Abstract

Manipulating Airy beams to symmetric Airy beams (SABs) with abruptly autofocusing and self-accelerating properties has attracted much attention. With such a particular propagation dynamic, SABs may provide great potential in dynamic signal imaging. On the other hand, the generation of SABs by spatial light modulators suffers from the limitations of phase gradient accuracy, low optical efficiency (<40%), and a bulky footprint. Therefore, exploring imaging applications and optimal generation methods of these Airy-type beams deserves further research. Here, based on the coordinate transformation of SAB, an asymmetric Airy beam (AAB) is realized. Symmetric/asymmetric cubic phase microplates (SCPPs/ACPPs) are designed and fabricated for generating SAB/AAB. The SCPP/ACPP demonstrates superior performance: compact construction (60  μm×60  μm×1.1  μm), continuous variation of phase, high efficiency (81% at 532 nm), and broadband operation from 405 to 780 nm. Dynamic imaging under monochromatic and polychromatic lights is realized by the SAB/AAB, indicating various results at different propagation distances with a certain initial signal. Further investigation reveals that the SCPP on a soft substrate maintains its physical dimensions and optical properties unchanged during stretching. Our work enables wide potential applications in integrated optics, beam manipulation, and imaging.

© 2020 Chinese Laser Press

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2019 (3)

P. Chen, B.-Y. Wei, W. Hu, and Y.-Q. Lu, “Liquid-crystal-mediated geometric phase: from transmissive to broadband reflective planar optics,” Adv. Mater., 1903665 (2019).
[Crossref]

H. Lin, B. C. P. Sturmberg, K.-T. Lin, Y. Yang, X. Zheng, T. K. Chong, C. Martijn de Sterke, and B. Jia, “A 90-nm-thick graphene metamaterial for strong and extremely broadband absorption of unpolarized light,” Nat. Photonics 13, 270–276 (2019).
[Crossref]

F. Mayer, S. Richter, J. Westhauser, E. Blasco, C. Barner-Kowollik, and M. Wegener, “Multimaterial 3D laser microprinting using an integrated microfluidic system,” Sci. Adv. 5, eaau9160 (2019).
[Crossref]

2018 (4)

D. Wei, C. Wang, H. Wang, X. Hu, D. Wei, X. Fang, Y. Zhang, D. Wu, Y. Hu, J. Li, S. Zhu, and M. Xiao, “Experimental demonstration of a three-dimensional lithium niobate nonlinear photonic crystal,” Nat. Photonics 12, 596–600 (2018).
[Crossref]

M. Henstridge, C. Pfeiffer, D. Wang, A. Boltasseva, V. M. Shalaev, A. Grbic, and R. Merlin, “Synchrotron radiation from an accelerating light pulse,” Science 362, 439–442 (2018).
[Crossref]

W. T. Chen, A. Y. Zhu, V. Sanjeev, M. Khorasaninejad, Z. Shi, E. Lee, and F. Capasso, “A broadband achromatic metalens for focusing and imaging in the visible,” Nat. Nanotechnol. 13, 220–226 (2018).
[Crossref]

Z.-X. Fang, Y. Chen, Y.-X. Ren, L. Gong, R.-D. Lu, A.-Q. Zhang, H.-Z. Zhao, and P. Wang, “Interplay between topological phase and self-acceleration in a vortex symmetric Airy beam,” Opt. Express 26, 7324–7335 (2018).
[Crossref]

2017 (3)

2016 (3)

T. Gissibl, S. Thiele, A. Herkommer, and H. Giessen, “Two-photon direct laser writing of ultracompact multi-lens objectives,” Nat. Photonics 10, 554–560 (2016).
[Crossref]

M. Malinauskas, A. Žukauskas, S. Hasegawa, Y. Hayasaki, V. Mizeikis, R. Buividas, and S. Juodkazis, “Ultrafast laser processing of materials: from science to industry,” Light Sci. Appl. 5, e16133 (2016).
[Crossref]

M. Manousidaki, D. G. Papazoglou, M. Farsari, and S. Tzortzakis, “Abruptly autofocusing beams enable advanced multiscale photo-polymerization,” Optica 3, 525–530 (2016).
[Crossref]

2015 (6)

Y. Liang, Y. Hu, D. Song, C. Lou, X. Zhang, Z. Chen, and J. Xu, “Image signal transmission with Airy beams,” Opt. Lett. 40, 5686–5689 (2015).
[Crossref]

