Abstract

All-dielectric nanostructures have recently emerged as a promising alternative to plasmonic devices, as they also possess pronounced electric and magnetic resonances and allow effective light manipulation. In this work, we study optical properties of a composite structure that consists of a silicon nanoparticle array (metasurface) and high-index substrate aiming at clarifying the role of substrate on reflective properties of the nanoparticles. We develop a simple semi-analytical model that describes interference of separate contributions from the nanoparticle array and the bare substrate to the total reflection. Applying this model, we show that matching the magnitudes and setting the π-phase difference of the electric and magnetic dipole moments induced in nanoparticles, one can obtain a suppression of reflection from the substrate coated with metasurface. We perform numerical simulations of sphere and disk nanoparticle arrays for different permittivities of the substrate. We find full agreement with the semi-analytical results, which means that the uncoupled-element model adequately describes nanostructure reflective properties, despite the effects of induced bi-anisotropy. The model explains the features of the reflectance spectrum, such as a number of dips and their spectral positions, and shows why it may not coincide with the spectral positions of Mie resonances of the single nanoparticles forming the system. We also address practical aspects of the antireflective device engineering: we show that the uncoupled-element model is applicable to the structures on top of silicon substrates, including lithographically defined nanopillars. The reflectance suppression from the nanoparticle array on top of the silicon substrate can be achieved in a broad spectral range with a disordered nanoparticle array and for a wide range of incidence angles.

© 2017 Optical Society of America

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2017 (1)

2016 (11)

M. A. Cole, D. A. Powell, and I. V. Shadrivov, “Strong terahertz absorption in all-dielectric Huygens’ metasurfaces,” Nanotechnology 27, 424003 (2016).
[Crossref]

P. A. Dmitriev, D. G. Baranov, V. A. Milichko, S. V. Makarov, I. S. Mukhin, A. K. Samusev, A. E. Krasnok, P. A. Belov, and Y. S. Kivshar, “Resonant Raman,” Nanoscale 8, 9721–9726 (2016).
[Crossref]

D. Markovich, K. Baryshnikova, A. Shalin, A. Samusev, A. Krasnok, P. Belov, and P. Ginzburg, “Enhancement of artificial magnetism via resonant bianisotropy,” Sci. Rep. 6, 22546 (2016).
[Crossref]

A. I. Kuznetsov, A. E. Miroshnichenko, M. L. Brongersma, Y. S. Kivshar, and B. Luk’yanchuk, “Optically resonant dielectric nanostructures,” Science 354, aag2472 (2016).
[Crossref]

K. V. Baryshnikova, M. I. Petrov, V. E. Babicheva, and P. A. Belov, “Plasmonic and silicon nanoparticle anti-reflective coatings,” Sci. Rep. 6, 22136 (2016).
[Crossref]

S. Tsoi, F. J. Bezares, A. Giles, J. P. Long, O. J. Glembocki, J. D. Caldwell, and J. Owrutsky, “Experimental demonstration of the optical lattice resonance in arrays of Si nanoresonators,” Appl. Phys. Lett. 108, 111101 (2016).
[Crossref]

P. A. Dmitriev, S. V. Makarov, V. A. Milichko, I. S. Mukhin, A. S. Gudovskikh, A. A. Sitnikova, A. K. Samusev, A. E. Krasnok, and P. A. Belov, “Laser fabrication of crystalline silicon nanoresonators from an amorphous film for low-loss all-dielectric nanophotonics,” Nanoscale 8, 5043–5048 (2016).
[Crossref]

M. Naffouti, T. David, A. Benkouider, L. Favre, A. Ronda, I. Berbezier, S. Bidault, N. Bonod, and M. Abbarchi, “Fabrication of poly-crystalline Si-based Mie resonators via amorphous Si on SiO2 dewetting,” Nanoscale 8, 2844–2849 (2016).
[Crossref]

S. Ishii, R. P. Sugavaneshwar, K. Chen, T. D. Dao, and T. Nagao, “Solar water heating and vaporization with silicon nanoparticles at Mie resonances,” Opt. Mater. Express 6, 640–648 (2016).
[Crossref]

J. Proust, A.-L. Fehrembach, F. Bedu, I. Ozerov, and N. Bonod, “Optimized 2D array of thin silicon pillars for efficient antireflective coatings in the visible spectrum,” Sci. Rep. 6, 24947 (2016).
[Crossref]

A. Andryieuski, A. V. Lavrinenko, M. Petrov, and S. A. Tretyakov, “Homogenization of metasurfaces formed by random resonant particles in periodical lattices,” Phys. Rev. B 93, 205127 (2016).
[Crossref]

