys. review letters 120, 213903 (2018).
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R. Barboza, U. Bortolozzo, M. G. Clerc, and S. Residori, “Berry phase of light under bragg reflection by chiral liquid-crystal media,” Phys. Rev. Lett. 117, 053903 (2016).
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M. A. Bandres, I. Kaminer, M. Mills, B. Rodríguez-Lara, E. Greenfield, M. Segev, and D. N. Christodoulides, “Accelerating optical beams,” Opt. Photonics News 24, 30–37 (2013).
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Segev, M.

M. A. Bandres, I. Kaminer, M. Mills, B. Rodríguez-Lara, E. Greenfield, M. Segev, and D. N. Christodoulides, “Accelerating optical beams,” Opt. Photonics News 24, 30–37 (2013).
[Crossref]

I. Kaminer, R. Bekenstein, J. Nemirovsky, and M. Segev, “Nondiffracting accelerating wave packets of maxwell’s equations,” Phys. Rev. Lett. 108, 163901 (2012).
[Crossref]

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

Siviloglou, G. A.

P. Polynkin, M. Kolesik, J. V. Moloney, G. A. Siviloglou, and D. N. Christodoulides, “Curved plasma channel generation using ultraintense Airy beams,” Science 324, 229–232 (2009).
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K. M. Lee, V. P. Tondiglia, T. Lee, I. I. Smalyukh, and T. J. White, “Large range electrically-induced reflection notch tuning in polymer stabilized cholesteric liquid crystals,” J. Mater. Chem. C 3, 8788–8793 (2015).
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P. Chen, L.-L. Ma, W. Duan, J. Chen, S.-J. Ge, Z.-H. Zhu, M.-J. Tang, R. Xu, W. Gao, T. Li, W. Hu, and Y.-Q. Lu, “Digitalizing self-assembled chiral superstructures for optical vortex processing,” Adv. Mater. 30, 1705865 (2018).

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Terborg, R.

Tkachenko, G.

M. Rafayelyan, G. Tkachenko, and E. Brasselet, “Reflective spin-orbit geometric phase from chiral anisotropic optical media,” Phys. Rev. Lett. 116, 253902 (2016).
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K. M. Lee, V. P. Tondiglia, T. Lee, I. I. Smalyukh, and T. J. White, “Large range electrically-induced reflection notch tuning in polymer stabilized cholesteric liquid crystals,” J. Mater. Chem. C 3, 8788–8793 (2015).
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T. Vettenburg, H. I. Dalgarno, J. Nylk, C. Coll-Lladó, D. E. Ferrier, T. Čižmár, F. J. Gunn-Moore, and K. Dholakia, “Light-sheet microscopy using an Airy beam,” Nat. Methods 11, 541 (2014).
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Wang, H.-T.

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B.-Y. Wei, S. Liu, P. Chen, S.-X. Qi, Y. Zhang, W. Hu, Y.-Q. Lu, and J.-L. Zhao, “Vortex Airy beams directly generated via liquid crystal q-Airy-plates,” Appl. Phys. Lett. 112, 121101 (2018).
[Crossref]

B.-Y. Wei, P. Chen, S.-J. Ge, W. Duan, W. Hu, and Y.-Q. Lu, “Generation of self-healing and transverse accelerating optical vortices,” Appl. Phys. Lett. 109, 121105 (2016).
[Crossref]

B.-Y. Wei, P. Chen, W. Hu, W. Ji, L.-Y. Zheng, S.-J. Ge, Y. Ming, V. Chigrinov, and Y.-Q. Lu, “Polarization-controllable Airy beams generated via a photoaligned director-variant liquid crystal mask,” Sci. Reports 5, 17484 (2015). Article.

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K. M. Lee, V. P. Tondiglia, T. Lee, I. I. Smalyukh, and T. J. White, “Large range electrically-induced reflection notch tuning in polymer stabilized cholesteric liquid crystals,” J. Mater. Chem. C 3, 8788–8793 (2015).
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P. Chen, L.-L. Ma, W. Duan, J. Chen, S.-J. Ge, Z.-H. Zhu, M.-J. Tang, R. Xu, W. Gao, T. Li, W. Hu, and Y.-Q. Lu, “Digitalizing self-assembled chiral superstructures for optical vortex processing,” Adv. Mater. 30, 1705865 (2018).

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P. Zhang, Y. Hu, T. Li, D. Cannan, X. Yin, R. Morandotti, Z. Chen, and X. Zhang, “Nonparaxial mathieu and weber accelerating beams,” Phys. Rev. Lett. 109, 193901 (2012).
[Crossref] [PubMed]

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M. G. Nassiri, S. Y. Cho, H. Yoshida, M. Ozaki, and E. Brasselet, “High-order laguerre-gauss polychromatic beams from bragg-berry flat optics,” Phys. Rev. A 98, 063834 (2018).
[Crossref]

J. Kobashi, H. Yoshida, and M. Ozaki, “Broadband optical vortex generation from patterned cholesteric liquid crystals,” Mol. Cryst. Liq. Cryst. 646, 116–124 (2017).
[Crossref]

H. Yoshida and J. Kobashi, “Flat optics with cholesteric and blue phase liquid crystals,” Liq. Cryst. 43, 1909–1919 (2016).
[Crossref]

J. Kobashi, H. Yoshida, and M. Ozaki, “Planar optics with patterned chiral liquid crystals,” Nat. Photonics 10, 389 (2016).
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J. Kobashi, H. Yoshida, and M. Ozaki, “Polychromatic optical vortex generation from patterned cholesteric liquid crystals,” Phys. Rev. Lett. 116, 253903 (2016).
[Crossref] [PubMed]

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Zhang, B.-F.