F. Aieta, M. A. Kats, P. Genevet, and F. Capasso, “Multiwavelength achromatic metasurfaces by dispersive phase compensation,” Science 347, 1342–1345 (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. Rep. 5, 17484 (2015).
[Crossref]

P. Vaveliuk, A. Lencina, J. A. Rodrigo, and O. M. Matos, “Caustics, catastrophes, and symmetries in curved beams,” Phys. Rev. A 92, 0033850 (2015).
[Crossref]

Z.-X. Fang, Y.-X. Ren, L. Gong, P. Vaveliuk, Y. Chen, and R.-D. Lu, “Shaping symmetric Airy beam through binary amplitude modulation for ultralong needle focus,” J. Appl. Phys. 118, 203102 (2015).
[Crossref]

P. Vaveliuk, A. Lencina, J. A. Rodrigo, and Ó. Martnez-Matos, “Intensity-symmetric Airy beams,” J. Opt. Soc. Am. A 32, 443–446 (2015).
[Crossref]

2014 (8)

M. Gecevičius, M. Beresna, R. Drevinskas, and P. G. Kazansky, “Airy beams generated by ultrafast laser-imprinted space-variant nanostructures in glass,” Opt. Lett. 39, 6791–6794 (2014).
[Crossref]

Z. Zhang, Z. You, and D. Chu, “Fundamentals of phase-only liquid crystal on silicon (LCOS) devices,” Light Sci. Appl. 3, e213 (2014).
[Crossref]

N. Yu and F. Capasso, “Flat optics with designer metasurfaces,” Nat. Mater. 13, 139–150 (2014).
[Crossref]

Y.-L. Sun, W.-F. Dong, L.-G. Niu, T. Jiang, D.-X. Liu, L. Zhang, Y.-S. Wang, Q.-D. Chen, D.-P. Kim, and H.-B. Sun, “Protein-based soft micro-optics fabricated by femtosecond laser direct writing,” Light Sci. Appl. 3, e129 (2014).
[Crossref]

S. Jia, J. C. Vaughan, and X. Zhuang, “Isotropic three-dimensional super-resolution imaging with a self-bending point spread function,” Nat. Photonics 8, 302–306 (2014).
[Crossref]

T. Vettenburg, H. I. C. Dalgarno, J. Nylk, C. Coll-Llado, D. E. K. Ferrier, T. Cizmar, F. J. Gunn-Moore, and K. Dholakia, “Light-sheet microscopy using an Airy beam,” Nat. Methods 11, 541–544 (2014).
[Crossref]

P. Vaveliuk, A. Lencina, J. A. Rodrigo, and O. M. Matos, “Symmetric Airy beams,” Opt. Lett. 39, 2370–2373 (2014).
[Crossref]

F. Chen and J. R. Vázquez de Aldana, “Optical waveguides in crystalline dielectric materials produced by femtosecond-laser micromachining,” Laser Photon. Rev. 8, 251–275 (2014).
[Crossref]

2013 (3)

E. Rueda, D. Muñetón, J. A. Gómez, and A. Lencina, “High-quality optical vortex-beam generation by using a multilevel vortex-producing lens,” Opt. Lett. 38, 3941–3943 (2013).
[Crossref]

P. Panagiotopoulos, D. G. Papazoglou, A. Couairon, and S. Tzortzakis, “Sharply autofocused ring-Airy beams transforming into non-linear intense light bullets,” Nat. Commun. 4, 2622 (2013).
[Crossref]

N. Voloch-Bloch, Y. Lereah, Y. Lilach, A. Gover, and A. Arie, “Generation of electron Airy beams,” Nature 494, 331–335 (2013).
[Crossref]

2012 (1)

A. Mathis, F. Courvoisier, L. Froehly, L. Furfaro, M. Jacquot, P. A. Lacourt, and J. M. Dudley, “Micromachining along a curve: femtosecond laser micromachining of curved profiles in diamond and silicon using accelerating beams,” Appl. Phys. Lett. 101, 071110 (2012).
[Crossref]

2011 (2)

2010 (2)

A. Chong, W. H. Renninger, D. N. Christodoulides, and F. W. Wise, “Airy-Bessel wave packets as versatile linear light bullets,” Nat. Photonics 4, 103–106 (2010).
[Crossref]

