Abstract

We review the current trends in the design of Huygens’ metasurfaces (HMSs), which are planar arrays of balanced electric and magnetic polarizable particles (meta-atoms) of subwavelength size. We focus on schemes that follow the equivalence principle, as these can be rigorously incorporated into Maxwell’s equations, leading to design specifications in the form of (electric and magnetic) surface-impedance distributions. The advantages of this approach with respect to the more common phase-shift stipulation approach are highlighted and discussed. We present a (microscopic) methodology to associate a general meta-atom configuration with an equivalent surface impedance, and derive metasurface (macroscopic) design procedures for various beam forming applications. The methods and concepts developed in the paper provide the basic tools for understanding and designing scalar, passive, and lossless HMSs, and we indicate possible extensions applicable to more complex structures.

© 2016 Optical Society of America

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2015 (25)

C. Pfeiffer and A. Grbic, “Generating stable tractor beams with dielectric metasurfaces,” Phys. Rev. B 91, 115408 (2015).
[Crossref]

Y. Ra’di, C. R. Simovski, and S. A. Tretyakov, “Thin perfect absorbers for electromagnetic waves: theory, design, and realizations,” Phys. Rev. Appl. 3, 037001 (2015).
[Crossref]

V. Asadchy, Y. Ra’di, J. Vehmas, and S. Tretyakov, “Functional metamirrors using bianisotropic elements,” Phys. Rev. Lett. 114, 095503 (2015).
[Crossref]

V. S. Asadchy, I. A. Faniayeu, Y. Ra’di, S. A. Khakhomov, I. V. Semchenko, and S. A. Tretyakov, “Broadband reflectionless metasheets: frequency-selective transmission and perfect absorption,” Phys. Rev. X 5, 031005 (2015).

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

F. Ding, Z. Wang, S. He, V. M. Shalaev, and A. V. Kildishev, “Broadband high-efficiency half-wave plate: a supercell-based plasmonic metasurface approach,” ACS Nano 9, 4111–4119 (2015).
[Crossref]

G. Spektor, A. David, B. Gjonaj, G. Bartal, and M. Orenstein, “Metafocusing by a metaspiral plasmonic lens,” Nano Lett. 15, 5739–5743 (2015).
[Crossref]

S. A. Tretyakov, “Metasurfaces for general transformations of electromagnetic fields,” Philos. Trans. R. Soc. A 373, 20140362 (2015).

S. L. Jia, X. Wan, X. J. Fu, Y. J. Zhao, and T. J. Cui, “Low-reflection beam refractions by ultrathin Huygens metasurface,” AIP Adv. 5, 067102 (2015).
[Crossref]

M. Decker, I. Staude, M. Falkner, J. Dominguez, D. N. Neshev, I. Brener, T. Pertsch, and Y. S. Kivshar, “High-efficiency dielectric Huygens’ surfaces,” Adv. Opt. Mater. 3, 813–820 (2015).
[Crossref]

K. E. Chong, I. Staude, A. James, J. Dominguez, S. Liu, S. Campione, G. S. Subramania, T. S. Luk, M. Decker, D. N. Neshev, I. Brener, and Y. S. Kivshar, “Polarization-independent silicon metadevices for efficient optical wavefront control,” Nano Lett. 15, 5369–5374 (2015), PMID: 26192100.
[Crossref]

K. Chen, Z. Yang, Y. Feng, B. Zhu, J. Zhao, and T. Jiang, “Improving microwave antenna gain and bandwidth with phase compensation metasurface,” AIP Adv. 5, 067152 (2015).
[Crossref]

S. L. Jia, X. Wan, D. Bao, Y. J. Zhao, and T. J. Cui, “Independent controls of orthogonally polarized transmitted waves using a Huygens metasurface,” Laser Photon. Rev. 9, 545–553 (2015).
[Crossref]

Y. F. Yu, A. Y. Zhu, R. Paniagua-Domínguez, Y. H. Fu, B. Luk’yanchuk, and A. I. Kuznetsov, “High-transmission dielectric metasurface with 2π phase control at visible wavelengths,” Laser Photon. Rev. 9, 412–418 (2015).
[Crossref]

M. I. Shalaev, J. Sun, A. Tsukernik, A. Pandey, K. Nikolskiy, and N. M. Litchinitser, “High-efficiency all-dielectric metasurfaces for ultracompact beam manipulation in transmission mode,” Nano Lett. 15, 6261–6266 (2015).
[Crossref]

G. Minatti, M. Faenzi, E. Martini, F. Caminita, P. De Vita, D. Gonzalez-Ovejero, M. Sabbadini, and S. Maci, “Modulated metasurface antennas for space: synthesis, analysis and realizations,” IEEE Trans. Antennas Propag. 63, 1288–1300 (2015).
[Crossref]

A. I. Dimitriadis, N. V. Kantartzis, T. D. Tsiboukis, and C. Hafner, “Generalized non-local surface susceptibility model and Fresnel coefficients for the characterization of periodic metafilms with bianisotropic scatterers,” J. Comput. Phys. 281, 251–268 (2015).
[Crossref]

M. Yazdi, M. Albooyeh, R. Alaee, V. Asadchy, N. Komjani, C. Rockstuhl, C. Simovski, and S. Tretyakov, “A bianisotropic metasurface with resonant asymmetric absorption,” IEEE Trans. Antennas Propag. 63, 3004–3015 (2015).
[Crossref]

R. Alaee, M. Albooyeh, M. Yazdi, N. Komjani, C. Simovski, F. Lederer, and C. Rockstuhl, “Magnetoelectric coupling in nonidentical plasmonic nanoparticles: theory and applications,” Phys. Rev. B 91, 115119 (2015).
[Crossref]

J. P. S. Wong, M. Selvanayagam, and G. V. Eleftheriades, “Polarization considerations for scalar Huygens metasurfaces and characterization for 2-D refraction,” IEEE Trans. Microwave Theor. Tech. 63, 913–924 (2015).
[Crossref]

P. P. Iyer, N. A. Butakov, and J. A. Schuller, “Reconfigurable semiconductor phased-array metasurfaces,” ACS Photon. 2, 1077–1084 (2015).
[Crossref]

J. Sautter, I. Staude, M. Decker, E. Rusak, D. N. Neshev, I. Brener, and Y. S. Kivshar, “Active tuning of all-dielectric metasurfaces,” ACS Nano 9, 4308–4315 (2015).
[Crossref]

G. Oliveri, D. Werner, and A. Massa, “Reconfigurable electromagnetics through metamaterials—a review,” Proc. IEEE 103, 1034–1056 (2015).
[Crossref]

S. Campione, L. I. Basilio, L. K. Warne, and M. B. Sinclair, “Tailoring dielectric resonator geometries for directional scattering and Huygens’ metasurfaces,” Opt. Express 23, 2293–2307 (2015).
[Crossref]

C. M. Roberts, S. Inampudi, and V. A. Podolskiy, “Diffractive interface theory: nonlocal susceptibility approach to the optics of metasurfaces,” Opt. Express 23, 2764–2776 (2015).
[Crossref]

2014 (18)

S. Abadi and N. Behdad, “Design of wideband, FSS-based multibeam antennas using the effective medium approach,” IEEE Trans. Antennas Propag. 62, 5557–5564 (2014).
[Crossref]

J. Luo, H. Yu, M. Song, and Z. Zhang, “Highly efficient wavefront manipulation in terahertz based on plasmonic gradient metasurfaces,” Opt. Lett. 39, 2229–2231 (2014).
[Crossref]

J. Cheng and H. Mosallaei, “Optical metasurfaces for beam scanning in space,” Opt. Lett. 39, 2719–2722 (2014).
[Crossref]

A. Epstein and G. V. Eleftheriades, “Passive lossless Huygens metasurfaces for conversion of arbitrary source field to directive radiation,” IEEE Trans. Antennas Propag. 62, 5680–5695 (2014).
[Crossref]

A. Epstein and G. V. Eleftheriades, “Floquet–Bloch analysis of refracting Huygens metasurfaces,” Phys. Rev. B 90, 235127 (2014).
[Crossref]

V. S. Asadchy, I. A. Faniayeu, Y. Ra’di, and S. A. Tretyakov, “Determining polarizability tensors for an arbitrary small electromagnetic scatterer,” Photon. Nanostruct. 12, 298–304 (2014).
[Crossref]

C. Pfeiffer, C. Zhang, V. Ray, L. J. Guo, and A. Grbic, “High performance bianisotropic metasurfaces: asymmetric transmission of light,” Phys. Rev. Lett. 113, 023902 (2014).
[Crossref]

B. O. Zhu, K. Chen, N. Jia, L. Sun, J. Zhao, T. Jiang, and Y. Feng, “Dynamic control of electromagnetic wave propagation with the equivalent principle inspired tunable metasurface,” Sci. Rep. 4, 4971 (2014).
[Crossref]

C. Pfeiffer, N. K. Emani, A. M. Shaltout, A. Boltasseva, V. M. Shalaev, and A. Grbic, “Efficient light bending with isotropic metamaterial Huygens’ surfaces,” Nano Lett. 14, 2491–2497 (2014).

