Abstract

We investigate Huygens’ optical vector wave field synthesis scheme for electric dipole metasurfaces with the capability of modulating in-plane polarization and complex amplitude and discuss the practical issues involved in realizing multi-modulation metasurfaces. The proposed Huygens’ vector wave field synthesis scheme identifies the vector Airy disk as a synthetic unit element and creates a designed vector optical field by integrating polarization-controlled and complex-modulated Airy disks. The metasurface structure for the proposed vector field synthesis is analyzed in terms of the signal-to-noise ratio of the synthesized field distribution. The design of practical metasurface structures with true vector modulation capability is possible through the analysis of the light field modulation characteristics of various complex modulated geometric phase metasurfaces. It is shown that the regularization of meta-atoms is a key factor that needs to be considered in field synthesis, given that it is essential for a wide range of optical field synthetic applications, including holographic displays, microscopy, and optical lithography.

© 2018 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]

2018 (1)

G.-Y. Lee, G. Yoon, S.-Y. Lee, H. Yun, J. Cho, K. Lee, H. Kim, J. Rho, and B. Lee, “Complete amplitude and phase control of light using broadband holographic metasurfaces,” Nanoscale 10(9), 4237–4245 (2018).
[Crossref] [PubMed]

2017 (11)

M. Khorasaninejad, Z. Shi, A. Y. Zhu, W. T. Chen, V. Sanjeev, A. Zaidi, and F. Capasso, “Achromatic metalens over 60 nm bandwidth in the visible and metalens with reverse chromatic dispersion,” Nano Lett. 17(3), 1819–1824 (2017).
[Crossref] [PubMed]

Y. Tsur, I. Epstein, R. Remez, and A. Arie, “Wavefront shaping of plasmonic beams by selective coupling,” ACS Photonics 4(6), 1339–1343 (2017).
[Crossref]

W. T. Chen, M. Khorasaninejad, A. Y. Zhu, J. Oh, R. C. Devlin, A. Zaidi, and F. Capasso, “Generation of wavelength-independent subwavelength Bessel beams using metasurfaces,” Light Sci. Appl. 6(5), e16259 (2017).
[Crossref]

B. Groever, W. T. Chen, and F. Capasso, “Meta-lens doublet in the visible region,” Nano Lett. 17(8), 4902–4907 (2017).
[Crossref] [PubMed]

A. Arbabi, E. Arbabi, Y. Horie, S. M. Kamali, and A. Faraon, “Planar metasurface retroreflector,” Nat. Photonics 11(7), 415–420 (2017).
[Crossref]

Z. Yue, G. Xue, J. Liu, Y. Wang, and M. Gu, “Nanometric holograms based on a topological insulator material,” Nat. Commun. 8, 15354 (2017).
[Crossref] [PubMed]

J. P. Balthasar Mueller, N. A. Rubin, R. C. Devlin, B. Groever, and F. Capasso, “Metasurface polarization optics: independent phase control of arbitrary orthogonal states of polarization,” Phys. Rev. Lett. 118(11), 113901 (2017).
[Crossref] [PubMed]

F. Yue, X. Zang, D. Wen, Z. Li, C. Zhang, H. Liu, B. D. Gerardot, W. Wang, G. Zheng, and X. Chen, “Geometric phase generated optical illusion,” Sci. Rep. 7(1), 11440 (2017).
[Crossref] [PubMed]

D. Wen, F. Yue, C. Zhang, X. Zang, H. Liu, W. Wang, and X. Chen, “Plasmonic metasurface for optical rotation,” Appl. Phys. Lett. 111(2), 023102 (2017).
[Crossref]

D. G. Baranov, D. A. Zuev, S. I. Lepeshov, O. V. Kotov, A. E. Krasnok, A. B. Evlyukhin, and B. N. Chichkov, “All-dielectric nanophotonics: the quest for better materials and fabrication techniques,” Optica 4(7), 814–825 (2017).
[Crossref]