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

2009 (2)

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]

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

2008 (3)

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

A. Ovsianikov, J. Viertl, B. Chichkov, M. Oubaha, B. MacCraith, I. Sakellari, A. Giakoumaki, D. Gray, M. Vamvakaki, M. Farsari, and C. Fotakis, “Ultra-low shrinkage hybrid photosensitive material for two-photon polymerization microfabrication,” ACS Nano 2, 2257–2262 (2008).
[Crossref]

2007 (3)

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]

Z. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, “Far-field optical hyperlens magnifying sub-diffraction-limited objects,” Science 315, 1686 (2007).
[Crossref]

2005 (2)

N. Fang, H. Lee, C. Sun, and X. Zhang, “Sub-diffraction-limited optical imaging with a silver superlens,” Science 308, 534–537 (2005).
[Crossref]

K. Takada, H.-B. Sun, and S. Kawata, “Improved spatial resolution and surface roughness in photopolymerization-based laser nanowriting,” Appl. Phys. Lett. 86, 071122 (2005).
[Crossref]

Aieta, F.

F. Aieta, M. A. Kats, P. Genevet, and F. Capasso, “Multiwavelength achromatic metasurfaces by dispersive phase compensation,” Science 347, 1342–1345 (2015).
[Crossref]

Arie, A.

N. Voloch-Bloch, Y. Lereah, Y. Lilach, A. Gover, and A. Arie, “Generation of electron Airy beams,” Nature 494, 331–335 (2013).
[Crossref]

Arzenbacher, K.

S. Thiele, K. Arzenbacher, T. Gissibl, H. Giessen, and A. M. Herkommer, “3D-printed eagle eye: compound microlens system for foveated imaging,” Sci. Adv. 3, e1602655 (2017).
[Crossref]

Barner-Kowollik, C.

F. Mayer, S. Richter, J. Westhauser, E. Blasco, C. Barner-Kowollik, and M. Wegener, “Multimaterial 3D laser microprinting using an integrated microfluidic system,” Sci. Adv. 5, eaau9160 (2019).
[Crossref]

Baumgartl, J.

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

Beresna, M.

Blasco, E.

F. Mayer, S. Richter, J. Westhauser, E. Blasco, C. Barner-Kowollik, and M. Wegener, “Multimaterial 3D laser microprinting using an integrated microfluidic system,” Sci. Adv. 5, eaau9160 (2019).
[Crossref]

Boltasseva, A.

M. Henstridge, C. Pfeiffer, D. Wang, A. Boltasseva, V. M. Shalaev, A. Grbic, and R. Merlin, “Synchrotron radiation from an accelerating light pulse,” Science 362, 439–442 (2018).
[Crossref]

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]

Buividas, R.

M. Malinauskas, A. Žukauskas, S. Hasegawa, Y. Hayasaki, V. Mizeikis, R. Buividas, and S. Juodkazis, “Ultrafast laser processing of materials: from science to industry,” Light Sci. Appl. 5, e16133 (2016).
[Crossref]

Capasso, F.

W. T. Chen, A. Y. Zhu, V. Sanjeev, M. Khorasaninejad, Z. Shi, E. Lee, and F. Capasso, “A broadband achromatic metalens for focusing and imaging in the visible,” Nat. Nanotechnol. 13, 220–226 (2018).
[Crossref]

F. Aieta, M. A. Kats, P. Genevet, and F. Capasso, “Multiwavelength achromatic metasurfaces by dispersive phase compensation,” Science 347, 1342–1345 (2015).
[Crossref]

N. Yu and F. Capasso, “Flat optics with designer metasurfaces,” Nat. Mater. 13, 139–150 (2014).
[Crossref]

Chen, F.

F. Chen and J. R. Vázquez de Aldana, “Optical waveguides in crystalline dielectric materials produced by femtosecond-laser micromachining,” Laser Photon. Rev. 8, 251–275 (2014).
[Crossref]

Chen, P.

P. Chen, B.-Y. Wei, W. Hu, and Y.-Q. Lu, “Liquid-crystal-mediated geometric phase: from transmissive to broadband reflective planar optics,” Adv. Mater., 1903665 (2019).
[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. Rep. 5, 17484 (2015).
[Crossref]

Chen, Q.-D.