N. Mohammadi Estakhri and A. Alù, “Manipulating optical reflections using engineered nanoscale metasurfaces,” Phys. Rev. B 89, 235419 (2014).
[Crossref]

J. P. S. Wong, M. Selvanayagam, and G. V. Eleftheriades, “Design of unit cells and demonstration of methods for synthesizing Huygens metasurfaces,” Photon. Nanostruct. 12, 360–375 (2014).
[Crossref]

M. Kim, A. M. H. Wong, and G. V. Eleftheriades, “Optical Huygens’ metasurfaces with independent control of the magnitude and phase of the local reflection coefficients,” Phys. Rev. X 4, 041042 (2014).

Y. Ra’di, V. S. Asadchy, and S. a. Tretyakov, “One-way transparent sheets,” Phys. Rev. B 89, 075109 (2014).
[Crossref]

M. Selvanayagam and G. V. Eleftheriades, “Polarization control using tensor Huygens surfaces,” IEEE Trans. Antennas Propag. 62, 6155–6168 (2014).
[Crossref]

D. Lin, P. Fan, E. Hasman, and M. L. Brongersma, “Dielectric gradient metasurface optical elements,” Science 345, 298–302 (2014).
[Crossref]

C. Pfeiffer and A. Grbic, “Controlling vector Bessel beams with metasurfaces,” Phys. Rev. Appl. 2, 044012 (2014).
[Crossref]

C. Pfeiffer and A. Grbic, “Bianisotropic metasurfaces for optimal polarization control: analysis and synthesis,” Phys. Rev. Appl. 2, 044011 (2014).
[Crossref]

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

2013 (10)

A. V. Kildishev, A. Boltasseva, and V. M. Shalaev, “Planar photonics with metasurfaces,” Science 339, 1232009 (2013).

M. Selvanayagam and G. V. Eleftheriades, “Circuit modelling of Huygens surfaces,” IEEE Antennas Wireless Propag. Lett. 12, 1642–1645 (2013).
[Crossref]

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

C. Pfeiffer and A. Grbic, “Millimeter-wave transmitarrays for wavefront and polarization control,” IEEE Trans. Microwave Theor. Tech. 61, 4407–4417 (2013).
[Crossref]

Y. Ra’di and S. A. Tretyakov, “Balanced and optimal bianisotropic particles: maximizing power extracted from electromagnetic fields,” New J. Phys. 15, 053008 (2013).
[Crossref]

T. Niemi, A. O. Karilainen, and S. A. Tretyakov, “Synthesis of polarization transformers,” IEEE Trans. Antennas Propag. 61, 3102–3111 (2013).
[Crossref]

M. Selvanayagam and G. V. Eleftheriades, “Experimental demonstration of active electromagnetic cloaking,” Phys. Rev. X 3, 041011 (2013).

C. Pfeiffer and A. Grbic, “Metamaterial Huygens’ surfaces: tailoring wave fronts with reflectionless sheets,” Phys. Rev. Lett. 110, 197401 (2013).
[Crossref]

P. E. Sieber and D. H. Werner, “Reconfigurable broadband infrared circularly polarizing reflectors based on phase changing birefringent metasurfaces,” Opt. Express 21, 1087–1100 (2013).
[Crossref]

M. Selvanayagam and G. V. Eleftheriades, “Discontinuous electromagnetic fields using orthogonal electric and magnetic currents for wavefront manipulation,” Opt. Express 21, 14409–14429 (2013).
[Crossref]

2012 (2)

Y. Zhao, M. A. Belkin, and A. Alù, “Twisted optical metamaterials for planarized ultrathin broadband circular polarizers,” Nat. Commun. 3, 870 (2012).
[Crossref]

C. L. Holloway, E. F. Kuester, J. A. Gordon, J. O’Hara, J. Booth, and D. R. Smith, “An overview of the theory and applications of metasurfaces: the two-dimensional equivalents of metamaterials,” IEEE Antennas Propag. Mag. 54(2), 10–35 (2012).
[Crossref]

2011 (5)

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,” Science 334, 333–337 (2011).
[Crossref]

S. Maci, G. Minatti, M. Casaletti, and M. Bosiljevac, “Metasurfing: addressing waves on impenetrable metasurfaces,” IEEE Antennas Wireless Propag. Lett. 10, 1499–1502 (2011).
[Crossref]

J. Y. Ou, E. Plum, L. Jiang, and N. I. Zheludev, “Reconfigurable photonic metamaterials,” Nano Lett. 11, 2142–2144 (2011).
[Crossref]

G. Minatti, F. Caminita, M. Casaletti, and S. Maci, “Spiral leaky-wave antennas based on modulated surface impedance,” IEEE Trans. Antennas Propag. 59, 4436–4444 (2011).
[Crossref]

A. M. Patel and A. Grbic, “A printed leaky-wave antenna based on a sinusoidally-modulated reactance surface,” IEEE Trans. Antennas Propag. 59, 2087–2096 (2011).
[Crossref]

2010 (2)

B. Fong, J. Colburn, J. Ottusch, J. Visher, and D. Sievenpiper, “Scalar and tensor holographic artificial impedance surfaces,” IEEE Trans. Antennas Propag. 58, 3212–3221 (2010).
[Crossref]

P. Jin and R. Ziolkowski, “Metamaterial-inspired, electrically small Huygens sources,” IEEE Antennas Wireless Propag. Lett. 9, 501–505 (2010).
[Crossref]

2008 (1)

O. Luukkonen, C. Simovski, G. Granet, G. Goussetis, D. Lioubtchenko, A. Raisanen, and S. Tretyakov, “Simple and accurate analytical model of planar grids and high-impedance surfaces comprising metal strips or patches,” IEEE Trans. Antennas Propag. 56, 1624–1632 (2008).
[Crossref]

2005 (3)

C. Holloway, M. Mohamed, E. F. Kuester, and A. Dienstfrey, “Reflection and transmission properties of a metafilm: with an application to a controllable surface composed of resonant particles,” IEEE Trans. Electromagn. Compat. 47, 853–865 (2005).
[Crossref]

C. Simovski, P. de Maagt, and I. Melchakova, “High-impedance surfaces having stable resonance with respect to polarization and incidence angle,” IEEE Trans. Antennas Propag. 53, 908–914 (2005).
[Crossref]

D. Sievenpiper, “Forward and backward leaky wave radiation with large effective aperture from an electronically tunable textured surface,” IEEE Trans. Antennas Propag. 53, 236–247 (2005).
[Crossref]

2003 (1)

E. Kuester, M. Mohamed, M. Piket-May, and C. Holloway, “Averaged transition conditions for electromagnetic fields at a metafilm,” IEEE Trans. Antennas Propag. 51, 2641–2651 (2003).
[Crossref]

2001 (1)

X. Wu, G. Eleftheriades, and T. van Deventer-Perkins, “Design and characterization of single- and multiple-beam mm-wave circularly polarized substrate lens antennas for wireless communications,” IEEE Trans. Microwave Theor. Tech. 49, 431–441 (2001).
[Crossref]

1997 (1)

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]

1976 (1)

A. Love, “Some highlights in reflector antenna development,” Radio Sci. 11, 671–684 (1976).
[Crossref]

Abadi, S.

S. Abadi and N. Behdad, “Design of wideband, FSS-based multibeam antennas using the effective medium approach,” IEEE Trans. Antennas Propag. 62, 5557–5564 (2014).
[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]

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,” Science 334, 333–337 (2011).
[Crossref]

Alaee, R.

M. Yazdi, M. Albooyeh, R. Alaee, V. Asadchy, N. Komjani, C. Rockstuhl, C. Simovski, and S. Tretyakov, “A bianisotropic metasurface with resonant asymmetric absorption,” IEEE Trans. Antennas Propag. 63, 3004–3015 (2015).
[Crossref]

R. Alaee, M. Albooyeh, M. Yazdi, N. Komjani, C. Simovski, F. Lederer, and C. Rockstuhl, “Magnetoelectric coupling in nonidentical plasmonic nanoparticles: theory and applications,” Phys. Rev. B 91, 115119 (2015).
[Crossref]

Albooyeh, M.

R. Alaee, M. Albooyeh, M. Yazdi, N. Komjani, C. Simovski, F. Lederer, and C. Rockstuhl, “Magnetoelectric coupling in nonidentical plasmonic nanoparticles: theory and applications,” Phys. Rev. B 91, 115119 (2015).
[Crossref]

M. Yazdi, M. Albooyeh, R. Alaee, V. Asadchy, N. Komjani, C. Rockstuhl, C. Simovski, and S. Tretyakov, “A bianisotropic metasurface with resonant asymmetric absorption,” IEEE Trans. Antennas Propag. 63, 3004–3015 (2015).
[Crossref]

Alù, A.