2015 (17)

R. Alaee, R. Filter, D. Lehr, F. Lederer, and C. Rockstuhl, “A generalized Kerker condition for highly directive nanoantennas,” Opt. Lett. 40, 2645–2648 (2015).
[Crossref]

U. Zywietz, M. K. Schmidt, A. B. Evlyukhin, C. Reinhardt, J. Aizpurua, and B. N. Chichkov, “Electromagnetic resonances of silicon nanoparticle dimers in the visible,” ACS Photon. 2, 913–920 (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]

S. Zhong, Y. Zeng, Z. Huang, and W. Shen, “Superior broadband antireflection from buried Mie resonator arrays for high-efficiency photovoltaics,” Sci. Rep. 5, 8915 (2015).
[Crossref]

T. Lewi, P. P. Iyer, N. A. Butakov, A. A. Mikhailovsky, and J. A. Schuller, “Widely tunable infrared antennas using free carrier refraction,” Nano Lett. 15, 8188–8193 (2015).
[Crossref]

A. Pors, S. K. H. Andersen, and S. I. Bozhevolnyi, “Unidirectional scattering by nanoparticles near substrates: generalized Kerker conditions,” Opt. Express 23, 28808–28828 (2015).
[Crossref]

A. E. Miroshnichenko, A. B. Evlyukhin, Y. S. Kivshar, and B. N. Chichkov, “Substrate-induced resonant magnetoelectric effects for dielectric nanoparticles,” ACS Photon. 2, 1423–1428 (2015).
[Crossref]

A. B. Evlyukhin and S. I. Bozhevolnyi, “Resonant unidirectional and elastic scattering of surface plasmon polaritons by high refractive index dielectric nanoparticles,” Phys. Rev. B 92, 245419 (2015).
[Crossref]

A. Krasnok, S. Makarov, M. Petrov, R. Savelev, P. Belov, and Y. Kivshar, “Towards all-dielectric metamaterials and nanophotonics,” Proc. SPIE 9502, 950203 (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]

R. Alaee, M. Albooyeh, A. Rahimzadegan, M. S. Mirmoosa, Y. S. Kivshar, and C. Rockstuhl, “All-dielectric reciprocal bianisotropic nanoparticles,” Phys. Rev. B 92, 245130 (2015).
[Crossref]

Y. F. Yu, A. Y. Zhu, R. Paniagua-Domınguez, 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]

D. Sikdar, W. Cheng, and M. Premaratne, “Optically resonant magneto-electric cubic nanoantennas for ultra-directional light scattering,” J. Appl. Phys. 117, 083101 (2015).
[Crossref]

S. Zhang, R. Jiang, Y. M. Xie, Q. Ruan, B. Yang, J. Wang, and H. Q. Lin, “Colloidal moderate-refractive-index Cu2O nanospheres as visible-region nanoantennas with electromagnetic resonance and directional light-scattering properties,” Adv. Mater. 27, 7432–7439 (2015).
[Crossref]

P. Moitra, B. A. Slovick, W. Li, I. I. Kravchencko, D. P. Briggs, S. Krishnamurthy, and J. Valentine, “Large-scale all-dielectric metamaterial perfect reflectors,” ACS Photon. 2, 692–698 (2015).
[Crossref]

R. Paniagua-Domínguez, Y. F. Yu, A. E. Miroschnichenko, L. A. Krivitsky, Y. H. Fu, V. Valuckas, L. Gonzaga, Y. T. Toh, A. Y. S. Kay, B. Luk’yanchuk, and A. I. Kuznetsov, “Generalized Brewster effect in dielectric metasurfaces,” Nat. Commun. 7, 10362 (2015).
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A. Jain, P. Moitra, T. Koschny, J. Valentine, and C. M. Soukoulis, “Electric and magnetic response in dielectric dark states for low loss subwavelength optical meta atoms,” Adv. Opt. Mater. 3, 1431–1438 (2015).
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2014 (12)

J. Cheng, D. Ansari-Oghol-Beig, and H. Mosallaei, “Wave manipulation with designer dielectric metasurfaces,” Opt. Lett. 39, 6285–6288 (2014).
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M. L. Brongersma, Y. Cui, and S. Fan, “Light management for photovoltaics using high-index nanostructures,” Nat. Mater. 13, 451–460 (2014).
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D. L. Markovich, P. Ginzburg, A. K. Samusev, P. A. Belov, and A. V. Zayats, “Magnetic dipole radiation tailored by substrates: numerical investigation,” Opt. Express 22, 10693–10702 (2014).
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N. Yu and F. Capasso, “Flat optics with designer metasurfaces,” Nat. Mater. 13, 139–150 (2014).
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N. Meinzer, W. L. Barnes, and I. R. Hooper, “Plasmonic meta-atoms and metasurfaces,” Nat. Photonics 8, 889–898 (2014).
[Crossref]