H. Park, J. Kim, Y. Jeon, B. Lee, and H. Kim, “Regularized Huygens’ plasmonic wave field synthesis using a metal-clad plasmonic waveguide array,” Opt. Lett. 42(18), 3610–3613 (2017).
[Crossref] [PubMed]

2016 (8)

E. Arbabi, A. Arbabi, S. M. Kamali, Y. Horie, and A. Faraon, “High efficiency double-wavelength dielectric metasurface lenses with dichroic birefringent meta-atoms,” Opt. Express 24(16), 18468–18477 (2016).
[Crossref] [PubMed]

R. C. Devlin, M. Khorasaninejad, W. T. Chen, J. Oh, and F. Capasso, “Broadband high-efficiency dielectric metasurfaces for the visible spectrum,” Proc. Natl. Acad. Sci. U.S.A. 113(38), 10473–10478 (2016).
[Crossref] [PubMed]

H. T. Chen, A. J. Taylor, and N. Yu, “A review of metasurfaces: physics and applications,” Rep. Prog. Phys. 79(7), 076401 (2016).
[Crossref] [PubMed]

M. Khorasaninejad, A. Y. Zhu, C. Roques-Carmes, W. T. Chen, J. Oh, I. Mishra, R. C. Devlin, and F. Capasso, “Polarization-insensitive metalenses at visible wavelengths,” Nano Lett. 16(11), 7229–7234 (2016).
[Crossref] [PubMed]

D. Lin, A. L. Holsteen, E. Maguid, G. Wetzstein, P. G. Kik, E. Hasman, and M. L. Brongersma, “Photonic multitasking interleaved Si nanoantenna phased array,” Nano Lett. 16(12), 7671–7676 (2016).
[Crossref] [PubMed]

E.-Y. Song, S.-Y. Lee, J. Hong, K. Lee, Y. Lee, G.-Y. Lee, H. Kim, and B. Lee, “A double-lined metasurface for plasmonic complex-field generation,” Laser Photonics Rev. 10(2), 299–306 (2016).
[Crossref]

J. Chen, L. Li, T. Li, and S. N. Zhu, “Indefinite plasmonic beam engineering by in-plane holography,” Sci. Rep. 6(1), 28926 (2016).
[Crossref] [PubMed]

F. Yue, D. Wen, J. Xin, B. D. Gerardot, J. Li, and X. Chen, “Vector vortex beam generation with a single plasmonic metasurface,” ACS Photonics 3(9), 1558–1563 (2016).
[Crossref]

2015 (4)

F. Aieta, M. A. Kats, P. Genevet, and F. Capasso, “Multiwavelength achromatic metasurfaces by dispersive phase compensation,” Science 347(6228), 1342–1345 (2015).
[Crossref] [PubMed]

X. Li, H. Ren, X. Chen, J. Liu, Q. Li, C. Li, G. Xue, J. Jia, L. Cao, A. Sahu, B. Hu, Y. Wang, G. Jin, and M. Gu, “Athermally photoreduced graphene oxides for three-dimensional holographic images,” Nat. Commun. 6(1), 6984 (2015).
[Crossref] [PubMed]

G. Zheng, H. Mühlenbernd, M. Kenney, G. Li, T. Zentgraf, and S. Zhang, “Metasurface holograms reaching 80% efficiency,” Nat. Nanotechnol. 10(4), 308–312 (2015).
[Crossref] [PubMed]

S.-Y. Lee, K. Kim, S.-J. Kim, H. Park, K.-Y. Kim, and B. Lee, “Plasmonic meta-slit: shaping and controlling near-field focus,” Optica 2(1), 6–13 (2015).
[Crossref]

2014 (1)

M. Khorasaninejad and K. B. Crozier, “Silicon nanofin grating as a miniature chirality-distinguishing beam-splitter,” Nat. Commun. 5, 5386 (2014).
[Crossref] [PubMed]

2011 (2)

2009 (1)

Q. Zhan, “Cylindrical vector beams: from mathematical concepts to applications,” Adv. Opt. Photonics 1(1), 1–57 (2009).
[Crossref]

2007 (3)

2003 (1)

R. Dorn, S. Quabis, and G. Leuchs, “The focus of light—linear polarization breaks the rotational symmetry of the focal spot,” J. Mod. Opt. 50(12), 1917–1926 (2003).

