Abstract

A functional metasurface of both transparent medium slices and multiple deflection prisms is proposed, where phase retardations for generating non-diffracting vortex lattices are integrated and encoded as rotation angles of nano-apertures. Under plane-wave illumination, the transmitted waves from the thin flat metasurface act analogously as multiple beams, each with a designed propagating direction and pre-scribed phase shift, that generate an optical lattice within their overlapping region of space. By altering the design parameters of the metasurface, lattice type and size can be controlled. Both numerical simulations and experiments were conducted, verifying the possibility of the proposed method and the non-diffracting properties of the generated vortex lattices.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref] [PubMed]

2018 (8)

A. Mondal, A. Yevick, L. C. Blackburn, N. Kanellakopoulos, and D. G. Grier, “Projecting non-diffracting waves with intermediate-plane holography,” Opt. Express 26(4), 3926–3931 (2018).
[Crossref] [PubMed]

L. Li, C. Chang, X. Yuan, C. Yuan, S. Feng, S. Nie, and J. Ding, “Generation of optical vortex array along arbitrary curvilinear arrangement,” Opt. Express 26(8), 9798–9812 (2018).
[Crossref] [PubMed]

H. Gao, Y. Li, L. Chen, J. Jin, M. Pu, X. Li, P. Gao, C. Wang, X. Luo, and M. Hong, “Quasi-Talbot effect of orbital angular momentum beams for generation of optical vortex arrays by multiplexing metasurface design,” Nanoscale 10(2), 666–671 (2018).
[Crossref] [PubMed]

A. Y. G. Fuh, Y. L. Tsai, C. H. Yang, and S. T. Wu, “Fabrication of optical vortex lattices based on holographic polymer-dispersed liquid crystal films,” Opt. Lett. 43(1), 154–157 (2018).
[Crossref] [PubMed]

E. Arbabi, A. Arbabi, S. M. Kamali, Y. Horie, M. Faraji-Dana, and A. Faraon, “MEMS-tunable dielectric metasurface lens,” Nat. Commun. 9(1), 812 (2018).
[Crossref] [PubMed]

M. Jang, Y. Horie, A. Shibukawa, J. Brake, Y. Liu, S. M. Kamali, A. Arbabi, H. Ruan, A. Faraon, and C. Yang, “Wavefront shaping with disorder-engineered metasurfaces,” Nat. Photonics 12(2), 84–90 (2018).
[Crossref] [PubMed]

K. Zhang, Y. Yuan, D. Zhang, X. Ding, B. Ratni, S. N. Burokur, M. Lu, K. Tang, and Q. Wu, “Phase-engineered metalenses to generate converging and non-diffractive vortex beam carrying orbital angular momentum in microwave region,” Opt. Express 26(2), 1351–1360 (2018).
[Crossref] [PubMed]

S. Keren-Zur, L. Michaeli, H. Suchowski, and T. Ellenbogen, “Shaping light with nonlinear metasurfaces,” Adv. Opt. Photonics 10(1), 309–353 (2018).
[Crossref]

2017 (4)

S. Wang, P. Ch. Wu, V. C. Su, Y. Ch. Lai, C. Hung Chu, J. W. Chen, S. H. Lu, J. Chen, B. Xu, C. H. Kuan, T. Li, S. Zhu, and D. P. Tsai, “Broadband achromatic optical metasurface devices,” Nat. Commun. 8(1), 187 (2017).
[Crossref] [PubMed]

P. Genevet, F. Capasso, F. Aieta, M. Khorasaninejad, and R. Devlin, “Recent advances in planar optics: from plasmonic to dielectric metasurfaces,” Optica 4(1), 139–152 (2017).
[Crossref]

A. Y. Zhu, A. I. Kuznetsov, B. Luk’yanchuk, N. Engheta, and P. Genevet, “Traditional and emerging materials for optical metasurfaces,” Nanophotonics 6(2), 452–471 (2017).
[Crossref]

A. Kapoor and J. Joseph, “Design of custom photonic crystal cavities using interference lithography in combination with sidelobe-suppressed Bessel beam and optical phase engineering,” J. Nanophotonics 11(4), 046024 (2017).