N. Mohammadi Estakhri and A. Alù, “Manipulating optical reflections using engineered nanoscale metasurfaces,” Phys. Rev. B 89, 235419 (2014).
[Crossref]

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

Y. Zhao, M. A. Belkin, and A. Alù, “Twisted optical metamaterials for planarized ultrathin broadband circular polarizers,” Nat. Commun. 3, 870 (2012).
[Crossref]

Asadchy, V.

V. Asadchy, Y. Ra’di, J. Vehmas, and S. Tretyakov, “Functional metamirrors using bianisotropic elements,” Phys. Rev. Lett. 114, 095503 (2015).
[Crossref]

M. Yazdi, M. Albooyeh, R. Alaee, V. Asadchy, N. Komjani, C. Rockstuhl, C. Simovski, and S. Tretyakov, “A bianisotropic metasurface with resonant asymmetric absorption,” IEEE Trans. Antennas Propag. 63, 3004–3015 (2015).
[Crossref]

Asadchy, V. S.

V. S. Asadchy, I. A. Faniayeu, Y. Ra’di, S. A. Khakhomov, I. V. Semchenko, and S. A. Tretyakov, “Broadband reflectionless metasheets: frequency-selective transmission and perfect absorption,” Phys. Rev. X 5, 031005 (2015).

Y. Ra’di, V. S. Asadchy, and S. a. Tretyakov, “One-way transparent sheets,” Phys. Rev. B 89, 075109 (2014).
[Crossref]

V. S. Asadchy, I. A. Faniayeu, Y. Ra’di, and S. A. Tretyakov, “Determining polarizability tensors for an arbitrary small electromagnetic scatterer,” Photon. Nanostruct. 12, 298–304 (2014).
[Crossref]

Balanis, C.

C. Balanis, Antenna Theory: Analysis and Design (Wiley, 1997), Chap. 12.

Bao, D.

S. L. Jia, X. Wan, D. Bao, Y. J. Zhao, and T. J. Cui, “Independent controls of orthogonally polarized transmitted waves using a Huygens metasurface,” Laser Photon. Rev. 9, 545–553 (2015).
[Crossref]

Bartal, G.

G. Spektor, A. David, B. Gjonaj, G. Bartal, and M. Orenstein, “Metafocusing by a metaspiral plasmonic lens,” Nano Lett. 15, 5739–5743 (2015).
[Crossref]

Basilio, L. I.

Behdad, N.

S. Abadi and N. Behdad, “Design of wideband, FSS-based multibeam antennas using the effective medium approach,” IEEE Trans. Antennas Propag. 62, 5557–5564 (2014).
[Crossref]

Belkin, M. A.

Y. Zhao, M. A. Belkin, and A. Alù, “Twisted optical metamaterials for planarized ultrathin broadband circular polarizers,” Nat. Commun. 3, 870 (2012).
[Crossref]

Boltasseva, A.

C. Pfeiffer, N. K. Emani, A. M. Shaltout, A. Boltasseva, V. M. Shalaev, and A. Grbic, “Efficient light bending with isotropic metamaterial Huygens’ surfaces,” Nano Lett. 14, 2491–2497 (2014).

A. V. Kildishev, A. Boltasseva, and V. M. Shalaev, “Planar photonics with metasurfaces,” Science 339, 1232009 (2013).

Booth, J.

C. L. Holloway, E. F. Kuester, J. A. Gordon, J. O’Hara, J. Booth, and D. R. Smith, “An overview of the theory and applications of metasurfaces: the two-dimensional equivalents of metamaterials,” IEEE Antennas Propag. Mag. 54(2), 10–35 (2012).
[Crossref]

Born, M.

M. Born and E. Wolf, Principles of Optics (Cambridge University, 1999).

Bosiljevac, M.

S. Maci, G. Minatti, M. Casaletti, and M. Bosiljevac, “Metasurfing: addressing waves on impenetrable metasurfaces,” IEEE Antennas Wireless Propag. Lett. 10, 1499–1502 (2011).
[Crossref]

Brener, I.

J. Sautter, I. Staude, M. Decker, E. Rusak, D. N. Neshev, I. Brener, and Y. S. Kivshar, “Active tuning of all-dielectric metasurfaces,” ACS Nano 9, 4308–4315 (2015).
[Crossref]

M. Decker, I. Staude, M. Falkner, J. Dominguez, D. N. Neshev, I. Brener, T. Pertsch, and Y. S. Kivshar, “High-efficiency dielectric Huygens’ surfaces,” Adv. Opt. Mater. 3, 813–820 (2015).
[Crossref]

K. E. Chong, I. Staude, A. James, J. Dominguez, S. Liu, S. Campione, G. S. Subramania, T. S. Luk, M. Decker, D. N. Neshev, I. Brener, and Y. S. Kivshar, “Polarization-independent silicon metadevices for efficient optical wavefront control,” Nano Lett. 15, 5369–5374 (2015), PMID: 26192100.
[Crossref]

Brongersma, M. L.

D. Lin, P. Fan, E. Hasman, and M. L. Brongersma, “Dielectric gradient metasurface optical elements,” Science 345, 298–302 (2014).
[Crossref]

Butakov, N. A.

P. P. Iyer, N. A. Butakov, and J. A. Schuller, “Reconfigurable semiconductor phased-array metasurfaces,” ACS Photon. 2, 1077–1084 (2015).
[Crossref]

Caminita, F.

G. Minatti, M. Faenzi, E. Martini, F. Caminita, P. De Vita, D. Gonzalez-Ovejero, M. Sabbadini, and S. Maci, “Modulated metasurface antennas for space: synthesis, analysis and realizations,” IEEE Trans. Antennas Propag. 63, 1288–1300 (2015).
[Crossref]

G. Minatti, F. Caminita, M. Casaletti, and S. Maci, “Spiral leaky-wave antennas based on modulated surface impedance,” IEEE Trans. Antennas Propag. 59, 4436–4444 (2011).
[Crossref]

Campione, S.

S. Campione, L. I. Basilio, L. K. Warne, and M. B. Sinclair, “Tailoring dielectric resonator geometries for directional scattering and Huygens’ metasurfaces,” Opt. Express 23, 2293–2307 (2015).
[Crossref]

K. E. Chong, I. Staude, A. James, J. Dominguez, S. Liu, S. Campione, G. S. Subramania, T. S. Luk, M. Decker, D. N. Neshev, I. Brener, and Y. S. Kivshar, “Polarization-independent silicon metadevices for efficient optical wavefront control,” Nano Lett. 15, 5369–5374 (2015), PMID: 26192100.
[Crossref]

Capasso, F.

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]

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,” Science 334, 333–337 (2011).
[Crossref]

Casaletti, M.

G. Minatti, F. Caminita, M. Casaletti, and S. Maci, “Spiral leaky-wave antennas based on modulated surface impedance,” IEEE Trans. Antennas Propag. 59, 4436–4444 (2011).
[Crossref]

S. Maci, G. Minatti, M. Casaletti, and M. Bosiljevac, “Metasurfing: addressing waves on impenetrable metasurfaces,” IEEE Antennas Wireless Propag. Lett. 10, 1499–1502 (2011).
[Crossref]

Chen, K.

K. Chen, Z. Yang, Y. Feng, B. Zhu, J. Zhao, and T. Jiang, “Improving microwave antenna gain and bandwidth with phase compensation metasurface,” AIP Adv. 5, 067152 (2015).
[Crossref]

B. O. Zhu, K. Chen, N. Jia, L. Sun, J. Zhao, T. Jiang, and Y. Feng, “Dynamic control of electromagnetic wave propagation with the equivalent principle inspired tunable metasurface,” Sci. Rep. 4, 4971 (2014).
[Crossref]

Cheng, J.

Chong, K. E.

K. E. Chong, I. Staude, A. James, J. Dominguez, S. Liu, S. Campione, G. S. Subramania, T. S. Luk, M. Decker, D. N. Neshev, I. Brener, and Y. S. Kivshar, “Polarization-independent silicon metadevices for efficient optical wavefront control,” Nano Lett. 15, 5369–5374 (2015), PMID: 26192100.
[Crossref]

Colburn, J.

B. Fong, J. Colburn, J. Ottusch, J. Visher, and D. Sievenpiper, “Scalar and tensor holographic artificial impedance surfaces,” IEEE Trans. Antennas Propag. 58, 3212–3221 (2010).
[Crossref]

Cui, T. J.

