Abstract

We numerically study the optical properties of metal-insulator-metal resonators and metasurfaces, emphasizing the presence of gap-surface plasmon (GSP) resonances and their connection to the optical response. In relation to birefringent metal-backed metasurfaces, we show how a combination of metal nanobrick and nanocross elements allows one to fully control the phase of reflected light for two orthogonal polarizations simultaneously. The approach is exemplified by the design of a gradient birefringent metasurface that reflects two orthogonal polarization states into +2 and −3 diffraction order, respectively, with a reflectivity up to ∼ 80% and in a broad wavelength range around the design wavelength of 800 nm. Finally, we introduce the concept of metascatterers, which are wavelength-sized polarization-sensitive scatterers.

© 2013 OSA

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    [CrossRef] [PubMed]
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    [CrossRef]
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  51. G. Lévêque and O. J. F. Martin, “Tunable composite nanoparticle for plasmonics,” Opt. Lett.31, 2750–2752 (2006).
    [CrossRef] [PubMed]
  52. J. Jung, T. Søndergaard, and S. I. Bozhevolnyi, “Gap plasmon-polariton nanoresonators: scattering enhancement and launching of surface plasmon polaritons,” Phys. Rev. B79, 035401 (2009).
    [CrossRef]
  53. M. G. Nielsen, D. K. Gramotnev, A. Pors, O. Albrektsen, and S. I. Bozhevolnyi, “Continuous layer gap plasmon resonators,” Opt. Express19, 19310–19322 (2011).
    [CrossRef] [PubMed]
  54. M. Bozzi, S. Germani, and L. Perregrini, “A figure of merit for losses in printed reflectarray elements,” IEEE Antennas Wirel. Propag. Lett.3, 257–260 (2004).
    [CrossRef]
  55. S. Larouche and D. R. Smith, “Reconciliation of generalized refraction with diffraction theory,” Opt. Lett.37, 2391–2393 (2012).
    [CrossRef] [PubMed]
  56. A. Pors, I. Tsukerman, and S. I. Bozhevolnyi, “Effective constitutive parameters of plasmonic metamaterials: homogenization by dual field interpolation,” Phys. Rev. E84, 016609 (2011).
    [CrossRef]
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2013

X. Chen, L. Huang, H. Mühlenbernd, G. Li, B. Bai, Q. Tan, G. Jin, C.-W. Qiu, T. Zentgraf, and S. Zhang, “Reversible three-dimensional focusing of visible light with ultrathin plasmonic flat lens,” Adv. Optical Mater.1, 517–521 (2013).
[CrossRef]

L. Huang, X. Chen, B. Bai, Q. Tan, G. Jin, T. Zentgraf, and S. Zhang, “Helicity dependent directional surface plasmon polariton excitation using a metasurface with interfacial phase discontinuity,” Light: Sci. Applications2, e70 (2013).
[CrossRef]

F. Monticone, N. M. Estakhri, and A. Alú, “Full control of nanoscale optical transmission with a composite metascreen,” Phys. Rev. Lett.110, 203903 (2013).
[CrossRef]

A. Pors, M. G. Nielsen, R. L. Eriksen, and S. I. Bozhevolnyi, “Broadband focusing flat mirrors based on plasmonic gradient metasurfaces,” Nano Lett.13, 829–834 (2013).
[CrossRef] [PubMed]

C. Qu, S. Xiao, S. Sun, Q. He, and L. Zhou, “A theoretical study on the conversion efficiencies of gradient meta-surfaces,” Europhys. Lett.101, 54002 (2013).
[CrossRef]

A. Pors, O. Albrektsen, I. P. Radko, and S. I. Bozhevolnyi, “Gap-plasmon-based metasurfaces for total control of reflected light,” Sci. Rep.3, 2155 (2013).
[CrossRef]

J. Lin, J. P. B. Mueller, Q. Wang, G. Yuan, N. Antoniou, X.-C. Yuan, and F. Capasso, “Polarization-controlled tunable directional coupling of surface plasmon polaritons,” Science340, 331–334 (2013).
[CrossRef] [PubMed]

P.-C. Li and E. T. Yu, “Wide-angle wavelength-selective multilayer optical metasurfaces robust to interlayer misalignment,” J. Opt. Soc. Am. B30, 27–32 (2013).
[CrossRef]