2016 (7)

J. A. Davis, I. Moreno, K. Badham, M. M. Sánchez-López, and D. M. Cottrell, “Nondiffracting vector beams where the charge and the polarization state vary with propagation distance,” Opt. Lett. 41(10), 2270–2273 (2016).
[Crossref] [PubMed]

N. Vuillemin, P. Mahou, D. Débarre, T. Gacoin, P. L. Tharaux, M. C. Schanne-Klein, W. Supatto, and E. Beaurepaire, “Efficient second-harmonic imaging of collagen in histological slides using Bessel beam excitation,” Sci. Rep. 6(1), 29863 (2016).
[Crossref] [PubMed]

N. Fläschner, B. S. Rem, M. Tarnowski, D. Vogel, D. S. Lühmann, K. Sengstock, and C. Weitenberg, “Experimental reconstruction of the Berry curvature in a Floquet Bloch band,” Science 352(6289), 1091–1094 (2016).
[Crossref] [PubMed]

N. Goldman, J. C. Budich, and P. Zoller, “Topological quantum matter with ultracold gases in optical lattices,” Nat. Phys. 12(7), 639–645 (2016).
[Crossref]

M. Di Liberto, A. Hemmerich, and C. Morais Smith, “Topological varma superfluid in optical lattices,” Phys. Rev. Lett. 117(16), 163001 (2016).
[Crossref] [PubMed]

M. Khorasaninejad, W. T. Chen, R. C. Devlin, J. Oh, A. Y. Zhu, and F. Capasso, “Metalenses at visible wavelengths: Diffraction-limited focusing and subwavelength resolution imaging,” Science 352(6290), 1190–1194 (2016).
[Crossref] [PubMed]

Z. Li, H. Liu, H. Liu, S. Xu, L. Ma, C. Cheng, L. Wang, and L. Mingzhen, “An interferometric patchwork to generate high-order quasi-nondiffracting vortex lattices,” Opt. Commun. 368, 86–94 (2016).
[Crossref]

2015 (1)

2014 (2)

N. Yu and F. Capasso, “Flat optics with designer metasurfaces,” Nat. Mater. 13(2), 139–150 (2014).
[Crossref] [PubMed]

K. Zhang, X. M. Ding, L. Zhang, and Q. Wu, “Anomalous three-dimensional refraction in the microwave region by ultra-thin high efficiency metalens with phase discontinuities in orthogonal directions,” New J. Phys. 16(10), 103020 (2014).
[Crossref]

2013 (2)

2012 (3)

L. Wang, B. Terhalle, V. A. Guzenko, A. Farhan, M. Hojeij, and Y. Ekinci, “Generation of high-resolution kagome lattice structures using extreme ultraviolet interference lithography,” Appl. Phys. Lett. 101(9), 093104 (2012).
[Crossref]

P. Rose, M. Boguslawski, and C. Denz, “Nonlinear lattice structures based on families of complex nondiffracting beams,” New J. Phys. 14(3), 033018 (2012).
[Crossref]

K. Toyoda, K. Miyamoto, N. Aoki, R. Morita, and T. Omatsu, “Using optical vortex to control the chirality of twisted metal nanostructures,” Nano Lett. 12(7), 3645–3649 (2012).
[Crossref] [PubMed]

2011 (3)

K. Dholakia and T. Čižmár, “Shaping the future of manipulation,” Nat. Photonics 5(6), 335–342 (2011).
[Crossref]

M. Boguslawski, P. Rose, and C. Denz, “Nondiffracting kagome lattice,” Appl. Phys. Lett. 98(6), 061111 (2011).
[Crossref]

M. Boguslawski, P. Rose, and C. Denz, “Increasing the structural variety of discrete nondiffracting wave fields,” Phys. Rev. A 84(1), 013832 (2011).
[Crossref]