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P. Zhang, Y. Hu, T. Li, D. Cannan, X. Yin, R. Morandotti, Z. Chen, and X. Zhang, “Nonparaxial mathieu and weber accelerating beams,” Phys. Rev. Lett. 109, 193901 (2012).
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P. Zhang, Y. Hu, T. Li, D. Cannan, X. Yin, R. Morandotti, Z. Chen, and X. Zhang, “Nonparaxial mathieu and weber accelerating beams,” Phys. Rev. Lett. 109, 193901 (2012).
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B.-Y. Wei, S. Liu, P. Chen, S.-X. Qi, Y. Zhang, W. Hu, Y.-Q. Lu, and J.-L. Zhao, “Vortex Airy beams directly generated via liquid crystal q-Airy-plates,” Appl. Phys. Lett. 112, 121101 (2018).
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B.-Y. Wei, S. Liu, P. Chen, S.-X. Qi, Y. Zhang, W. Hu, Y.-Q. Lu, and J.-L. Zhao, “Vortex Airy beams directly generated via liquid crystal q-Airy-plates,” Appl. Phys. Lett. 112, 121101 (2018).
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B.-Y. Wei, P. Chen, W. Hu, W. Ji, L.-Y. Zheng, S.-J. Ge, Y. Ming, V. Chigrinov, and Y.-Q. Lu, “Polarization-controllable Airy beams generated via a photoaligned director-variant liquid crystal mask,” Sci. Reports 5, 17484 (2015). Article.

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Zhu, Z.-H.

P. Chen, L.-L. Ma, W. Duan, J. Chen, S.-J. Ge, Z.-H. Zhu, M.-J. Tang, R. Xu, W. Gao, T. Li, W. Hu, and Y.-Q. Lu, “Digitalizing self-assembled chiral superstructures for optical vortex processing,” Adv. Mater. 30, 1705865 (2018).

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P. Chen, L.-L. Ma, W. Duan, J. Chen, S.-J. Ge, Z.-H. Zhu, M.-J. Tang, R. Xu, W. Gao, T. Li, W. Hu, and Y.-Q. Lu, “Digitalizing self-assembled chiral superstructures for optical vortex processing,” Adv. Mater. 30, 1705865 (2018).

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Figures (6)

Fig. 1
Fig. 1 (a) Cholesteric liquid crystals in a uniform alignment cell self-assemble into a chiral Bragg reflector. An incident beam with the matching circular polarization is reflected with a flat phase front. (b) In the case of non-uniform alignment, regions with an initial helix angle of α impart a Pancharatnam-Berry or geometric phase modulation of 2α upon the reflected beam.
Fig. 2
Fig. 2 (a) Optical train for polarization modulation, along with (b) the Poincare sphere representation of its operation. (i) The initially s-polarized beam makes its first pass through the quarter-wave plate (QWP) with optic axis oriented at 45deg, and becomes circularly polarized. (ii) The beam is reflected from the LCoS spatial light modulator (SLM), each pixel of which acts as an independently variable waveplate. The accessible polarization states trace out an arc on the Poincare sphere. (iii) A second pass through the QWP maps each of these polarization states back to a different linear polarization state. (iv) Crucially, as long as the retardance of the SLM pixels can be modulated through a full 2π of phase, all linear polarizations are accessible. Finally, the SLM plane is imaged onto the photoalignment cell, with a Fourier plane filter to reject higher diffracted orders.
Fig. 3
Fig. 3 2D cubic phase mask to generate Airy beam. (a) Computer generated wrapped phase mask based on a total absolute phase change of 20π across a 4 mm × 4 mm area; white and black areas correspond to 0 and 2π phases respectively and therefore 0 and π initial helix angles. (b). Polarized optical micrograph to confirm the recording of the desired pattern into the alignment layer. For this figure only, a layer of nematic liquid crystal 5CB has been added for visualization.
Fig. 4
Fig. 4 Reflection band of PSCLC cell is red-shifted by applied voltage. Transmittance spectra are measured for right-circularly polarized light, matching the handedness of the PSCLC formulation. At zero applied voltage, the reflection band is centered at 570 nm with FWHM of 80 nm. When a DC voltage of 56 V is applied, the reflection band shifted to 715 nm with 110 nm FWHM.
Fig. 5
Fig. 5 (a) Far-field CCD images of reflection from element illuminated by multiple beamlines at 532 nm and 633 nm, demonstrating electrically switchable generation of Airy beams. CCD image dimensions are 6.4 × 4.8 mm. (b) Theoretical 2D Airy beam intensity distribution, for comparison.
Fig. 6
Fig. 6 Additional helix angle landscapes, and the corresponding far-field generated beams. CCD image dimensions are again 6.4 × 4.8 mm. (a) Computer-generated hologram, calculated via the Gerchberg-Saxton algorithm to spell out “AFRL”. (b) Mathieu beam with q = 6, m = 27 (these parameters are related to the radial and angular portions of Mathieu functions [22,37]). Slight defocus to show characteristic caustic curves.

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