A. Pors and S. I. Bozhevolnyi, “Efficient and broadband quarter-wave plates by gap-plasmon resonators,” Opt. Express21, 2942–2952 (2013).
[CrossRef] [PubMed]

M. Farmahini-Farahani and H. Mosallaei, “Birefringent reflectarray metasurface for beam engineering in infrared,” Opt. Lett.38, 462–464 (2013).
[CrossRef] [PubMed]

A. Pors, M. G. Nielsen, and S. I. Bozhevolnyi, “Broadband plasmonic half-wave plates in reflection,” Opt. Lett.38, 513–515 (2013).
[CrossRef] [PubMed]

2012

D. K. Gramotnev, A. Pors, M. Willatzen, and S. I. Bozhevolnyi, “Gap-plasmon nanoantennas and bowtie resonators,” Phys. Rev. B85, 045434 (2012).
[CrossRef]

E. Kallos, I. Chremmos, and V. Yannopapas, “Resonance properties of optical all-dielectric metamaterials using two-dimensional multipole expansion,” Phys. Rev. B86, 245108 (2012).
[CrossRef]

A. Roberts and L. Lin, “Plasmonic quarter-wave plate,” Opt. Lett.37, 1820–1822 (2012).
[CrossRef] [PubMed]

M. G. Nielsen, A. Pors, O. Albrektsen, and S. I. Bozhevolnyi, “Efficient absorption of visible radiation by gap plasmon resonators,” Opt. Express20, 13311–13319 (2012).
[CrossRef] [PubMed]

S. Larouche and D. R. Smith, “Reconciliation of generalized refraction with diffraction theory,” Opt. Lett.37, 2391–2393 (2012).
[CrossRef] [PubMed]

X. Li, S. Xiao, B. Cai, Q. He, T. J. Cui, and L. Zhou, “Flat metasurfaces to focus electromagnetic waves in reflection geometry,” Opt. Lett.37, 4940–4942 (2012).
[CrossRef] [PubMed]

S. Sun, K.-Y. Yang, C.-M. Wang, T.-K. Juan, W. T. Chen, C. Y. Liao, Q. He, S. Xiao, W.-T. Kung, G.-Y. Guo, L. Zhou, and D. P. Tsai, “High-efficiency broadband anomalous reflection by gradient meta-surfaces,” Nano Lett.12, 6223–6229 (2012).
[CrossRef] [PubMed]

S. Sun, Q. He, S. Xiao, Q. Xu, X. Li, and L. Zhou, “Gradient-index meta-surfaces as a bridge linking propagating waves and surface waves,” Nat. Mater.11, 426–431 (2012).
[CrossRef] [PubMed]

X. Ni, N. K. Emani, A. V. Kildishev, A. Boltasseva, and V. M. Shalaev, “Broadband light bending with plasmonic nanoantennas,” Science335, 427 (2012).
[CrossRef]

F. Aieta, P. Genevet, N. Yu, M. A. Kats, Z. Gaburro, and F. Capasso, “Out-of-plane reflection and refraction of light by anisotropic optical antennas metasurfaces with phase discontinuities,” Nano Lett.12, 1702–1706 (2012).
[CrossRef] [PubMed]

F. Aieta, P. Genevet, M. A. Kats, N. Yu, R. Blanchard, Z. Gaburro, and F. Capasso, “Aberration-free ultrathin flat lenses and axicons at telecom wavelengths based on plasmonic metasurfaces,” Nano Lett.12, 4932–4936 (2012).
[CrossRef] [PubMed]

N. Yu, F. Aieta, P. Genevet, M. A. Kats, Z. Gaburro, and F. Capasso, “A broadband, background-free quarter-wave plate based on plasmonic metasurfaces,” Nano Lett.12, 6328–6333 (2012).
[CrossRef] [PubMed]

X. Chen, L. Huang, H. Mühlenbernd, G. Li, B. Bai, Q. Tan, G. Jin, C.-W. Qiu, S. Zhang, and T. Zentgraf, “Dual-polarity plasmonic metalens for visible light,” Nat. Commun.3, 1198 (2012).
[CrossRef] [PubMed]