2010 (1)

M. Mazilu, D. J. Stevenson, F. Gunn-Moore, and K. Dholakia, “Light beats the spread: “non-diffracting” beams,” Laser Photonics Rev. 4(4), 529–547 (2010).
[Crossref]

2009 (1)

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, “Soliton shape and mobility control in optical lattices,” Prog. Opt. 52, 63–148 (2009).
[Crossref]

2007 (1)

2003 (1)

Z. Bouchal, “Nondiffracting Optical Beams: Physical Properties, Experiments, and Applications,” Czech. J. Phys. 53(7), 537–578 (2003).
[Crossref]

2002 (1)

V. Garcés-Chávez, D. McGloin, H. Melville, W. Sibbett, and K. Dholakia, “Simultaneous micromanipulation in multiple planes using a self-reconstructing light beam,” Nature 419(6903), 145–147 (2002).
[Crossref] [PubMed]

1999 (1)

J. Arlt, K. Dholakia, L. Allen, and M. J. Padgett, “Efficiency of second-harmonic generation with Bessel beams,” Phys. Rev. A 60(3), 2438–2441 (1999).
[Crossref]

1987 (1)

J. Durnin, J. Miceli, and J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58(15), 1499–1501 (1987).
[Crossref] [PubMed]

Aieta, F.

Allen, L.

J. Arlt, K. Dholakia, L. Allen, and M. J. Padgett, “Efficiency of second-harmonic generation with Bessel beams,” Phys. Rev. A 60(3), 2438–2441 (1999).
[Crossref]

Aoki, N.

K. Toyoda, K. Miyamoto, N. Aoki, R. Morita, and T. Omatsu, “Using optical vortex to control the chirality of twisted metal nanostructures,” Nano Lett. 12(7), 3645–3649 (2012).
[Crossref] [PubMed]

Arbabi, A.

E. Arbabi, A. Arbabi, S. M. Kamali, Y. Horie, M. Faraji-Dana, and A. Faraon, “MEMS-tunable dielectric metasurface lens,” Nat. Commun. 9(1), 812 (2018).
[Crossref] [PubMed]

M. Jang, Y. Horie, A. Shibukawa, J. Brake, Y. Liu, S. M. Kamali, A. Arbabi, H. Ruan, A. Faraon, and C. Yang, “Wavefront shaping with disorder-engineered metasurfaces,” Nat. Photonics 12(2), 84–90 (2018).
[Crossref] [PubMed]

Arbabi, E.

E. Arbabi, A. Arbabi, S. M. Kamali, Y. Horie, M. Faraji-Dana, and A. Faraon, “MEMS-tunable dielectric metasurface lens,” Nat. Commun. 9(1), 812 (2018).
[Crossref] [PubMed]

Arlt, J.

J. Arlt, K. Dholakia, L. Allen, and M. J. Padgett, “Efficiency of second-harmonic generation with Bessel beams,” Phys. Rev. A 60(3), 2438–2441 (1999).
[Crossref]

Badham, K.

Beaurepaire, E.

N. Vuillemin, P. Mahou, D. Débarre, T. Gacoin, P. L. Tharaux, M. C. Schanne-Klein, W. Supatto, and E. Beaurepaire, “Efficient second-harmonic imaging of collagen in histological slides using Bessel beam excitation,” Sci. Rep. 6(1), 29863 (2016).
[Crossref] [PubMed]

Blackburn, L. C.

Boguslawski, M.

P. Rose, M. Boguslawski, and C. Denz, “Nonlinear lattice structures based on families of complex nondiffracting beams,” New J. Phys. 14(3), 033018 (2012).
[Crossref]

M. Boguslawski, P. Rose, and C. Denz, “Nondiffracting kagome lattice,” Appl. Phys. Lett. 98(6), 061111 (2011).
[Crossref]

M. Boguslawski, P. Rose, and C. Denz, “Increasing the structural variety of discrete nondiffracting wave fields,” Phys. Rev. A 84(1), 013832 (2011).
[Crossref]

Bouchal, Z.