2002 (1)

J. W. Chon, X. Gan, and M. Gu, “Splitting of the focal spot of a high numerical-aperture objective in free space,” Appl. Phys. Lett. 81(9), 1576–1578 (2002).
[Crossref]

2001 (1)

1997 (1)

C. J. R. Sheppard and P. Török, “Efficient calculation of electromagnetic diffraction in optical systems using a multipole expansion,” J. Mod. Opt. 44(4), 803–818 (1997).
[Crossref]

1996 (1)

1995 (1)

Z. Bouchal and M. Olivík, “Non-diffractive vector Bessel beams,” J. Mod. Opt. 42(8), 1555–1566 (1995).
[Crossref]

1993 (1)

R. Kant, “An analytical solution of vector diffraction for focusing optical systems,” J. Mod. Opt. 40(2), 337–347 (1993).
[Crossref]

1959 (2)

B. Richards and E. Wolf, “Electromagnetic diffraction in optical systems I. An integral representation of the image field,” Proc. R. Soc. Lond. A Math. Phys. Sci. 253(1274), 349–357 (1959).
[Crossref]

B. Richards and E. Wolf, “Electromagnetic diffraction in optical systems II. Structure of the image field in an aplanatic system,” Proc. R. Soc. Lond. A Math. Phys. Sci. 253(1274), 358–379 (1959).
[Crossref]

Aieta, F.

F. Aieta, M. A. Kats, P. Genevet, and F. Capasso, “Multiwavelength achromatic metasurfaces by dispersive phase compensation,” Science 347(6228), 1342–1345 (2015).
[Crossref] [PubMed]

Anokhov, S. P.

April, A.

Arbabi, A.

Arbabi, E.

Arie, A.

Y. Tsur, I. Epstein, R. Remez, and A. Arie, “Wavefront shaping of plasmonic beams by selective coupling,” ACS Photonics 4(6), 1339–1343 (2017).
[Crossref]

Balthasar Mueller, J. P.

J. P. Balthasar Mueller, N. A. Rubin, R. C. Devlin, B. Groever, and F. Capasso, “Metasurface polarization optics: independent phase control of arbitrary orthogonal states of polarization,” Phys. Rev. Lett. 118(11), 113901 (2017).
[Crossref] [PubMed]

Baranov, D. G.

Bouchal, Z.

Z. Bouchal and M. Olivík, “Non-diffractive vector Bessel beams,” J. Mod. Opt. 42(8), 1555–1566 (1995).
[Crossref]

Brongersma, M. L.

D. Lin, A. L. Holsteen, E. Maguid, G. Wetzstein, P. G. Kik, E. Hasman, and M. L. Brongersma, “Photonic multitasking interleaved Si nanoantenna phased array,” Nano Lett. 16(12), 7671–7676 (2016).
[Crossref] [PubMed]

Cao, G. W.

Cao, L.

X. Li, H. Ren, X. Chen, J. Liu, Q. Li, C. Li, G. Xue, J. Jia, L. Cao, A. Sahu, B. Hu, Y. Wang, G. Jin, and M. Gu, “Athermally photoreduced graphene oxides for three-dimensional holographic images,” Nat. Commun. 6(1), 6984 (2015).
[Crossref] [PubMed]

Capasso, F.