O. Hess, J. B. Pendry, S. A. Maier, R. F. Oulton, J. M. Hamm, and K. L. Tsakmakidis, “Active nanoplasmonic metamaterials,” Nat. Mater.11, 573–584 (2012).
[CrossRef] [PubMed]

2011

Y. Zhao, N. Engheta, and A. Alú, “Homogenization of plasmonic metasurfaces modeled as transmission-line loads,” Metamaterials5, 90–96 (2011).
[CrossRef]

N. Yu, P. Genevet, M. A. Kats, F. Aieta, J.-P. Tetienne, F. Capasso, and Z. Gaburro, “Light propagation with phase discontinuities: generalized laws of reflection and refraction,” Science334, 333–337 (2011).
[CrossRef] [PubMed]

Y. Zhao and A. Alú, “Manipulating light polarization with ultrathin plasmonic metasurfaces,” Phys. Rev. B84, 205428 (2011).
[CrossRef]

P.-C. Li, Y. Zhao, A. Alú, and E. T. Yua, “Experimental realization and modeling of a subwavelength frequency- selective plasmonic metasurface,” Appl. Phys. Lett.99, 221106 (2011).
[CrossRef]

K. Aydin, V. E. Ferry, R. M. Briggs, and H. A. Atwater, “Broadband polarization-independent resonant light absorption using ultrathin plasmonic super absorbers,” Nat. Commun.2, 1–7 (2011).
[CrossRef]

A. Pors, M. G. Nielsen, G. D. Valle, M. Willatzen, O. Albrektsen, and S. I. Bozhevolnyi, “Plasmonic metamaterial wave retarders in reflection by orthogonally oriented detuned electrical dipoles,” Opt. Lett.36, 1626–1628 (2011).
[CrossRef] [PubMed]

M. G. Nielsen, D. K. Gramotnev, A. Pors, O. Albrektsen, and S. I. Bozhevolnyi, “Continuous layer gap plasmon resonators,” Opt. Express19, 19310–19322 (2011).
[CrossRef] [PubMed]

A. Pors, I. Tsukerman, and S. I. Bozhevolnyi, “Effective constitutive parameters of plasmonic metamaterials: homogenization by dual field interpolation,” Phys. Rev. E84, 016609 (2011).
[CrossRef]

2010

N. Liu, M. Mesch, T. Weiss, M. Hentschel, and H. Giessen, “Infrared perfect absorber and its application as plasmonic sensor,” Nano Lett.10, 2342–2348 (2010).
[CrossRef] [PubMed]

J. Hao, J. Wang, X. Liu, W. J. Padilla, L. Zhou, and M. Qiu, “High performance optical absorber based on a plasmonic matematerial,” Appl. Phys. Lett.96, 251104 (2010).
[CrossRef]

L. Lin, X. M. Goh, L. P. McGuinness, and A. Roberts, “Plasmonic lenses formed by two-dimensional nanometric cross-shaped aperture arrays for fresnel-region focusing,” Nano Lett.10, 1936–1940 (2010).
[CrossRef] [PubMed]

2009

J. Hao, Q. Ren, Z. An, X. Huang, Z. Chen, M. Qiu, and L. Zhou, “Optical metamaterial for polarization control,” Phys. Rev. A80, 023807 (2009).
[CrossRef]

J. Jung, T. Søndergaard, and S. I. Bozhevolnyi, “Gap plasmon-polariton nanoresonators: scattering enhancement and launching of surface plasmon polaritons,” Phys. Rev. B79, 035401 (2009).
[CrossRef]

2008

T. Søndergaard, J. Jung, S. I. Bozhevolnyi, and G. Della Valle, “Theoretical analysis of gold nano-strip gap plasmon resonators,” New J. Phys.10, 105008 (2008).
[CrossRef]

T. Søndergaard and S. I. Bozhevolnyi, “Strip and gap plasmon polariton optical resonators,” Phys. Stat. Sol. B245, 9–19 (2008).
[CrossRef]

2007

2006

G. Lévêque and O. J. F. Martin, “Tunable composite nanoparticle for plasmonics,” Opt. Lett.31, 2750–2752 (2006).
[CrossRef] [PubMed]

H. T. Miyazaki and Y. Kurokawa, “Squeezing visible light waves into a 3-nm-thick and 55-nm-long plasmon cavity,” Phys. Rev. Lett.96, 097401 (2006).
[CrossRef] [PubMed]