Z. Bouchal, “Nondiffracting Optical Beams: Physical Properties, Experiments, and Applications,” Czech. J. Phys. 53(7), 537–578 (2003).
[Crossref]

Brake, J.

M. Jang, Y. Horie, A. Shibukawa, J. Brake, Y. Liu, S. M. Kamali, A. Arbabi, H. Ruan, A. Faraon, and C. Yang, “Wavefront shaping with disorder-engineered metasurfaces,” Nat. Photonics 12(2), 84–90 (2018).
[Crossref] [PubMed]

Budich, J. C.

N. Goldman, J. C. Budich, and P. Zoller, “Topological quantum matter with ultracold gases in optical lattices,” Nat. Phys. 12(7), 639–645 (2016).
[Crossref]

Burokur, S. N.

Capasso, F.

P. Genevet, F. Capasso, F. Aieta, M. Khorasaninejad, and R. Devlin, “Recent advances in planar optics: from plasmonic to dielectric metasurfaces,” Optica 4(1), 139–152 (2017).
[Crossref]

M. Khorasaninejad, W. T. Chen, R. C. Devlin, J. Oh, A. Y. Zhu, and F. Capasso, “Metalenses at visible wavelengths: Diffraction-limited focusing and subwavelength resolution imaging,” Science 352(6290), 1190–1194 (2016).
[Crossref] [PubMed]

N. Yu and F. Capasso, “Flat optics with designer metasurfaces,” Nat. Mater. 13(2), 139–150 (2014).
[Crossref] [PubMed]

Chang, C.

Chen, J.

S. Wang, P. Ch. Wu, V. C. Su, Y. Ch. Lai, C. Hung Chu, J. W. Chen, S. H. Lu, J. Chen, B. Xu, C. H. Kuan, T. Li, S. Zhu, and D. P. Tsai, “Broadband achromatic optical metasurface devices,” Nat. Commun. 8(1), 187 (2017).
[Crossref] [PubMed]

Chen, J. W.

S. Wang, P. Ch. Wu, V. C. Su, Y. Ch. Lai, C. Hung Chu, J. W. Chen, S. H. Lu, J. Chen, B. Xu, C. H. Kuan, T. Li, S. Zhu, and D. P. Tsai, “Broadband achromatic optical metasurface devices,” Nat. Commun. 8(1), 187 (2017).
[Crossref] [PubMed]

Chen, L.

H. Gao, Y. Li, L. Chen, J. Jin, M. Pu, X. Li, P. Gao, C. Wang, X. Luo, and M. Hong, “Quasi-Talbot effect of orbital angular momentum beams for generation of optical vortex arrays by multiplexing metasurface design,” Nanoscale 10(2), 666–671 (2018).
[Crossref] [PubMed]

Chen, W. T.

M. Khorasaninejad, W. T. Chen, R. C. Devlin, J. Oh, A. Y. Zhu, and F. Capasso, “Metalenses at visible wavelengths: Diffraction-limited focusing and subwavelength resolution imaging,” Science 352(6290), 1190–1194 (2016).
[Crossref] [PubMed]

Chen, Y. F.

Cheng, C.

Z. Li, H. Liu, H. Liu, S. Xu, L. Ma, C. Cheng, L. Wang, and L. Mingzhen, “An interferometric patchwork to generate high-order quasi-nondiffracting vortex lattices,” Opt. Commun. 368, 86–94 (2016).
[Crossref]

Cižmár, T.

K. Dholakia and T. Čižmár, “Shaping the future of manipulation,” Nat. Photonics 5(6), 335–342 (2011).
[Crossref]

Cottrell, D. M.

Davis, J. A.

Débarre, D.

N. Vuillemin, P. Mahou, D. Débarre, T. Gacoin, P. L. Tharaux, M. C. Schanne-Klein, W. Supatto, and E. Beaurepaire, “Efficient second-harmonic imaging of collagen in histological slides using Bessel beam excitation,” Sci. Rep. 6(1), 29863 (2016).
[Crossref] [PubMed]

Denz, C.