S. L. Jia, X. Wan, X. J. Fu, Y. J. Zhao, and T. J. Cui, “Low-reflection beam refractions by ultrathin Huygens metasurface,” AIP Adv. 5, 067102 (2015).
[Crossref]

S. L. Jia, X. Wan, D. Bao, Y. J. Zhao, and T. J. Cui, “Independent controls of orthogonally polarized transmitted waves using a Huygens metasurface,” Laser Photon. Rev. 9, 545–553 (2015).
[Crossref]

David, A.

G. Spektor, A. David, B. Gjonaj, G. Bartal, and M. Orenstein, “Metafocusing by a metaspiral plasmonic lens,” Nano Lett. 15, 5739–5743 (2015).
[Crossref]

de Maagt, P.

C. Simovski, P. de Maagt, and I. Melchakova, “High-impedance surfaces having stable resonance with respect to polarization and incidence angle,” IEEE Trans. Antennas Propag. 53, 908–914 (2005).
[Crossref]

De Vita, P.

G. Minatti, M. Faenzi, E. Martini, F. Caminita, P. De Vita, D. Gonzalez-Ovejero, M. Sabbadini, and S. Maci, “Modulated metasurface antennas for space: synthesis, analysis and realizations,” IEEE Trans. Antennas Propag. 63, 1288–1300 (2015).
[Crossref]

Decker, M.

M. Decker, I. Staude, M. Falkner, J. Dominguez, D. N. Neshev, I. Brener, T. Pertsch, and Y. S. Kivshar, “High-efficiency dielectric Huygens’ surfaces,” Adv. Opt. Mater. 3, 813–820 (2015).
[Crossref]

J. Sautter, I. Staude, M. Decker, E. Rusak, D. N. Neshev, I. Brener, and Y. S. Kivshar, “Active tuning of all-dielectric metasurfaces,” ACS Nano 9, 4308–4315 (2015).
[Crossref]

K. E. Chong, I. Staude, A. James, J. Dominguez, S. Liu, S. Campione, G. S. Subramania, T. S. Luk, M. Decker, D. N. Neshev, I. Brener, and Y. S. Kivshar, “Polarization-independent silicon metadevices for efficient optical wavefront control,” Nano Lett. 15, 5369–5374 (2015), PMID: 26192100.
[Crossref]

Dienstfrey, A.

C. Holloway, M. Mohamed, E. F. Kuester, and A. Dienstfrey, “Reflection and transmission properties of a metafilm: with an application to a controllable surface composed of resonant particles,” IEEE Trans. Electromagn. Compat. 47, 853–865 (2005).
[Crossref]

Dimitriadis, A. I.

A. I. Dimitriadis, N. V. Kantartzis, T. D. Tsiboukis, and C. Hafner, “Generalized non-local surface susceptibility model and Fresnel coefficients for the characterization of periodic metafilms with bianisotropic scatterers,” J. Comput. Phys. 281, 251–268 (2015).
[Crossref]

Ding, F.

F. Ding, Z. Wang, S. He, V. M. Shalaev, and A. V. Kildishev, “Broadband high-efficiency half-wave plate: a supercell-based plasmonic metasurface approach,” ACS Nano 9, 4111–4119 (2015).
[Crossref]

Dominguez, J.

K. E. Chong, I. Staude, A. James, J. Dominguez, S. Liu, S. Campione, G. S. Subramania, T. S. Luk, M. Decker, D. N. Neshev, I. Brener, and Y. S. Kivshar, “Polarization-independent silicon metadevices for efficient optical wavefront control,” Nano Lett. 15, 5369–5374 (2015), PMID: 26192100.
[Crossref]

M. Decker, I. Staude, M. Falkner, J. Dominguez, D. N. Neshev, I. Brener, T. Pertsch, and Y. S. Kivshar, “High-efficiency dielectric Huygens’ surfaces,” Adv. Opt. Mater. 3, 813–820 (2015).
[Crossref]

Eleftheriades, G.

X. Wu, G. Eleftheriades, and T. van Deventer-Perkins, “Design and characterization of single- and multiple-beam mm-wave circularly polarized substrate lens antennas for wireless communications,” IEEE Trans. Microwave Theor. Tech. 49, 431–441 (2001).
[Crossref]

Eleftheriades, G. V.

J. P. S. Wong, M. Selvanayagam, and G. V. Eleftheriades, “Polarization considerations for scalar Huygens metasurfaces and characterization for 2-D refraction,” IEEE Trans. Microwave Theor. Tech. 63, 913–924 (2015).
[Crossref]

M. Selvanayagam and G. V. Eleftheriades, “Polarization control using tensor Huygens surfaces,” IEEE Trans. Antennas Propag. 62, 6155–6168 (2014).
[Crossref]

A. Epstein and G. V. Eleftheriades, “Floquet–Bloch analysis of refracting Huygens metasurfaces,” Phys. Rev. B 90, 235127 (2014).
[Crossref]

J. P. S. Wong, M. Selvanayagam, and G. V. Eleftheriades, “Design of unit cells and demonstration of methods for synthesizing Huygens metasurfaces,” Photon. Nanostruct. 12, 360–375 (2014).
[Crossref]

M. Kim, A. M. H. Wong, and G. V. Eleftheriades, “Optical Huygens’ metasurfaces with independent control of the magnitude and phase of the local reflection coefficients,” Phys. Rev. X 4, 041042 (2014).

A. Epstein and G. V. Eleftheriades, “Passive lossless Huygens metasurfaces for conversion of arbitrary source field to directive radiation,” IEEE Trans. Antennas Propag. 62, 5680–5695 (2014).
[Crossref]

M. Selvanayagam and G. V. Eleftheriades, “Discontinuous electromagnetic fields using orthogonal electric and magnetic currents for wavefront manipulation,” Opt. Express 21, 14409–14429 (2013).
[Crossref]

M. Selvanayagam and G. V. Eleftheriades, “Experimental demonstration of active electromagnetic cloaking,” Phys. Rev. X 3, 041011 (2013).

M. Selvanayagam and G. V. Eleftheriades, “Circuit modelling of Huygens surfaces,” IEEE Antennas Wireless Propag. Lett. 12, 1642–1645 (2013).
[Crossref]

A. Epstein, J. P. S. Wong, and G. V. Eleftheriades, “Cavity-excited Huygens’ metasurface antennas for near-unity aperture illumination efficiency from arbitrarily large apertures,” Nat. Commun. (to be published), doi:10.1038/ncomms10360.

A. Epstein and G. V. Eleftheriades, “Ray-oriented design of Huygens metasurfaces for multiple source excitation,” in Proceedings of the IEEE International Symposium on Antennas and Propagation (APS/URSI) (2015), p. 135.

A. Epstein and G. V. Eleftheriades, “Coupling of localized sources to controlled polarized broadside radiation using Huygens’ metasurfaces,” in Proceedings of the IEEE International Symposium on Antennas and Propagation (APS/URSI) (2015), pp. 866–867.

Emani, N. K.

C. Pfeiffer, N. K. Emani, A. M. Shaltout, A. Boltasseva, V. M. Shalaev, and A. Grbic, “Efficient light bending with isotropic metamaterial Huygens’ surfaces,” Nano Lett. 14, 2491–2497 (2014).

Epstein, A.

A. Epstein and G. V. Eleftheriades, “Floquet–Bloch analysis of refracting Huygens metasurfaces,” Phys. Rev. B 90, 235127 (2014).
[Crossref]

A. Epstein and G. V. Eleftheriades, “Passive lossless Huygens metasurfaces for conversion of arbitrary source field to directive radiation,” IEEE Trans. Antennas Propag. 62, 5680–5695 (2014).
[Crossref]

A. Epstein and G. V. Eleftheriades, “Coupling of localized sources to controlled polarized broadside radiation using Huygens’ metasurfaces,” in Proceedings of the IEEE International Symposium on Antennas and Propagation (APS/URSI) (2015), pp. 866–867.

A. Epstein and G. V. Eleftheriades, “Ray-oriented design of Huygens metasurfaces for multiple source excitation,” in Proceedings of the IEEE International Symposium on Antennas and Propagation (APS/URSI) (2015), p. 135.

A. Epstein, J. P. S. Wong, and G. V. Eleftheriades, “Cavity-excited Huygens’ metasurface antennas for near-unity aperture illumination efficiency from arbitrarily large apertures,” Nat. Commun. (to be published), doi:10.1038/ncomms10360.

Estakhri, N. M.

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

Faenzi, M.

G. Minatti, M. Faenzi, E. Martini, F. Caminita, P. De Vita, D. Gonzalez-Ovejero, M. Sabbadini, and S. Maci, “Modulated metasurface antennas for space: synthesis, analysis and realizations,” IEEE Trans. Antennas Propag. 63, 1288–1300 (2015).
[Crossref]

Falkner, M.