J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science312, 1780–1782 (2006).
[CrossRef] [PubMed]

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, “Metamaterial electromagnetic cloak at microwave frequencies,” Science314, 977–980 (2006).
[CrossRef] [PubMed]

2005

N. Engheta, A. Salandrino, and A. Alú, “Circuit elements at optical frequencies: Nanoinductors, nanocapacitors, and nanoresistors,” Phys. Rev. Lett.95, 095504 (2005).
[CrossRef] [PubMed]

N. Fang, H. Lee, C. Sun, and X. Zhang, “Subdiffraction-limited optical imaging with a silver superlens,” Science308, 534–537 (2005).
[CrossRef] [PubMed]

2004

D. R. Solli and J. M. Hickmann, “Photonic crystal based polarization control devices,” J. Phys. D: Appl. Phys.37, R263–R268 (2004).
[CrossRef]

M. Bozzi, S. Germani, and L. Perregrini, “A figure of merit for losses in printed reflectarray elements,” IEEE Antennas Wirel. Propag. Lett.3, 257–260 (2004).
[CrossRef]

2001

R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental verification of a negative index of refraction,” Science292, 77–79 (2001).
[CrossRef] [PubMed]

2000

J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett.85, 3966–3969 (2000).
[CrossRef] [PubMed]

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, “Composite medium with simultaneously negative permeability and permittivity,” Phys. Rev. Lett.84, 4184–4187 (2000).
[CrossRef] [PubMed]

1997

D. M. Pozar, S. D. Targonski, and H. D. Syrigos, “Design of millimeter wave microstrip reflectarrays,” IEEE Trans. Antennas Propag.45, 287–296 (1997).
[CrossRef]

1972

P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B6, 4370–4379 (1972).
[CrossRef]

Aieta, F.

N. Yu, F. Aieta, P. Genevet, M. A. Kats, Z. Gaburro, and F. Capasso, “A broadband, background-free quarter-wave plate based on plasmonic metasurfaces,” Nano Lett.12, 6328–6333 (2012).
[CrossRef] [PubMed]

F. Aieta, P. Genevet, M. A. Kats, N. Yu, R. Blanchard, Z. Gaburro, and F. Capasso, “Aberration-free ultrathin flat lenses and axicons at telecom wavelengths based on plasmonic metasurfaces,” Nano Lett.12, 4932–4936 (2012).
[CrossRef] [PubMed]

F. Aieta, P. Genevet, N. Yu, M. A. Kats, Z. Gaburro, and F. Capasso, “Out-of-plane reflection and refraction of light by anisotropic optical antennas metasurfaces with phase discontinuities,” Nano Lett.12, 1702–1706 (2012).
[CrossRef] [PubMed]