W. T. Chen, M. Khorasaninejad, A. Y. Zhu, J. Oh, R. C. Devlin, A. Zaidi, and F. Capasso, “Generation of wavelength-independent subwavelength Bessel beams using metasurfaces,” Light Sci. Appl. 6(5), e16259 (2017).
[Crossref]

B. Groever, W. T. Chen, and F. Capasso, “Meta-lens doublet in the visible region,” Nano Lett. 17(8), 4902–4907 (2017).
[Crossref] [PubMed]

J. P. Balthasar Mueller, N. A. Rubin, R. C. Devlin, B. Groever, and F. Capasso, “Metasurface polarization optics: independent phase control of arbitrary orthogonal states of polarization,” Phys. Rev. Lett. 118(11), 113901 (2017).
[Crossref] [PubMed]

M. Khorasaninejad, Z. Shi, A. Y. Zhu, W. T. Chen, V. Sanjeev, A. Zaidi, and F. Capasso, “Achromatic metalens over 60 nm bandwidth in the visible and metalens with reverse chromatic dispersion,” Nano Lett. 17(3), 1819–1824 (2017).
[Crossref] [PubMed]

R. C. Devlin, M. Khorasaninejad, W. T. Chen, J. Oh, and F. Capasso, “Broadband high-efficiency dielectric metasurfaces for the visible spectrum,” Proc. Natl. Acad. Sci. U.S.A. 113(38), 10473–10478 (2016).
[Crossref] [PubMed]

M. Khorasaninejad, A. Y. Zhu, C. Roques-Carmes, W. T. Chen, J. Oh, I. Mishra, R. C. Devlin, and F. Capasso, “Polarization-insensitive metalenses at visible wavelengths,” Nano Lett. 16(11), 7229–7234 (2016).
[Crossref] [PubMed]

F. Aieta, M. A. Kats, P. Genevet, and F. Capasso, “Multiwavelength achromatic metasurfaces by dispersive phase compensation,” Science 347(6228), 1342–1345 (2015).
[Crossref] [PubMed]

Chen, H. T.

H. T. Chen, A. J. Taylor, and N. Yu, “A review of metasurfaces: physics and applications,” Rep. Prog. Phys. 79(7), 076401 (2016).
[Crossref] [PubMed]

Chen, J.

J. Chen, L. Li, T. Li, and S. N. Zhu, “Indefinite plasmonic beam engineering by in-plane holography,” Sci. Rep. 6(1), 28926 (2016).
[Crossref] [PubMed]

Chen, W. T.

W. T. Chen, M. Khorasaninejad, A. Y. Zhu, J. Oh, R. C. Devlin, A. Zaidi, and F. Capasso, “Generation of wavelength-independent subwavelength Bessel beams using metasurfaces,” Light Sci. Appl. 6(5), e16259 (2017).
[Crossref]

M. Khorasaninejad, Z. Shi, A. Y. Zhu, W. T. Chen, V. Sanjeev, A. Zaidi, and F. Capasso, “Achromatic metalens over 60 nm bandwidth in the visible and metalens with reverse chromatic dispersion,” Nano Lett. 17(3), 1819–1824 (2017).
[Crossref] [PubMed]

B. Groever, W. T. Chen, and F. Capasso, “Meta-lens doublet in the visible region,” Nano Lett. 17(8), 4902–4907 (2017).
[Crossref] [PubMed]

M. Khorasaninejad, A. Y. Zhu, C. Roques-Carmes, W. T. Chen, J. Oh, I. Mishra, R. C. Devlin, and F. Capasso, “Polarization-insensitive metalenses at visible wavelengths,” Nano Lett. 16(11), 7229–7234 (2016).
[Crossref] [PubMed]

R. C. Devlin, M. Khorasaninejad, W. T. Chen, J. Oh, and F. Capasso, “Broadband high-efficiency dielectric metasurfaces for the visible spectrum,” Proc. Natl. Acad. Sci. U.S.A. 113(38), 10473–10478 (2016).
[Crossref] [PubMed]

Chen, X.