Y.-L. Sun, W.-F. Dong, L.-G. Niu, T. Jiang, D.-X. Liu, L. Zhang, Y.-S. Wang, Q.-D. Chen, D.-P. Kim, and H.-B. Sun, “Protein-based soft micro-optics fabricated by femtosecond laser direct writing,” Light Sci. Appl. 3, e129 (2014).
[Crossref]

Chen, W. T.

W. T. Chen, A. Y. Zhu, V. Sanjeev, M. Khorasaninejad, Z. Shi, E. Lee, and F. Capasso, “A broadband achromatic metalens for focusing and imaging in the visible,” Nat. Nanotechnol. 13, 220–226 (2018).
[Crossref]

Chen, Y.

Z.-X. Fang, Y. Chen, Y.-X. Ren, L. Gong, R.-D. Lu, A.-Q. Zhang, H.-Z. Zhao, and P. Wang, “Interplay between topological phase and self-acceleration in a vortex symmetric Airy beam,” Opt. Express 26, 7324–7335 (2018).
[Crossref]

Z.-X. Fang, Y.-X. Ren, L. Gong, P. Vaveliuk, Y. Chen, and R.-D. Lu, “Shaping symmetric Airy beam through binary amplitude modulation for ultralong needle focus,” J. Appl. Phys. 118, 203102 (2015).
[Crossref]

Chen, Z.

Chichkov, B.

A. Ovsianikov, J. Viertl, B. Chichkov, M. Oubaha, B. MacCraith, I. Sakellari, A. Giakoumaki, D. Gray, M. Vamvakaki, M. Farsari, and C. Fotakis, “Ultra-low shrinkage hybrid photosensitive material for two-photon polymerization microfabrication,” ACS Nano 2, 2257–2262 (2008).
[Crossref]

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. Rep. 5, 17484 (2015).
[Crossref]

Chong, A.

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W. T. Chen, A. Y. Zhu, V. Sanjeev, M. Khorasaninejad, Z. Shi, E. Lee, and F. Capasso, “A broadband achromatic metalens for focusing and imaging in the visible,” Nat. Nanotechnol. 13, 220–226 (2018).
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M. Henstridge, C. Pfeiffer, D. Wang, A. Boltasseva, V. M. Shalaev, A. Grbic, and R. Merlin, “Synchrotron radiation from an accelerating light pulse,” Science 362, 439–442 (2018).
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W. T. Chen, A. Y. Zhu, V. Sanjeev, M. Khorasaninejad, Z. Shi, E. Lee, and F. Capasso, “A broadband achromatic metalens for focusing and imaging in the visible,” Nat. Nanotechnol. 13, 220–226 (2018).
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Sun, Y.-L.

Y.-L. Sun, W.-F. Dong, L.-G. Niu, T. Jiang, D.-X. Liu, L. Zhang, Y.-S. Wang, Q.-D. Chen, D.-P. Kim, and H.-B. Sun, “Protein-based soft micro-optics fabricated by femtosecond laser direct writing,” Light Sci. Appl. 3, e129 (2014).
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K. Takada, H.-B. Sun, and S. Kawata, “Improved spatial resolution and surface roughness in photopolymerization-based laser nanowriting,” Appl. Phys. Lett. 86, 071122 (2005).
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S. Thiele, K. Arzenbacher, T. Gissibl, H. Giessen, and A. M. Herkommer, “3D-printed eagle eye: compound microlens system for foveated imaging,” Sci. Adv. 3, e1602655 (2017).
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N. Yu and F. Capasso, “Flat optics with designer metasurfaces,” Nat. Mater. 13, 139–150 (2014).
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Y.-L. Sun, W.-F. Dong, L.-G. Niu, T. Jiang, D.-X. Liu, L. Zhang, Y.-S. Wang, Q.-D. Chen, D.-P. Kim, and H.-B. Sun, “Protein-based soft micro-optics fabricated by femtosecond laser direct writing,” Light Sci. Appl. 3, e129 (2014).
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Z. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, “Far-field optical hyperlens magnifying sub-diffraction-limited objects,” Science 315, 1686 (2007).
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D. Wei, C. Wang, H. Wang, X. Hu, D. Wei, X. Fang, Y. Zhang, D. Wu, Y. Hu, J. Li, S. Zhu, and M. Xiao, “Experimental demonstration of a three-dimensional lithium niobate nonlinear photonic crystal,” Nat. Photonics 12, 596–600 (2018).
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Zhao, H.-Z.