M. Decker, I. Staude, M. Falkner, J. Dominguez, D. N. Neshev, I. Brener, T. Pertsch, and Y. S. Kivshar, “High-efficiency dielectric Huygens’ surfaces,” Adv. Opt. Mater. 3, 813–820 (2015).
[Crossref]

Fan, P.

D. Lin, P. Fan, E. Hasman, and M. L. Brongersma, “Dielectric gradient metasurface optical elements,” Science 345, 298–302 (2014).
[Crossref]

Faniayeu, I. A.

V. S. Asadchy, I. A. Faniayeu, Y. Ra’di, S. A. Khakhomov, I. V. Semchenko, and S. A. Tretyakov, “Broadband reflectionless metasheets: frequency-selective transmission and perfect absorption,” Phys. Rev. X 5, 031005 (2015).

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K. Chen, Z. Yang, Y. Feng, B. Zhu, J. Zhao, and T. Jiang, “Improving microwave antenna gain and bandwidth with phase compensation metasurface,” AIP Adv. 5, 067152 (2015).
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B. O. Zhu, K. Chen, N. Jia, L. Sun, J. Zhao, T. Jiang, and Y. Feng, “Dynamic control of electromagnetic wave propagation with the equivalent principle inspired tunable metasurface,” Sci. Rep. 4, 4971 (2014).
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B. Fong, J. Colburn, J. Ottusch, J. Visher, and D. Sievenpiper, “Scalar and tensor holographic artificial impedance surfaces,” IEEE Trans. Antennas Propag. 58, 3212–3221 (2010).
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S. L. Jia, X. Wan, X. J. Fu, Y. J. Zhao, and T. J. Cui, “Low-reflection beam refractions by ultrathin Huygens metasurface,” AIP Adv. 5, 067102 (2015).
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Y. F. Yu, A. Y. Zhu, R. Paniagua-Domínguez, Y. H. Fu, B. Luk’yanchuk, and A. I. Kuznetsov, “High-transmission dielectric metasurface with 2π phase control at visible wavelengths,” Laser Photon. Rev. 9, 412–418 (2015).
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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,” Science 334, 333–337 (2011).
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O. Luukkonen, C. Simovski, G. Granet, G. Goussetis, D. Lioubtchenko, A. Raisanen, and S. Tretyakov, “Simple and accurate analytical model of planar grids and high-impedance surfaces comprising metal strips or patches,” IEEE Trans. Antennas Propag. 56, 1624–1632 (2008).
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C. Pfeiffer and A. Grbic, “Generating stable tractor beams with dielectric metasurfaces,” Phys. Rev. B 91, 115408 (2015).
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C. Pfeiffer and A. Grbic, “Bianisotropic metasurfaces for optimal polarization control: analysis and synthesis,” Phys. Rev. Appl. 2, 044011 (2014).
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C. Pfeiffer and A. Grbic, “Controlling vector Bessel beams with metasurfaces,” Phys. Rev. Appl. 2, 044012 (2014).
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C. Pfeiffer, C. Zhang, V. Ray, L. J. Guo, and A. Grbic, “High performance bianisotropic metasurfaces: asymmetric transmission of light,” Phys. Rev. Lett. 113, 023902 (2014).
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C. Pfeiffer, N. K. Emani, A. M. Shaltout, A. Boltasseva, V. M. Shalaev, and A. Grbic, “Efficient light bending with isotropic metamaterial Huygens’ surfaces,” Nano Lett. 14, 2491–2497 (2014).

C. Pfeiffer and A. Grbic, “Metamaterial Huygens’ surfaces: tailoring wave fronts with reflectionless sheets,” Phys. Rev. Lett. 110, 197401 (2013).
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C. Pfeiffer and A. Grbic, “Millimeter-wave transmitarrays for wavefront and polarization control,” IEEE Trans. Microwave Theor. Tech. 61, 4407–4417 (2013).
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A. M. Patel and A. Grbic, “A printed leaky-wave antenna based on a sinusoidally-modulated reactance surface,” IEEE Trans. Antennas Propag. 59, 2087–2096 (2011).
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C. Pfeiffer, C. Zhang, V. Ray, L. J. Guo, and A. Grbic, “High performance bianisotropic metasurfaces: asymmetric transmission of light,” Phys. Rev. Lett. 113, 023902 (2014).
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F. Ding, Z. Wang, S. He, V. M. Shalaev, and A. V. Kildishev, “Broadband high-efficiency half-wave plate: a supercell-based plasmonic metasurface approach,” ACS Nano 9, 4111–4119 (2015).
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C. Holloway, M. Mohamed, E. F. Kuester, and A. Dienstfrey, “Reflection and transmission properties of a metafilm: with an application to a controllable surface composed of resonant particles,” IEEE Trans. Electromagn. Compat. 47, 853–865 (2005).
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E. Kuester, M. Mohamed, M. Piket-May, and C. Holloway, “Averaged transition conditions for electromagnetic fields at a metafilm,” IEEE Trans. Antennas Propag. 51, 2641–2651 (2003).
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Holloway, C. L.

C. L. Holloway, E. F. Kuester, J. A. Gordon, J. O’Hara, J. Booth, and D. R. Smith, “An overview of the theory and applications of metasurfaces: the two-dimensional equivalents of metamaterials,” IEEE Antennas Propag. Mag. 54(2), 10–35 (2012).
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B. O. Zhu, K. Chen, N. Jia, L. Sun, J. Zhao, T. Jiang, and Y. Feng, “Dynamic control of electromagnetic wave propagation with the equivalent principle inspired tunable metasurface,” Sci. Rep. 4, 4971 (2014).
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Jia, S. L.

S. L. Jia, X. Wan, X. J. Fu, Y. J. Zhao, and T. J. Cui, “Low-reflection beam refractions by ultrathin Huygens metasurface,” AIP Adv. 5, 067102 (2015).
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S. L. Jia, X. Wan, D. Bao, Y. J. Zhao, and T. J. Cui, “Independent controls of orthogonally polarized transmitted waves using a Huygens metasurface,” Laser Photon. Rev. 9, 545–553 (2015).
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J. Y. Ou, E. Plum, L. Jiang, and N. I. Zheludev, “Reconfigurable photonic metamaterials,” Nano Lett. 11, 2142–2144 (2011).
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Jiang, T.

K. Chen, Z. Yang, Y. Feng, B. Zhu, J. Zhao, and T. Jiang, “Improving microwave antenna gain and bandwidth with phase compensation metasurface,” AIP Adv. 5, 067152 (2015).
[Crossref]

B. O. Zhu, K. Chen, N. Jia, L. Sun, J. Zhao, T. Jiang, and Y. Feng, “Dynamic control of electromagnetic wave propagation with the equivalent principle inspired tunable metasurface,” Sci. Rep. 4, 4971 (2014).
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A. I. Dimitriadis, N. V. Kantartzis, T. D. Tsiboukis, and C. Hafner, “Generalized non-local surface susceptibility model and Fresnel coefficients for the characterization of periodic metafilms with bianisotropic scatterers,” J. Comput. Phys. 281, 251–268 (2015).
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T. Niemi, A. O. Karilainen, and S. A. Tretyakov, “Synthesis of polarization transformers,” IEEE Trans. Antennas Propag. 61, 3102–3111 (2013).
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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).
[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,” Science 334, 333–337 (2011).
[Crossref]

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V. S. Asadchy, I. A. Faniayeu, Y. Ra’di, S. A. Khakhomov, I. V. Semchenko, and S. A. Tretyakov, “Broadband reflectionless metasheets: frequency-selective transmission and perfect absorption,” Phys. Rev. X 5, 031005 (2015).

Kildishev, A. V.

F. Ding, Z. Wang, S. He, V. M. Shalaev, and A. V. Kildishev, “Broadband high-efficiency half-wave plate: a supercell-based plasmonic metasurface approach,” ACS Nano 9, 4111–4119 (2015).
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A. V. Kildishev, A. Boltasseva, and V. M. Shalaev, “Planar photonics with metasurfaces,” Science 339, 1232009 (2013).