D. Wen, F. Yue, C. Zhang, X. Zang, H. Liu, W. Wang, and X. Chen, “Plasmonic metasurface for optical rotation,” Appl. Phys. Lett. 111(2), 023102 (2017).
[Crossref]

F. Yue, X. Zang, D. Wen, Z. Li, C. Zhang, H. Liu, B. D. Gerardot, W. Wang, G. Zheng, and X. Chen, “Geometric phase generated optical illusion,” Sci. Rep. 7(1), 11440 (2017).
[Crossref] [PubMed]

F. Yue, D. Wen, J. Xin, B. D. Gerardot, J. Li, and X. Chen, “Vector vortex beam generation with a single plasmonic metasurface,” ACS Photonics 3(9), 1558–1563 (2016).
[Crossref]

X. Li, H. Ren, X. Chen, J. Liu, Q. Li, C. Li, G. Xue, J. Jia, L. Cao, A. Sahu, B. Hu, Y. Wang, G. Jin, and M. Gu, “Athermally photoreduced graphene oxides for three-dimensional holographic images,” Nat. Commun. 6(1), 6984 (2015).
[Crossref] [PubMed]

Chichkov, B. N.

Cho, J.

G.-Y. Lee, G. Yoon, S.-Y. Lee, H. Yun, J. Cho, K. Lee, H. Kim, J. Rho, and B. Lee, “Complete amplitude and phase control of light using broadband holographic metasurfaces,” Nanoscale 10(9), 4237–4245 (2018).
[Crossref] [PubMed]

Chon, J. W.

J. W. Chon, X. Gan, and M. Gu, “Splitting of the focal spot of a high numerical-aperture objective in free space,” Appl. Phys. Lett. 81(9), 1576–1578 (2002).
[Crossref]

Crozier, K. B.

M. Khorasaninejad and K. B. Crozier, “Silicon nanofin grating as a miniature chirality-distinguishing beam-splitter,” Nat. Commun. 5, 5386 (2014).
[Crossref] [PubMed]

Devlin, R. C.

J. P. Balthasar Mueller, N. A. Rubin, R. C. Devlin, B. Groever, and F. Capasso, “Metasurface polarization optics: independent phase control of arbitrary orthogonal states of polarization,” Phys. Rev. Lett. 118(11), 113901 (2017).
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[Crossref]

F. Yue, D. Wen, J. Xin, B. D. Gerardot, J. Li, and X. Chen, “Vector vortex beam generation with a single plasmonic metasurface,” ACS Photonics 3(9), 1558–1563 (2016).
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Z. Yue, G. Xue, J. Liu, Y. Wang, and M. Gu, “Nanometric holograms based on a topological insulator material,” Nat. Commun. 8, 15354 (2017).
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G.-Y. Lee, G. Yoon, S.-Y. Lee, H. Yun, J. Cho, K. Lee, H. Kim, J. Rho, and B. Lee, “Complete amplitude and phase control of light using broadband holographic metasurfaces,” Nanoscale 10(9), 4237–4245 (2018).
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D. Wen, F. Yue, C. Zhang, X. Zang, H. Liu, W. Wang, and X. Chen, “Plasmonic metasurface for optical rotation,” Appl. Phys. Lett. 111(2), 023102 (2017).
[Crossref]

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G. Zheng, H. Mühlenbernd, M. Kenney, G. Li, T. Zentgraf, and S. Zhang, “Metasurface holograms reaching 80% efficiency,” Nat. Nanotechnol. 10(4), 308–312 (2015).
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[Crossref]

F. Yue, X. Zang, D. Wen, Z. Li, C. Zhang, H. Liu, B. D. Gerardot, W. Wang, G. Zheng, and X. Chen, “Geometric phase generated optical illusion,” Sci. Rep. 7(1), 11440 (2017).
[Crossref] [PubMed]

Zhang, S.

G. Zheng, H. Mühlenbernd, M. Kenney, G. Li, T. Zentgraf, and S. Zhang, “Metasurface holograms reaching 80% efficiency,” Nat. Nanotechnol. 10(4), 308–312 (2015).
[Crossref] [PubMed]

Zhang, X. B.