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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. Rep. 5, 17484 (2015).
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H. Lin, B. C. P. Sturmberg, K.-T. Lin, Y. Yang, X. Zheng, T. K. Chong, C. Martijn de Sterke, and B. Jia, “A 90-nm-thick graphene metamaterial for strong and extremely broadband absorption of unpolarized light,” Nat. Photonics 13, 270–276 (2019).
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W. T. Chen, A. Y. Zhu, V. Sanjeev, M. Khorasaninejad, Z. Shi, E. Lee, and F. Capasso, “A broadband achromatic metalens for focusing and imaging in the visible,” Nat. Nanotechnol. 13, 220–226 (2018).
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D. Wei, C. Wang, H. Wang, X. Hu, D. Wei, X. Fang, Y. Zhang, D. Wu, Y. Hu, J. Li, S. Zhu, and M. Xiao, “Experimental demonstration of a three-dimensional lithium niobate nonlinear photonic crystal,” Nat. Photonics 12, 596–600 (2018).
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S. Jia, J. C. Vaughan, and X. Zhuang, “Isotropic three-dimensional super-resolution imaging with a self-bending point spread function,” Nat. Photonics 8, 302–306 (2014).
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M. Malinauskas, A. Žukauskas, S. Hasegawa, Y. Hayasaki, V. Mizeikis, R. Buividas, and S. Juodkazis, “Ultrafast laser processing of materials: from science to industry,” Light Sci. Appl. 5, e16133 (2016).
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ACS Nano (1)

A. Ovsianikov, J. Viertl, B. Chichkov, M. Oubaha, B. MacCraith, I. Sakellari, A. Giakoumaki, D. Gray, M. Vamvakaki, M. Farsari, and C. Fotakis, “Ultra-low shrinkage hybrid photosensitive material for two-photon polymerization microfabrication,” ACS Nano 2, 2257–2262 (2008).
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Adv. Mater. (1)

P. Chen, B.-Y. Wei, W. Hu, and Y.-Q. Lu, “Liquid-crystal-mediated geometric phase: from transmissive to broadband reflective planar optics,” Adv. Mater., 1903665 (2019).
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Appl. Phys. Lett. (2)

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J. Appl. Phys. (1)

Z.-X. Fang, Y.-X. Ren, L. Gong, P. Vaveliuk, Y. Chen, and R.-D. Lu, “Shaping symmetric Airy beam through binary amplitude modulation for ultralong needle focus,” J. Appl. Phys. 118, 203102 (2015).
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J. Opt. Soc. Am. A (1)

Laser Photon. Rev. (1)

F. Chen and J. R. Vázquez de Aldana, “Optical waveguides in crystalline dielectric materials produced by femtosecond-laser micromachining,” Laser Photon. Rev. 8, 251–275 (2014).
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Light Sci. Appl. (3)

M. Malinauskas, A. Žukauskas, S. Hasegawa, Y. Hayasaki, V. Mizeikis, R. Buividas, and S. Juodkazis, “Ultrafast laser processing of materials: from science to industry,” Light Sci. Appl. 5, e16133 (2016).
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Nat. Commun. (1)

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Nat. Mater. (1)

N. Yu and F. Capasso, “Flat optics with designer metasurfaces,” Nat. Mater. 13, 139–150 (2014).
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Nat. Methods (1)

T. Vettenburg, H. I. C. Dalgarno, J. Nylk, C. Coll-Llado, D. E. K. Ferrier, T. Cizmar, F. J. Gunn-Moore, and K. Dholakia, “Light-sheet microscopy using an Airy beam,” Nat. Methods 11, 541–544 (2014).
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Nat. Nanotechnol. (1)

W. T. Chen, A. Y. Zhu, V. Sanjeev, M. Khorasaninejad, Z. Shi, E. Lee, and F. Capasso, “A broadband achromatic metalens for focusing and imaging in the visible,” Nat. Nanotechnol. 13, 220–226 (2018).
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Nat. Photonics (6)