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K. E. Chong, I. Staude, A. James, J. Dominguez, S. Liu, S. Campione, G. S. Subramania, T. S. Luk, M. Decker, D. N. Neshev, I. Brener, and Y. S. Kivshar, “Polarization-independent silicon metadevices for efficient optical wavefront control,” Nano Lett. 15, 5369–5374 (2015), PMID: 26192100.
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J. Sautter, I. Staude, M. Decker, E. Rusak, D. N. Neshev, I. Brener, and Y. S. Kivshar, “Active tuning of all-dielectric metasurfaces,” ACS Nano 9, 4308–4315 (2015).
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M. Decker, I. Staude, M. Falkner, J. Dominguez, D. N. Neshev, I. Brener, T. Pertsch, and Y. S. Kivshar, “High-efficiency dielectric Huygens’ surfaces,” Adv. Opt. Mater. 3, 813–820 (2015).
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C. L. Holloway, E. F. Kuester, J. A. Gordon, J. O’Hara, J. Booth, and D. R. Smith, “An overview of the theory and applications of metasurfaces: the two-dimensional equivalents of metamaterials,” IEEE Antennas Propag. Mag. 54(2), 10–35 (2012).
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C. Holloway, M. Mohamed, E. F. Kuester, and A. Dienstfrey, “Reflection and transmission properties of a metafilm: with an application to a controllable surface composed of resonant particles,” IEEE Trans. Electromagn. Compat. 47, 853–865 (2005).
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Y. F. Yu, A. Y. Zhu, R. Paniagua-Domínguez, Y. H. Fu, B. Luk’yanchuk, and A. I. Kuznetsov, “High-transmission dielectric metasurface with 2π phase control at visible wavelengths,” Laser Photon. Rev. 9, 412–418 (2015).
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D. Lin, P. Fan, E. Hasman, and M. L. Brongersma, “Dielectric gradient metasurface optical elements,” Science 345, 298–302 (2014).
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O. Luukkonen, C. Simovski, G. Granet, G. Goussetis, D. Lioubtchenko, A. Raisanen, and S. Tretyakov, “Simple and accurate analytical model of planar grids and high-impedance surfaces comprising metal strips or patches,” IEEE Trans. Antennas Propag. 56, 1624–1632 (2008).
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M. I. Shalaev, J. Sun, A. Tsukernik, A. Pandey, K. Nikolskiy, and N. M. Litchinitser, “High-efficiency all-dielectric metasurfaces for ultracompact beam manipulation in transmission mode,” Nano Lett. 15, 6261–6266 (2015).
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Y. F. Yu, A. Y. Zhu, R. Paniagua-Domínguez, Y. H. Fu, B. Luk’yanchuk, and A. I. Kuznetsov, “High-transmission dielectric metasurface with 2π phase control at visible wavelengths,” Laser Photon. Rev. 9, 412–418 (2015).
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Luukkonen, O.

O. Luukkonen, C. Simovski, G. Granet, G. Goussetis, D. Lioubtchenko, A. Raisanen, and S. Tretyakov, “Simple and accurate analytical model of planar grids and high-impedance surfaces comprising metal strips or patches,” IEEE Trans. Antennas Propag. 56, 1624–1632 (2008).
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G. Minatti, M. Faenzi, E. Martini, F. Caminita, P. De Vita, D. Gonzalez-Ovejero, M. Sabbadini, and S. Maci, “Modulated metasurface antennas for space: synthesis, analysis and realizations,” IEEE Trans. Antennas Propag. 63, 1288–1300 (2015).
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G. Minatti, F. Caminita, M. Casaletti, and S. Maci, “Spiral leaky-wave antennas based on modulated surface impedance,” IEEE Trans. Antennas Propag. 59, 4436–4444 (2011).
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S. Maci, G. Minatti, M. Casaletti, and M. Bosiljevac, “Metasurfing: addressing waves on impenetrable metasurfaces,” IEEE Antennas Wireless Propag. Lett. 10, 1499–1502 (2011).
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G. Minatti, M. Faenzi, E. Martini, F. Caminita, P. De Vita, D. Gonzalez-Ovejero, M. Sabbadini, and S. Maci, “Modulated metasurface antennas for space: synthesis, analysis and realizations,” IEEE Trans. Antennas Propag. 63, 1288–1300 (2015).
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G. Oliveri, D. Werner, and A. Massa, “Reconfigurable electromagnetics through metamaterials—a review,” Proc. IEEE 103, 1034–1056 (2015).
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G. Minatti, M. Faenzi, E. Martini, F. Caminita, P. De Vita, D. Gonzalez-Ovejero, M. Sabbadini, and S. Maci, “Modulated metasurface antennas for space: synthesis, analysis and realizations,” IEEE Trans. Antennas Propag. 63, 1288–1300 (2015).
[Crossref]

G. Minatti, F. Caminita, M. Casaletti, and S. Maci, “Spiral leaky-wave antennas based on modulated surface impedance,” IEEE Trans. Antennas Propag. 59, 4436–4444 (2011).
[Crossref]

S. Maci, G. Minatti, M. Casaletti, and M. Bosiljevac, “Metasurfing: addressing waves on impenetrable metasurfaces,” IEEE Antennas Wireless Propag. Lett. 10, 1499–1502 (2011).
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C. Holloway, M. Mohamed, E. F. Kuester, and A. Dienstfrey, “Reflection and transmission properties of a metafilm: with an application to a controllable surface composed of resonant particles,” IEEE Trans. Electromagn. Compat. 47, 853–865 (2005).
[Crossref]

E. Kuester, M. Mohamed, M. Piket-May, and C. Holloway, “Averaged transition conditions for electromagnetic fields at a metafilm,” IEEE Trans. Antennas Propag. 51, 2641–2651 (2003).
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Neshev, D. N.

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[Crossref]

J. Sautter, I. Staude, M. Decker, E. Rusak, D. N. Neshev, I. Brener, and Y. S. Kivshar, “Active tuning of all-dielectric metasurfaces,” ACS Nano 9, 4308–4315 (2015).
[Crossref]

K. E. Chong, I. Staude, A. James, J. Dominguez, S. Liu, S. Campione, G. S. Subramania, T. S. Luk, M. Decker, D. N. Neshev, I. Brener, and Y. S. Kivshar, “Polarization-independent silicon metadevices for efficient optical wavefront control,” Nano Lett. 15, 5369–5374 (2015), PMID: 26192100.
[Crossref]

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T. Niemi, A. O. Karilainen, and S. A. Tretyakov, “Synthesis of polarization transformers,” IEEE Trans. Antennas Propag. 61, 3102–3111 (2013).
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M. I. Shalaev, J. Sun, A. Tsukernik, A. Pandey, K. Nikolskiy, and N. M. Litchinitser, “High-efficiency all-dielectric metasurfaces for ultracompact beam manipulation in transmission mode,” Nano Lett. 15, 6261–6266 (2015).
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C. L. Holloway, E. F. Kuester, J. A. Gordon, J. O’Hara, J. Booth, and D. R. Smith, “An overview of the theory and applications of metasurfaces: the two-dimensional equivalents of metamaterials,” IEEE Antennas Propag. Mag. 54(2), 10–35 (2012).
[Crossref]

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G. Oliveri, D. Werner, and A. Massa, “Reconfigurable electromagnetics through metamaterials—a review,” Proc. IEEE 103, 1034–1056 (2015).
[Crossref]

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G. Spektor, A. David, B. Gjonaj, G. Bartal, and M. Orenstein, “Metafocusing by a metaspiral plasmonic lens,” Nano Lett. 15, 5739–5743 (2015).
[Crossref]

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B. Fong, J. Colburn, J. Ottusch, J. Visher, and D. Sievenpiper, “Scalar and tensor holographic artificial impedance surfaces,” IEEE Trans. Antennas Propag. 58, 3212–3221 (2010).
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J. Y. Ou, E. Plum, L. Jiang, and N. I. Zheludev, “Reconfigurable photonic metamaterials,” Nano Lett. 11, 2142–2144 (2011).
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M. I. Shalaev, J. Sun, A. Tsukernik, A. Pandey, K. Nikolskiy, and N. M. Litchinitser, “High-efficiency all-dielectric metasurfaces for ultracompact beam manipulation in transmission mode,” Nano Lett. 15, 6261–6266 (2015).
[Crossref]

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Y. F. Yu, A. Y. Zhu, R. Paniagua-Domínguez, Y. H. Fu, B. Luk’yanchuk, and A. I. Kuznetsov, “High-transmission dielectric metasurface with 2π phase control at visible wavelengths,” Laser Photon. Rev. 9, 412–418 (2015).
[Crossref]

Patel, A. M.

A. M. Patel and A. Grbic, “A printed leaky-wave antenna based on a sinusoidally-modulated reactance surface,” IEEE Trans. Antennas Propag. 59, 2087–2096 (2011).
[Crossref]

Pertsch, T.

M. Decker, I. Staude, M. Falkner, J. Dominguez, D. N. Neshev, I. Brener, T. Pertsch, and Y. S. Kivshar, “High-efficiency dielectric Huygens’ surfaces,” Adv. Opt. Mater. 3, 813–820 (2015).
[Crossref]

Pfeiffer, C.