P. Rose, M. Boguslawski, and C. Denz, “Nonlinear lattice structures based on families of complex nondiffracting beams,” New J. Phys. 14(3), 033018 (2012).
[Crossref]

M. Boguslawski, P. Rose, and C. Denz, “Nondiffracting kagome lattice,” Appl. Phys. Lett. 98(6), 061111 (2011).
[Crossref]

M. Boguslawski, P. Rose, and C. Denz, “Increasing the structural variety of discrete nondiffracting wave fields,” Phys. Rev. A 84(1), 013832 (2011).
[Crossref]

Devlin, R.

Devlin, R. C.

M. Khorasaninejad, W. T. Chen, R. C. Devlin, J. Oh, A. Y. Zhu, and F. Capasso, “Metalenses at visible wavelengths: Diffraction-limited focusing and subwavelength resolution imaging,” Science 352(6290), 1190–1194 (2016).
[Crossref] [PubMed]

Dholakia, K.

K. Dholakia and T. Čižmár, “Shaping the future of manipulation,” Nat. Photonics 5(6), 335–342 (2011).
[Crossref]

M. Mazilu, D. J. Stevenson, F. Gunn-Moore, and K. Dholakia, “Light beats the spread: “non-diffracting” beams,” Laser Photonics Rev. 4(4), 529–547 (2010).
[Crossref]

V. Garcés-Chávez, D. McGloin, H. Melville, W. Sibbett, and K. Dholakia, “Simultaneous micromanipulation in multiple planes using a self-reconstructing light beam,” Nature 419(6903), 145–147 (2002).
[Crossref] [PubMed]

J. Arlt, K. Dholakia, L. Allen, and M. J. Padgett, “Efficiency of second-harmonic generation with Bessel beams,” Phys. Rev. A 60(3), 2438–2441 (1999).
[Crossref]

Di Liberto, M.

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Z. Li, H. Liu, H. Liu, S. Xu, L. Ma, C. Cheng, L. Wang, and L. Mingzhen, “An interferometric patchwork to generate high-order quasi-nondiffracting vortex lattices,” Opt. Commun. 368, 86–94 (2016).
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S. Wang, P. Ch. Wu, V. C. Su, Y. Ch. Lai, C. Hung Chu, J. W. Chen, S. H. Lu, J. Chen, B. Xu, C. H. Kuan, T. Li, S. Zhu, and D. P. Tsai, “Broadband achromatic optical metasurface devices,” Nat. Commun. 8(1), 187 (2017).
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N. Goldman, J. C. Budich, and P. Zoller, “Topological quantum matter with ultracold gases in optical lattices,” Nat. Phys. 12(7), 639–645 (2016).
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S. Keren-Zur, L. Michaeli, H. Suchowski, and T. Ellenbogen, “Shaping light with nonlinear metasurfaces,” Adv. Opt. Photonics 10(1), 309–353 (2018).
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Nanoscale (1)

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S. Wang, P. Ch. Wu, V. C. Su, Y. Ch. Lai, C. Hung Chu, J. W. Chen, S. H. Lu, J. Chen, B. Xu, C. H. Kuan, T. Li, S. Zhu, and D. P. Tsai, “Broadband achromatic optical metasurface devices,” Nat. Commun. 8(1), 187 (2017).
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N. Goldman, J. C. Budich, and P. Zoller, “Topological quantum matter with ultracold gases in optical lattices,” Nat. Phys. 12(7), 639–645 (2016).
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Nature (1)

V. Garcés-Chávez, D. McGloin, H. Melville, W. Sibbett, and K. Dholakia, “Simultaneous micromanipulation in multiple planes using a self-reconstructing light beam,” Nature 419(6903), 145–147 (2002).
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Opt. Commun. (1)

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Science (2)