A. Chong, W. H. Renninger, D. N. Christodoulides, and F. W. Wise, “Airy-Bessel wave packets as versatile linear light bullets,” Nat. Photonics 4, 103–106 (2010).
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H. Lin, B. C. P. Sturmberg, K.-T. Lin, Y. Yang, X. Zheng, T. K. Chong, C. Martijn de Sterke, and B. Jia, “A 90-nm-thick graphene metamaterial for strong and extremely broadband absorption of unpolarized light,” Nat. Photonics 13, 270–276 (2019).
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J. Baumgartl, M. Mazilu, and K. Dholakia, “Optically mediated particle clearing using Airy wavepackets,” Nat. Photonics 2, 675–678 (2008).
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S. Jia, J. C. Vaughan, and X. Zhuang, “Isotropic three-dimensional super-resolution imaging with a self-bending point spread function,” Nat. Photonics 8, 302–306 (2014).
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D. Wei, C. Wang, H. Wang, X. Hu, D. Wei, X. Fang, Y. Zhang, D. Wu, Y. Hu, J. Li, S. Zhu, and M. Xiao, “Experimental demonstration of a three-dimensional lithium niobate nonlinear photonic crystal,” Nat. Photonics 12, 596–600 (2018).
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Nature (1)

N. Voloch-Bloch, Y. Lereah, Y. Lilach, A. Gover, and A. Arie, “Generation of electron Airy beams,” Nature 494, 331–335 (2013).
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Opt. Express (4)

Opt. Lett. (9)

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P. Vaveliuk, A. Lencina, J. A. Rodrigo, and O. M. Matos, “Symmetric Airy beams,” Opt. Lett. 39, 2370–2373 (2014).
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Optica (1)

Phys. Rev. A (1)

P. Vaveliuk, A. Lencina, J. A. Rodrigo, and O. M. Matos, “Caustics, catastrophes, and symmetries in curved beams,” Phys. Rev. A 92, 0033850 (2015).
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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).
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Sci. Adv. (2)

F. Mayer, S. Richter, J. Westhauser, E. Blasco, C. Barner-Kowollik, and M. Wegener, “Multimaterial 3D laser microprinting using an integrated microfluidic system,” Sci. Adv. 5, eaau9160 (2019).
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S. Thiele, K. Arzenbacher, T. Gissibl, H. Giessen, and A. M. Herkommer, “3D-printed eagle eye: compound microlens system for foveated imaging,” Sci. Adv. 3, e1602655 (2017).
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Sci. Rep. (1)

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. Rep. 5, 17484 (2015).
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Science (5)

M. Henstridge, C. Pfeiffer, D. Wang, A. Boltasseva, V. M. Shalaev, A. Grbic, and R. Merlin, “Synchrotron radiation from an accelerating light pulse,” Science 362, 439–442 (2018).
[Crossref]

N. Fang, H. Lee, C. Sun, and X. Zhang, “Sub-diffraction-limited optical imaging with a silver superlens,” Science 308, 534–537 (2005).
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Z. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, “Far-field optical hyperlens magnifying sub-diffraction-limited objects,” Science 315, 1686 (2007).
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F. Aieta, M. A. Kats, P. Genevet, and F. Capasso, “Multiwavelength achromatic metasurfaces by dispersive phase compensation,” Science 347, 1342–1345 (2015).
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[Crossref]

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Figures (6)