C. Pfeiffer and A. Grbic, “Generating stable tractor beams with dielectric metasurfaces,” Phys. Rev. B 91, 115408 (2015).
[Crossref]

C. Pfeiffer and A. Grbic, “Bianisotropic metasurfaces for optimal polarization control: analysis and synthesis,” Phys. Rev. Appl. 2, 044011 (2014).
[Crossref]

C. Pfeiffer, C. Zhang, V. Ray, L. J. Guo, and A. Grbic, “High performance bianisotropic metasurfaces: asymmetric transmission of light,” Phys. Rev. Lett. 113, 023902 (2014).
[Crossref]

C. Pfeiffer, N. K. Emani, A. M. Shaltout, A. Boltasseva, V. M. Shalaev, and A. Grbic, “Efficient light bending with isotropic metamaterial Huygens’ surfaces,” Nano Lett. 14, 2491–2497 (2014).

C. Pfeiffer and A. Grbic, “Controlling vector Bessel beams with metasurfaces,” Phys. Rev. Appl. 2, 044012 (2014).
[Crossref]

C. Pfeiffer and A. Grbic, “Metamaterial Huygens’ surfaces: tailoring wave fronts with reflectionless sheets,” Phys. Rev. Lett. 110, 197401 (2013).
[Crossref]

C. Pfeiffer and A. Grbic, “Millimeter-wave transmitarrays for wavefront and polarization control,” IEEE Trans. Microwave Theor. Tech. 61, 4407–4417 (2013).
[Crossref]

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E. Kuester, M. Mohamed, M. Piket-May, and C. Holloway, “Averaged transition conditions for electromagnetic fields at a metafilm,” IEEE Trans. Antennas Propag. 51, 2641–2651 (2003).
[Crossref]

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J. Y. Ou, E. Plum, L. Jiang, and N. I. Zheludev, “Reconfigurable photonic metamaterials,” Nano Lett. 11, 2142–2144 (2011).
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ACS Nano (2)

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IEEE Antennas Propag. Mag. (1)

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Figures (21)

Fig. 1.
Fig. 1.

Physical configuration of a general sheet of polarizable particles (metasurface), characterized by an electric surface impedance Z¯¯se(x,y) and a magnetic surface admittance Y¯¯sm(x,y). The electric and magnetic currents induced on the metasurface by the averaged applied field introduce a discontinuity between the fields below and above the surface, providing a means for wavefront manipulation.

Fig. 2.
Fig. 2.

Illustration of the definition of a θ Huygens’ meta-atom (θ-HMA). When replicated to form an infinite periodic planar array, it exhibits minimal reflections for a plane wave incident with an angle of θ with respect to the z axis, while providing the ability to control the phase of the transmitted plane wave. In the illustration the incident plane wave has a transverse electric (TE) polarization (Ez=0, /x=0), and the introduced phase shift is ξout.

Fig. 3.
Fig. 3.

Various structures forming HMAs at different frequency regimes, using (a)–(c) copper, (d)–(f) plasmonic, or (g)–(i) dielectric resonators. (a) Loaded loops (formed by vias) and wires forming a HMA at f=10GHz fabricated on a PCB (reprinted from [25], Copyright 2014, with permission from Elsevier). (b) Loaded loops and wires forming a HMA at f=10GHz, avoiding vias by stacking multiple PCBs (reprinted with permission from [23], Copyright 2013 by the American Physical Society). (c) Symmetric three-layer PCB unit cell forming a HMA at f=77GHz, with magnetic dipoles formed by capacitive coupling, as schematically demonstrated (Copyright 2013 IEEE. Reprinted, with permission, from [41]). (d) Symmetric three-layer unit cell based on composite AZO–silicon plasmonic nanorods, forming a HMA at λ=3μm (reprinted with permission from [31], Copyright 2013 by the American Physical Society). (e) Symmetric three-layer unit cell based on gold traces and SU-8 spacers, fabricated on a silicon substrate to form a HMA at λ=1.5μm; scanning electron microscope image of fabricated refracting metasurface is also shown (reprinted with permission from [32], Copyright 2013 American Chemical Society). (f) Gap-surface plasmon resonator made of gold bar separated from a gold ground plane by a silica layer, forming a HMA at λ=800nm; typical HMA current distributions and radiation patterns are shown as well (reprinted from [26], Copyright 2014 by the American Physical Society). (g) Silicon nanodisc resonators acting as HMAs at the range λ(1μm,1.7μm), shown along with the typical HMA current distributions (reprinted with permission from [35], Copyright 2015 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim). (h) Silicon box resonators forming a HMA at λ=1.55μm (reprinted with permission from [45], Copyright 2015 American Chemical Society). (i) Split lead telluride cube forming a HMA at λ=10μm (reprinted with permission from [37]. Copyright 2015 Optical Society of America).

Fig. 4.
Fig. 4.

Electric field snapshots for (TE-polarized) plane-wave scattering off θ-HMAs, as simulated in ANSYS HFSS using periodic boundary conditions (see Fig. 5 for details regarding the TE simulation configuration used); spider-type HMAs were used for these demonstrations (Appendix A). The relative transmitted power |T|2 and transmission phase shift T are denoted for each case. (a) 0°-HMA illuminated by a normally incident plane wave. (b) Same 0°-HMA illuminated by plane wave propagating at θ=60°. (c) 60°-HMA illuminated by plane wave propagating at θ=60°.

Fig. 5.
Fig. 5.

Typical simulation configuration for HMA characterization (microdesign). The W×L×H meta-atom is centered around the origin at z=0, with periodic boundary conditions at the planes x=±L/2 and y=±W/2. Excitation port 1 and “measurement” port 2 are defined at a safe distance (where high-order Floquet–Bloch modes are considered negligible). The meta-atom response is then probed by TE-polarized or TM-polarized normally-incident plane waves excited by port 1, and the scattering parameters are evaluated from the fields recorded in port 2.

Fig. 6.
Fig. 6.

Lattice circuit model for a scalar HMA [30]. The electric and magnetic responses correspond to shunt and series elements, respectively, while electric and magnetic fields are associated with voltages and currents, respectively (reprinted from [25], Copyright 2014, with permission from Elsevier).

Fig. 7.
Fig. 7.

Transmission line model for a scalar three-layer HMA (reprinted with permission from [31], Copyright 2013 by the American Physical Society). The three shunt reactance sheets X1,X2,X3 are separated by spacers of length d having a characteristic impedance Zd and a propagation constant kd. The structure is embedded in a homogeneous medium with characteristic impedance Z0 and propagation constant k0. Following this model, transmission line theory allows evaluation of the reflection (r) and transmission (t) coefficients.

Fig. 8.
Fig. 8.

Physical configuration of a refracting HMS. A plane wave incident at θin is refracted toward θout, possibly with some specular reflection. The HMS can be engineered to add a uniform phase of ξout to the transmitted fields (Copyright 2014 IEEE. Reprinted, with permission, from [63]).

Fig. 9.
Fig. 9.

Refraction efficiency ηrefr(θin,θout) as a function of the output angle θout, for a normally incident plane wave and a HMS designed following Eq. (12) with θin=0 and different values of θout.

Fig. 10.
Fig. 10.

Physical configuration of a refracting HMS excited by a plane wave at an arbitrary angle ψin=ψ0. In general, if ψinθin, the scattered field consists of an infinite number of transmitted and reflected FB modes (reprinted with permission from [54], Copyright 2014 by the American Physical Society).

Fig. 11.
Fig. 11.

Ray-optical interpretation of the Floquet–Bloch analysis presented in [54]. To obtain the contribution to the FB transmission (purple) or reflection (green) coefficients [Eq. (13)], one should trace the rays from the incident ray (brown) to the respective mode, multiplying the Fresnel reflection (red) or transmission (blue) coefficients encountered along the trajectory (reprinted with permission from [54], Copyright 2014 by the American Physical Society).

Fig. 12.
Fig. 12.

Refraction efficiency ηrefr(ψ0,ψ1) for a wide range of angles of incidence ψ0, for a HMS designed following Eq. (12) with θin=0 and θout=45°. The refraction efficiency is the fraction of the incident power coupled to the first Floquet–Bloch mode in transmission, departing at the angle ψ1=arcsin(sinψ0+sinθoutsinθin) corresponding to generalized Snell’s law.

Fig. 13.
Fig. 13.

Enhancement of refraction efficiency as a function of the output angle θout, for a normally incident plane wave and a HMS designed following the optimized scheme of Eq. (15) with θin=0 and different values of θout. The enhancement factor is the ratio between the optimized refraction efficiency [Eq. (16)] and the refraction efficiency obtained by the standard procedure following Eq. (12) and presented in Fig. 9, namely, ηrefr,opt(θin,θout)/ηrefr(θin,θout).

Fig. 14.
Fig. 14.

Physical configuration of a HMS converting a given source excitation to directive radiation toward θout [63]. The source configuration at zz can also include dielectric and conducting scatterers as long as it allows evaluation of the source plane-wave spectrum via modal analysis [67] (Copyright 2014 IEEE. Reprinted, with permission, from [63]).

Fig. 15.
Fig. 15.