N. Fläschner, B. S. Rem, M. Tarnowski, D. Vogel, D. S. Lühmann, K. Sengstock, and C. Weitenberg, “Experimental reconstruction of the Berry curvature in a Floquet Bloch band,” Science 352(6289), 1091–1094 (2016).
[Crossref] [PubMed]

M. Khorasaninejad, W. T. Chen, R. C. Devlin, J. Oh, A. Y. Zhu, and F. Capasso, “Metalenses at visible wavelengths: Diffraction-limited focusing and subwavelength resolution imaging,” Science 352(6290), 1190–1194 (2016).
[Crossref] [PubMed]

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Figures (4)

Fig. 1
Fig. 1 Schematic map of metasurface of deflection prisms. (a) N prism spots with prescribed phase profiles are placed at the vertices of regular polygons. Each prism spot imposes on its transmitted wave a phase shift and directs the wave to a target plane with a given propagation angle. (b) Each prescribed phase profile acts analogously to a combination of deflection prisms and transparent material discs. (c) Longitudinal section of a generated non-diffracting vortex lattice, i.e., at the region where all N propagating waves overlap. (d) Cross section of the generated non-diffracting vortex lattice.
Fig. 2
Fig. 2 (a) Schematic of the phase modulation principle using nano-apertures. The thickness of the gold film on the quartz substrate is 100nm. The length of each nano-aperture is L = 150μm, the width is w = 70μm, and the distance between neighboring aperture is 220μm. With an orient angle difference of α between two apertures, their transmitted waves have a phase shift of 2α for illumination of left circular polarized light. (b) Phase retardation profile for generating a non-diffracting Kagome-type vortex lattice. The diameter of each prism spot is 8μm. (c) SEM image of the fabricated metasurface corresponding to the phase profile in (b). (d) Experimental intensity pattern at the plane 16μm from the metasurface. Kagome-type lattice is generated. (e) Retrieved phase map corresponding to (d). For clear observation, the hexagonal spot unit possessing second-order vortex and the hourglass-type intensity pattern possessing two first-order vortices are marked by dashed white lines.
Fig. 3
Fig. 3 FDTD simulation of the metasurface of deflecting prisms. (a) and (b) Intensity pattern and phase map corresponding to the metasurface in the experiment. The lattice period is about 1.4μm (c) and (d) Intensity patterns in the x-z plane and y-z planes. The red dashed lines outline the nondiffracting region of the generated lattice. (e) and (f) Intensity patterns at the planes 14μm and 17μm apart from the metasurface, respectively. (g) Intensity pattern in the x-z plane with an altered illuminating wavelength 632nm. The non-diffracting region decreases whereas the lattice period remains unchanged.
Fig. 4
Fig. 4 (a) Fabricated metasurface for generating a hollow hexagonal vortex lattice. (b) and (c) Experimental intensity pattern and retrieved phase map using the above metasurface. A first-order vortex lattice is generated. (d) and (e) FDTD results using a metasurface with large prism spot number of 36.

Equations (7)

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φ( x samp,1 , y samp,1 )=k( x samp,1 d)sin θ 1 = kd( x samp,1 d) d 2 + z tar 2 ,
φ( x samp,n , y samp,n )= kd[ x samp,n 2 + y samp,n 2 cos( ϕ samp,n ϕ n )d] d 2 + z tar 2 ,
ψ n ˜ exp[i( k t cos ϕ n + k t sin ϕ n + k z )],
φ( x samp,n , y samp,n )= kd[ x samp,n 2 + y samp,n 2 cos( ϕ samp,n ϕ n )d] d 2 + z tar 2 + φ n ,
ψ n ˜ exp[i( k t cos ϕ n + k t sin ϕ n + k z + φ n )].
ψ ˜ (X,Y)= n=1 N ψ n ˜ (X,Y) n=1 N exp[ ikd(Xcos ϕ n +Ysin ϕ n + φ n ) d 2 + z tar 2 ] .
= 2 3 λ 0 d 2 + z tar 2 3d .

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