Fig. 1.
Fig. 1. Symmetric and asymmetric Airy beams and their dynamic imaging of a letter “T”. (a1) Cubic phase mask. (a2) Intensity distribution of the corresponding 2D Airy beam at the Fourier plane. (a3) Propagation dynamic of the Airy beam versus (sx,ξ). (b1) Symmetric cubic phase mask. (b2) The side-view profiles of the corresponding SAB. (b3) Intensity distribution of the SAB at the distances ξ/ξf=0,1,2,3 from the initial plane. (c1) Asymmetric cubic phase mask. (c2), (c3) The corresponding AAB (c2) during propagation and (c3) at the certain planes. (d) Schematic illustration of dynamic imaging of a letter “T” by the SAB at different distances. Insets: simulation. In the gray scale pattern, black corresponds to 0 and white to 2π radians. In the intensity scale, [0,1] for each pattern corresponds to [0, Imax].
Fig. 2.
Fig. 2. Femtosecond laser two-photon polymerization of symmetric and asymmetric cubic phase microplates. (a) Schematic illustration of the fabrication of SCPP and ACPP. (b) Image of the designed SCPP according to the phase mask by converting the phase to the corresponding height and discretization with a step of 100 nm. (c) SEM and AFM micrographs (half of the image) of the fabricated SCPP. (d) Height profiles of the desired, designed, and fabricated SCPP along the dashed lines in (b) and (c). (e), (f) Top-view SEM and three-dimensional AFM images of the fabricated ACPP.
Fig. 3.
Fig. 3. Generation of symmetric and asymmetric Airy beams. (a) Schematic of the experimental setup for generating and observing SAB and AAB. (b1)–(b2) Intensity distribution of the (b1) SAB and (b2) AAB generated by the fabricated phase plates at the propagation planes z=0,60,120, and 180 μm. (c) Transverse acceleration of the main lobes of the SAB and AAB as a function of beam propagation distance. (d) Lateral and vertical FWHMs of the main lobes of the SAB and AAB varying with propagation distance. Error bars in (c), (d) indicate standard deviation (s.d.). The ellipses with arrows indicate the corresponding coordinate axis according to the color.
Fig. 4.
Fig. 4. Broadband generation of symmetric and asymmetric Airy beams. (a) Experimentally measured intensity profiles and optical efficiency of the generated SAB and AAB over a broadband illumination from 405 to 780 nm. All the intensity profiles are captured at z=180  μm. Error bars in efficiency represent s.d. (b) Distance between main lobes in lateral and vertical directions of the generated SAB (upper) and AAB (lower) as a function of beam propagation distance at 488, 532, and 633 nm. (c1) and (d1) Simulated (top row) and experimental (bottom row) results of the chromatic (c1) SAB and (d1) AAB at z=0,60,120,180  μm. (c2) Simulated (left) and experimental (right) results of the chromatic SAB in the xz plane; (d2) experimental profiles of the chromatic AAB in the xz plane (left) and in the yz plane (right).
Fig. 5.
Fig. 5. Dynamic imaging by symmetric and asymmetric Airy beams. (a) Schematic illustration for the characterization of dynamic Airy imaging. (b1), (b2) Imaging results of letter “T” at different propagation planes via the (b1) SAB and (b2) AAB at 532 nm. Different imaging results are exhibited at different propagation planes by the SAB and AAB. (c1) A square shows various imaging results at different propagation planes via the SAB at 633 nm, the initial shape “square” (Chinese character “�?�”) at z=0, a Chinese character “田” at z=146  μm, and an ancient Chinese character “㗊” at z=177  μm. (c2) A circle shows various imaging results at different propagation planes via the AAB at 488 nm, a number “0” at z=0, a horizontal number “8” at z=67  μm, and a double-digit number “88” at z=122  μm. (d) Imaging results of the letter “T” at different propagation planes via the ACPP under white light illumination. Different information can be extracted at a certain propagation plane z=90  μm with different wavelength elements, a Chinese word “开” in the blue ingredient (488 nm), and a Greek symbol “π” in the red ingredient (633 nm).
Fig. 6.
Fig. 6. Flexibility and robustness of the symmetric cubic phase during mechanical stretch. (a) The length and width of the SCPP on a PDMS substrate almost remain unchanged during the stretch coefficient in the x direction varying from 0% to 85%, and the optical efficiency maintains stable as well. Error bars on Dx,Dy, and efficiency indicate s.d. (b) The optical efficiency of the SCPP on a PDMS substrate has a good consistency during 100 cyclic stretch with a stretch coefficient of 50%. Error bars represent s.d. (c1)–(c3) Images of the SCPP on a PDMS substrate, the generated intensity profiles, and the imaging results (c1) before, (c2) during, and (c3) after stretch. The SCPP can keep its structure and optical properties unchanged. (d) Higher stretch coefficient (>90%) makes the structure break along the vein. After releasing the stretch, the cracked parts can joint together perfectly. The SEM micrograph shows the tiny crack at the joint. Because of the nice restoration, the corresponding intensity profiles and imaging results are not influenced.

Equations (4)

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ϕ(ξ,s)=Ai[s(ξ/2)2+iaξ]exp[as(aξ2/2)i(ξ3/12)+i(a2ξ/2)+i(sξ/2)].
Φ0(k)=exp(ak2)exp[i(k33a2kia3)/3].
u(s)=exp(as){Ai(s)+i[Gi(s)]}/2+exp(as){Ai(s)+i[Gi(s)]}/2,
U(x,y,z)=exp(ikz)iλz+Eint(kx,ky)exp[iφSAB(kx,ky)]exp{ik2z[(xkx)2+(yky)2]}dkxdky.