Physical configuration of a HMS converting an electric line source at z=z backed by a PEC at z=d to directive radiation toward θout [63]. The respective positions of the source and the PEC can be used to tune the aperture illumination by harnessing the interference between the source and its image, induced by the PEC (Copyright 2014 IEEE. Reprinted, with permission, from [63]).

Fig. 16.
Fig. 16.

Performance of a HMS of length L=10λ converting the fields from a line source at z=z=λ backed by a PEC at z=d=1.5λ to broadside radiation (Fig. 15). (a) HMS design specifications Xse/η=Bsmη as stipulated by Eq. (21) (solid black line), and the electric surface reactance Xse=I{Zse} (blue circles) and magnetic surface susceptance Bsm=I{Ysm} (red circles) as realized by the spider unit cells used for the implementation in HFSS (Appendix A). (b) Radiation pattern produced by full-wave simulations (red solid line) and semianalytical formulas [Eq. (17)] (blue dashed line). (c) Field distribution |R{Ex(y,z)}| produced by full-wave simulations. (d) Semianalytical prediction of |R{Ex(y,z)}|.

Fig. 17.
Fig. 17.

Physical configuration of a cavity-excited HMS antenna radiating toward θout [68]. The respective positions of the source and the PEC can be used to engineer the lateral cavity mode excitations such that a uniform illumination of the metasurface is achieved, yielding high aperture illumination efficiency (reprinted from [68], Copyright (2016) Macmillan Publishers Limited. All rights reserved.).

Fig. 18.
Fig. 18.

Physical configuration of a HMS-based switched-beam lens antenna. Five magnetic dipole lines are distributed in the focal plane z=z separated by Δy. The mth source is positioned at y=y=mΔy, where magenta, green, blue, red, and cyan arrows denote the m=2,1,0,1,2 source, respectively. The PEC located at z=z does not affect the ray-optical picture, as it merely doubles the magnitude of the magnetic sources following image theory (HMSs typically exhibit small reflections).

Fig. 19.
Fig. 19.

Main beam angle produced by the source at y for the HMS-based switched-beam antenna discussed in Subsection 4.D. The figure compares the estimation following the approximate ray-optical synthesis method [Eq. (25)] (blue squares), the evaluation using the ray-optical analysis with the full Floquet–Bloch series [Eq. (13)] (green diamonds), and the results from the full-wave simulations carried with the spider-type meta-atom implementation of the HMS (red circles).

Fig. 20.
Fig. 20.

Performance of the HMS-based switched-beam antenna discussed in Subsection 4.D. The HMS length is L=5λ, and the five magnetic dipole lines are situated at z=z=3λ, separated by Δy=0.6λ (Fig. 18). The figure compares results from full-wave simulations using the spider unit cells [(a)–(d)] with semianalytical predictions [(e)–(h)]. Field distributions |R{Ex(y,z)}| for the sources at (a),(e) y=0, (b),(f) y=0.6λ, and (c),(g) y=1.2λ. (d) Simulated and (h) semianalytically predicted radiation patterns of all sources, following the color code presented in Fig. 18.

Fig. 21.
Fig. 21.

Physical configuration of the spider-type meta-atoms used for implementing the HMSs at a frequency of f=20GHz (λ15mm). The electric response is controlled by the capacitor width We of the electric dipole, while the magnetic response is determined by the magnetic dipole arm length Lm (reprinted from [68], Copyright (2016) Macmillan Publishers Limited. All rights reserved.).

Equations (29)

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{12(E⃗t|z0++E⃗t|z0)=Z¯¯se·J⃗s12(H⃗t|z0++H⃗t|z0)=Y¯¯sm·M⃗s,
{J⃗s=z^×(H⃗|z0+H⃗|z0)M⃗s=z^×(E⃗|z0+E⃗|z0).
{12(E⃗t|z0++E⃗t|z0)=Z¯¯se·[z^×(H⃗|z0+H⃗|z0)]12(H⃗t|z0++H⃗t|z0)=Y¯¯sm·[z^×(E⃗|z0+E⃗|z0)].
(t^1·E⃗|z0t^1·E⃗|z0+)=(Z11Z12Z21Z22)(t^2·[z^×H⃗]z0t^2·[z^×H⃗]z0+),
{Zse=14[(Z11+Z22)+(Z21+Z12)]Ysm=(Zsm)1=[(Z11+Z22)(Z21+Z12)]1.
{12(Ex|z0++Ex|z0)=ZseTE(Hy|z0+Hy|z0)12(Hy|z0++Hy|z0)=YsmTE(Ex|z0+Ex|z0).
{12(Ey|z0++Ey|z0)=ZseTM(Hx|z0+Hx|z0)12(Hx|z0++Hx|z0)=YsmTM(Ey|z0+Ey|z0).
{Z¯¯se=(ZseTEZseTE/TMZseTE/TMZseTM)Y¯¯sm=(Z¯¯sm)1=(ZsmTEZsmTE/TMZsmTE/TMZsmTM)1.
{Exinc(y,z)=kηI0ejkzcosθinejkysinθinExref(y,z)=kηI0Γ0ejkzcosθinejkysinθinExtrans(y,z)=kηI0T1ejkzcosθoutejkysinθout,
{Hyinc(y,z)=kI0cosθinejkzcosθinejkysinθinHyref(y,z)=kI0Γ0cosθinejkzcosθinejkysinθinHytrans(y,z)=kI0T1cosθoutejkzcosθoutejkysinθout,
{Zse=η2cosθoutT1ejkysinθout+(1Γ0)ejkysinθinT1ejkysinθout(1+Γ0)cosθincosθoutejkysinθinYsm=cosθout2ηT1ejkysinθout+(1+Γ0)cosθincosθoutejkysinθinT1ejkysinθout(1Γ0)ejkysinθin.
{Γ0=ZoutZinZout+Zin=cosθoutcosθincosθout+cosθinT1=(1Γ0)ejξout=2cosθincosθout+cosθinejξout
{Zse(y)=jZout2cot[ky(sinθoutsinθin)+ξout2]Ysm(y)=jYout2cot[ky(sinθoutsinθin)+ξout2],
{Exinc(y,z)=kηI0ejkzcosψ0ejkysinψ0Exref(y,z)=kηI0n=Rnejβnzejky(sinψ0+nΔsin)ejnξoutExtrans(y,z)=kηI0n=Tnejβnzejky(sinψ0+nΔsin)ejnξout,
{Hyinc(y,z)=kI0cosψ0ejkzcosψinejkysinψ0Hyref(y,z)=I0n=βnRnejβnzejky(sinψ0+nΔsin)ejnξoutHytrans(y,z)=I0n=βnTnejβnzejky(sinψ0+nΔsin)ejnξout,
T1(1Γ0)(1+Γ1)=4cosψ0cosθout(cosψ0+cosθout)(cosψ1+cosθout).
{Zse(y)=jZinZout2cot[ky(sinθoutsinθin)+ξout2]Ysm(y)=jYinYout2cot[ky(sinθoutsinθin)+ξout2].
ηrefr,opt(θin,θout)16(1+cosθincosθout)2(1+cosθoutcosθin)2.
{Exinc(y,z)=kηI0F1{12βf(kt)ejβz}Exref(y,z)=kηI0F1{12βΓ(kt)f(kt)ejβz}Extrans(y,z)=kηI0F1{12β[1+Γ(kt)]T(kt)ejβz},
{Hyinc(y,z)=I0F1{12ββf(kt)ejβz}Hyref(y,z)=I0F1{12ββΓ(kt)f(kt)ejβz}Hytrans(y,z)=I0F1{12ββ[1+Γ(kt)]T(kt)ejβz},
Ex(y,z)|z0+ZoutHy(y,z)|z0+kηI0F1{12βT(kt)}kηI0W0(y)ejkysinθoutejξout,
Γ(kt)=kcosθoutβkcosθout+β,
W0(y)F1{12βT(kt)}ejkysinθoutejξout=|Ex(y,z)|z0=|F1{12β[1Γ(kt)]f(kt)}|.
{Zse(y)=jZout2cot[ϕ(y)ϕ+(y)2]Ysm(y)=jYout2cot[ϕ(y)ϕ+(y)2],
E(y)|F1{12βT(kt)Γ(kt)}F1{12βT(kt)}|1,
f(kt)=ejβ(d+z)ejβ(d+z)ejβdΓ(kt)ejβd,
{Zse(y)=jZout(y)2cot[kyΔsin(y)+ξout(y))2]Ysm(y)=jYout(y)2cot[kyΔsin(y)+ξout(y)2],
Extrans(y,z)|z0+T1(y)Exinc(y,z)|z0ejΔϕ(y),
T1(y)4cosψ0(y)cosθout(y)[cosψ0(y)+cosθout(y)][cosψ1(y)+cosθout(y)].

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