N. Yu, P. Genevet, M. A. Kats, F. Aieta, J.-P. Tetienne, F. Capasso, and Z. Gaburro, “Light propagation with phase discontinuities: generalized laws of reflection and refraction,” Science334, 333–337 (2011).
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F. Aieta, P. Genevet, N. Yu, M. A. Kats, Z. Gaburro, and F. Capasso, “Out-of-plane reflection and refraction of light by anisotropic optical antennas metasurfaces with phase discontinuities,” Nano Lett.12, 1702–1706 (2012).
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N. Yu, P. Genevet, M. A. Kats, F. Aieta, J.-P. Tetienne, F. Capasso, and Z. Gaburro, “Light propagation with phase discontinuities: generalized laws of reflection and refraction,” Science334, 333–337 (2011).
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L. Huang, X. Chen, B. Bai, Q. Tan, G. Jin, T. Zentgraf, and S. Zhang, “Helicity dependent directional surface plasmon polariton excitation using a metasurface with interfacial phase discontinuity,” Light: Sci. Applications2, e70 (2013).
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J. Hao, Q. Ren, Z. An, X. Huang, Z. Chen, M. Qiu, and L. Zhou, “Optical metamaterial for polarization control,” Phys. Rev. A80, 023807 (2009).
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A. Pors, M. G. Nielsen, R. L. Eriksen, and S. I. Bozhevolnyi, “Broadband focusing flat mirrors based on plasmonic gradient metasurfaces,” Nano Lett.13, 829–834 (2013).
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F. Monticone, N. M. Estakhri, and A. Alú, “Full control of nanoscale optical transmission with a composite metascreen,” Phys. Rev. Lett.110, 203903 (2013).
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K. Aydin, V. E. Ferry, R. M. Briggs, and H. A. Atwater, “Broadband polarization-independent resonant light absorption using ultrathin plasmonic super absorbers,” Nat. Commun.2, 1–7 (2011).
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F. Aieta, P. Genevet, N. Yu, M. A. Kats, Z. Gaburro, and F. Capasso, “Out-of-plane reflection and refraction of light by anisotropic optical antennas metasurfaces with phase discontinuities,” Nano Lett.12, 1702–1706 (2012).
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N. Yu, F. Aieta, P. Genevet, M. A. Kats, Z. Gaburro, and F. Capasso, “A broadband, background-free quarter-wave plate based on plasmonic metasurfaces,” Nano Lett.12, 6328–6333 (2012).
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F. Aieta, P. Genevet, M. A. Kats, N. Yu, R. Blanchard, Z. Gaburro, and F. Capasso, “Aberration-free ultrathin flat lenses and axicons at telecom wavelengths based on plasmonic metasurfaces,” Nano Lett.12, 4932–4936 (2012).
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N. Yu, P. Genevet, M. A. Kats, F. Aieta, J.-P. Tetienne, F. Capasso, and Z. Gaburro, “Light propagation with phase discontinuities: generalized laws of reflection and refraction,” Science334, 333–337 (2011).
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S. Sun, K.-Y. Yang, C.-M. Wang, T.-K. Juan, W. T. Chen, C. Y. Liao, Q. He, S. Xiao, W.-T. Kung, G.-Y. Guo, L. Zhou, and D. P. Tsai, “High-efficiency broadband anomalous reflection by gradient meta-surfaces,” Nano Lett.12, 6223–6229 (2012).
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X. Chen, L. Huang, H. Mühlenbernd, G. Li, B. Bai, Q. Tan, G. Jin, C.-W. Qiu, T. Zentgraf, and S. Zhang, “Reversible three-dimensional focusing of visible light with ultrathin plasmonic flat lens,” Adv. Optical Mater.1, 517–521 (2013).
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X. Chen, L. Huang, H. Mühlenbernd, G. Li, B. Bai, Q. Tan, G. Jin, C.-W. Qiu, T. Zentgraf, and S. Zhang, “Reversible three-dimensional focusing of visible light with ultrathin plasmonic flat lens,” Adv. Optical Mater.1, 517–521 (2013).
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L. Huang, X. Chen, B. Bai, Q. Tan, G. Jin, T. Zentgraf, and S. Zhang, “Helicity dependent directional surface plasmon polariton excitation using a metasurface with interfacial phase discontinuity,” Light: Sci. Applications2, e70 (2013).
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S. Sun, K.-Y. Yang, C.-M. Wang, T.-K. Juan, W. T. Chen, C. Y. Liao, Q. He, S. Xiao, W.-T. Kung, G.-Y. Guo, L. Zhou, and D. P. Tsai, “High-efficiency broadband anomalous reflection by gradient meta-surfaces,” Nano Lett.12, 6223–6229 (2012).
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J. Jung, T. Søndergaard, and S. I. Bozhevolnyi, “Gap plasmon-polariton nanoresonators: scattering enhancement and launching of surface plasmon polaritons,” Phys. Rev. B79, 035401 (2009).
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D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, “Metamaterial electromagnetic cloak at microwave frequencies,” Science314, 977–980 (2006).
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E. Kallos, I. Chremmos, and V. Yannopapas, “Resonance properties of optical all-dielectric metamaterials using two-dimensional multipole expansion,” Phys. Rev. B86, 245108 (2012).
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N. Yu, F. Aieta, P. Genevet, M. A. Kats, Z. Gaburro, and F. Capasso, “A broadband, background-free quarter-wave plate based on plasmonic metasurfaces,” Nano Lett.12, 6328–6333 (2012).
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Figures (7)

Fig. 1
Fig. 1

(a) Sketch of a two-dimensional gold-SiO2-gold resonator surrounded by air. The incident field is TM-polarized and propagates along the y-axis. (b) Scattering and absorption cross sections (CS) normalized to the width w of the gold strips for three different combinations of w and d. The strip thickness is fixed at t = 30 nm.