Zheng, G.

F. Yue, X. Zang, D. Wen, Z. Li, C. Zhang, H. Liu, B. D. Gerardot, W. Wang, G. Zheng, and X. Chen, “Geometric phase generated optical illusion,” Sci. Rep. 7(1), 11440 (2017).
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[Crossref] [PubMed]

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M. Khorasaninejad, Z. Shi, A. Y. Zhu, W. T. Chen, V. Sanjeev, A. Zaidi, and F. Capasso, “Achromatic metalens over 60 nm bandwidth in the visible and metalens with reverse chromatic dispersion,” Nano Lett. 17(3), 1819–1824 (2017).
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J. Chen, L. Li, T. Li, and S. N. Zhu, “Indefinite plasmonic beam engineering by in-plane holography,” Sci. Rep. 6(1), 28926 (2016).
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F. Yue, X. Zang, D. Wen, Z. Li, C. Zhang, H. Liu, B. D. Gerardot, W. Wang, G. Zheng, and X. Chen, “Geometric phase generated optical illusion,” Sci. Rep. 7(1), 11440 (2017).
[Crossref] [PubMed]

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Figures (6)

Fig. 1
Fig. 1 (a) A schematic of an electric dipole metasurface (EDM) with subwavelength-sized dielectric rods on a flat substrate. (b) Illustration of the derivation of the electric dipole moment density of the EDM generating an x-polarized Airy disk pattern. The dipole moment densities, p ρ and p ϕ , in the infinitesimal area d S r correspond to the angular spectral components of the x-polarized Airy disk E ρ and E ϕ on the output plane, respectively.
Fig. 2
Fig. 2 Comparison between EDM distributions generating the amplitude of normalized Airy disk 2 J 1 (NA k 0 ρ)/[NA k 0 ρ], with NA=sin(75°)=0.966,focal length z 0 =5um, and wavenumber k 0 =2π/( 1um ), and the reconstructed field distributions of an EDM for an x-polarized Airy disk (left column) and an EDM with a nullified p y (right column). Upper row: plots of the amplitude distributions of the EDM. Middle row: generated electric field distributions on the focal plane. Lower row: electric field distributions on the y=0 plane showing the focusing characteristics in three dimensions.
Fig. 3
Fig. 3 Schematics for the (a) sampling and (b) reconstruction scheme for a Bessel-Gauss beam with topological charge m=2. The transverse electric field on the z= z 0 plane is sampled at the sampling grid points, with a sampling period that satisfies the Nyquist rate of the wavefront of the beam. The transverse electric field for the Bessel-Gauss beam is always linear. The linearly polarized Airy disks, whose numerical aperture is defined by the sampling period Λ, are superposed to reconstruct the Bessel-Gauss beam. (c) Schematic of the wavefronts of the Bessel-Gauss beam. (d) Generation of the Bessel-Gauss beam via the EDM by sampling the transverse electric field on the focal plane z= z 0 =20um. The amplitude distributions of p RCP and p LCP of the EDM (upper row) that generate the Bessel-Gauss beam with the parameters m=2, w 0 =2λ=2um, and β=0.3 k 0 =1884 mm 1 . Plots of the amplitude distributions of E RCP , E LCP , E z , and E of the Bessel-Gauss beam on the focal plane (lower row) and the distribution of the polarization of the transverse electric field on the focal plane, and amplitude distributions of the transverse electric field at z=5,10,15,20,25,30 and 35um(lower row).
Fig. 4
Fig. 4 z 0 SNRsemi-log plot (center) for various NAs and focal lengths for EDMs. Four intensity profiles (the four corners of the figure) of the residual fields, which represent the difference between E x generated by the EDM and the Airy disk on the focal plane. The sidelobes of the Airy disk are properly reconstructed when z 0 and NA are large enough. The peak intensity of the residual field is also greatly suppressed.
Fig. 5
Fig. 5 (a) Schematic for hologram generation. EDM at z=0 illuminated by an LCP plane wave along the + z-axis is derived by the superposition of sampled Airy disk units on the image plane z= z 0 . (b) Plots of the target image, the electric dipole distribution of the EDM, and the corresponding field distributions on the image plane. The wavelength λ=1um. The PSNR is 76.81. (The trademark of Seoul National University was used with permission from Seoul National University R&DB foundation. All rights reserved, used with permission)
Fig. 6
Fig. 6 Schematics of the meta-molecules for a DGPM, QGPM, and XAM (left-most panel). Amplitude distribution of the E RCP for the unit RCP Airy disks via the DGPM, QGPM, and XAM on the focal plane z= z 0 =5um and on the y=0um plane (left panel). The three metasurfaces have the NA=sin75°=0.966 and the wavelength λ=1um. The holograms of the same target image in Fig. 5 are generated via the conventional metasurfaces DGPM, QGPM and XAM, respectively, at the focal plane z 0 =5um(right-most panel). The corresponding structural parameters θ 1 and θ 2 are presented in the third panel.

Equations (12)

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E tan ( k x , k y )= F xy { z ^ ×( E (ρ,θ, z 0 )× z ^ )}= 1 k ρ NA k 0 x ^ ,
E = G p =[1+ ] e i k 0 | r r | 4π ϵ 0 | r r | p e i k 0 | r r | 4π ϵ 0 | r r | 3 (| r r | 2 I ( r r )( r r )) p .
[ E TM ( r ) E TE ( r ) ]= 1 ϵ 0 e i k 0 | r r | 4π| r r | [ z/| r r | 0 0 1 ][ p ρ p ϕ ].
[ ε ρ ( k ) ε ϕ ( k ) ]| d S r d S k |[ E ΤΜ ( r 0 )cosθ E ΤΕ ( r 0 ) ]= | r 0 r ' |e i k 0 | r 0 r ' | 0 4π [ p ρ p ϕ /cosθ ].
[ p ρ p ϕ ] e i k 0 | r 0 r | | r 0 r | [ E ρ E ϕ cos 2 θ ]= e i k 0 | r 0 r | | r 0 r | [ cosϕ cos 2 θsinϕ ] 1 θψ .
[ p x p y ]=[ cosϕ sinϕ sinϕ cosϕ ][ p ρ p ϕ ] e i k 0 | r 0 r | | r 0 r | [ cos 2 ϕ+ cos 2 θ sin 2 ϕ sin 2 θsinϕcosϕ ] 1 θψ .
E gen ( r ) x 2 +y 2 z 0 2 tan 2 ψ dxdy e i k 0 | r r | | r r | 3 e i k 0 | r 0 r | | r 0 r | × [ (rr) 2 (xx) 2 (yy)(xx) (zz)(xx) (xx)(yy) (rr) 2 (yy) 2 (zz)(yy) (xx)(zz) (yy)(zz) (rr) 2 (zz) 2 ][ cos 2 ϕ+ cos 2 θ sin 2 ϕ sin 2 θsinϕcosϕ 0 ].
E x =NA k 0 J 1 (NA k 0 ρ) 2πρ ,
SNR= [ |α J 1 (NA k 0 ρ)/ρ | 2 dxdy ]/ [ (| E x α J 1 (NA k 0 ρ)/ρ | 2 +| E y | 2 )dxdy ] ,
{ E x (ρ,θ)=cos(mθ)exp( ρ 2 / w 0 2 ) J m (βρ) E y (ρ,θ)=sin(mθ)exp( ρ 2 / w 0 2 ) J m (βρ) ,
{ θ 1 θ 2 = cos 1 ηA θ 1 + θ 2 =ϕ ,
SNR RCP = [ |α J 1 (NA k 0 ρ)/ρ | 2 dxdy ]/ [ (| E RCP α J 1 (NA k 0 ρ)/ρ | 2 )dxdy ] ,

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