Fig. 2
Fig. 2

(a,b) Contribution to the scattering cross section (SCS) from the lowest order multi-poles (ED=electric dipole, MD=magnetic dipole, EQ=electric quadrupole). SCS is normalized with the resonator width w, and t = 30 nm [see Fig. 1(a)]. Note that in order to compare the relative contributions to the scattering from MD and EQ, we choose the center of mass as the coordinate origin. (c,d) Electric field enhancement at the ED mode (λ = 585 nm) and GSP mode (λ = 800 nm). The color bars are chosen as to emphasize the mode profiles rather than the high electrostatic field enhancement at the corners. Arrows indicate the direction of polarization current at a representative moment of time.

Fig. 3
Fig. 3

(a,b) Scattering, absorption, and SPP cross sections normalized to the width w of the gold strip for normal incident TM-polarized light. The Insets show the configurations and dimensions of the GSP resonators. (c,d) Electric field enhancement at the GSP mode for the configurations in a) and b), respectively. The color bars are chosen as to visualize the mode profiles rather than the high electrostatic field enhancement at the corners. Arrows indicate the direction of polarization current at a representative moment of time.

Fig. 4
Fig. 4

(a) Sketch of 1D-periodic GSP-based metasurface. The incident field is TM-polarized and propagates normal to the surface. (b) Amplitude and phase of reflected light from metasurface in a) as a function of strip width w when λ = 800 nm, Λ = 260 nm, d = 50 nm, and t = 30 nm. The time convention is exp(−iωt). (c) Color maps show electric field enhancement within one unit cell of the metasurface for three different widths of the strips. Arrows represent the strength and direction of Poynting’s vector of the reflected light in the air and spacer region.

Fig. 5
Fig. 5

(a) Sketch of unit cell of nanobrick metasurface. (b) Calculated reflection coefficient r as a function of nanobrick widths for Λ = 240 nm, d = t = 50 nm, and λ = 800 nm. Color map shows the reflection coefficient amplitude for TM polarization, while lines are contours of the reflection phase for both TM and TE polarization. Note that the reflection amplitude map for TE polarization can be obtained by mirroring the map for TM polarization along the line Lx = Ly. (c) Sketch of unit cell of nanocross metasurface. (d) Reflection coefficient as a function of nanocross arm lengths (Lx and Ly) for two values of w. The other parameters are as in b).

Fig. 6
Fig. 6

(a) Super cell of gradient birefringent metasurface functioning as a polarization beam splitter: TM (TE) waves are reflected into +2 (−3) diffraction order. (b,c) Theoretical performance of the metasurface for TM polarization, displaying b) the x-component of the reflected E-field ( E x r) just above the metasurface at the design wavelength (the amplitude of the incident E-field is 1 V/m), and c) amount of incident light reflected into the |m| ≤ 3 diffraction orders as a function of wavelength. (d,e) Performance of the metasurface for TE polarization.

Fig. 7
Fig. 7

(a,b) Calculated reflection coefficient r as a function of Lx and Ly for nanobrick and nanocross (w = 50 nm) metasurfaces, respectively. The parameters are Λ = 240 nm, d = t = 50 nm, and λ = 800 nm [see, e.g., Figs. 5(a) and 5(c)]. Color map shows the reflection coefficient amplitude for TM polarization, while lines are contours of the reflection phase for both TM and TE polarization. Note that the reflection amplitude map for TE polarization can be obtained by mirroring the map for TM polarization along the line Lx = Ly. (c) Top-view of metascatterer functioning as wavelength-sized polarization beam splitter: TM and TE waves are scattered into orthogonal directions. (d) Normalized Poynting’s vector of reflected/scattered light evaluated on a hemispherical surface with radius 1.6 μm centered at the metascatterer. The incident wave is a TM or TE polarized Gaussian beam with beam radius w0 = 800 nm propagating normal to the surface. The power flow is displayed in spherical coordinates, where the polar angle θ (measured from the z-axis) is represented by the radial distance, whereas the azimuthal angle ϕ (counted in the xy-plane from the x-axis) is displayed in the figure plane with the x-axis being horizontal.

Equations (1)

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w k 0 n g s p + ϕ = p π ,

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