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

A. E. Krasnok, C. R. Simovski, P. A. Belov, and Y. S. Kivshar, “Superdirective dielectric nanoantennas,” Nanoscale 6, 7354–7361 (2014).
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U. Zywietz, A. B. Evlyukhin, C. Reinhardt, and B. N. Chichkov, “Laser printing of silicon nanoparticles with resonant optical electric and magnetic responses,” Nat. Commun. 5, 3402 (2014).
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M. Abbarchi, M. Naffouti, B. Vial, A. Benkouider, L. Lermusiaux, L. Favre, A. Ronda, S. Bidault, I. Berbezier, and N. Bonod, “Wafer scale formation of monocrystalline silicon-based Mie resonators via silicon-on-insulator dewetting,” ACS Nano 8, 11181–11190 (2014).
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P. Spinelli and A. Polman, “Light trapping in thin crystalline Si solar cells using surface Mie scatterers,” IEEE J. Photovolt. 4, 554–559 (2014).
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K. X. Wang, Z. Yu, S. Sandhu, V. Liu, and S. Fan, “Condition for perfect antireflection by optical resonance at material interface,” Optica 1, 388–395 (2014).
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S. Collin, “Nanostructure arrays in free-space: optical properties and applications,” Rep. Prog. Phys. 77, 126402 (2014).
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2013 (11)

E. Almpanis and N. Papanikolaou, “Designing photonic structures of nanosphere arrays on reflectors for total absorption,” J. Appl. Phys. 114, 083106 (2013).
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L. Shi, J. T. Harris, R. Fenollosa, I. Rodriguez, X. Lu, B. A. Korgel, and F. Meseguer, “Monodisperse silicon nanocavities and photonic crystals with magnetic response in the optical region,” Nat. Commun. 4, 1904 (2013).
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F. J. Bezares, J. P. Long, O. J. Glembocki, J. Guo, R. W. Rendell, R. Kasica, L. Shirey, J. C. Owrutsky, and J. D. Caldwell, “Mie resonance-enhanced light absorption in periodic silicon nanopillar arrays,” Opt. Express 21, 27587–27601 (2013).
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A. B. Evlyukhin, C. Reinhardt, E. Evlyukhin, and B. N. Chichkov, “Multipole analysis of light scattering by arbitrary-shaped nanoparticles on a plane surface,” J. Opt. Soc. Am. B 30, 2589–2598 (2013).
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E. Xifré-Pérez, L. Shi, U. Tuzer, R. Fenollosa, F. Ramiro-Manzano, R. Quidant, and F. Meseguer, “Mirror-image-induced magnetic modes,” ACS Nano 7, 664–668 (2013).
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Y. H. Fu, A. I. Kuznetsov, A. E. Miroshnichenko, Y. F. Yu, and B. Luk’yanchuk, “Directional visible light scattering by silicon nanoparticles,” Nat. Commun. 4, 1527 (2013).
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S. Person, M. Jain, Z. Lapin, J. J. Sáenz, G. Wicks, and L. Novotny, “Demonstration of zero optical backscattering from single nanoparticles,” Nano Lett. 13, 1806–1809 (2013).
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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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J. van de Groep and A. Polman, “Designing dielectric resonators on substrates: combining magnetic and electric resonances,” Opt. Express 21, 26285–26302 (2013).
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I. Staude, A. E. Miroshnichenko, M. Decker, N. T. Fofang, S. Liu, E. Gonzales, J. Dominguez, T. S. Luk, D. N. Neshev, I. Brener, and Y. Kivshar, “Tailoring directional scattering through magnetic and electric resonances in subwavelength silicon nanodisks,” ACS Nano 7, 7824–7832 (2013).
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B. Slovick, Z. G. Yu, M. Berding, and S. Krishnamurthy, “Perfect dielectric-metamaterial reflector,” Phys. Rev. B 88, 165116 (2013).
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2012 (11)

A. I. Kuznetsov, A. E. Miroshnichenko, Y. H. Fu, J. Zhang, and B. Luk’yanchuk, “Magnetic light,” Sci. Rep. 2, 492 (2012).
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P. Spinelli, M. A. Verschuuren, and A. Polman, “Broadband omnidirectional antireflection coating based on subwavelength surface Mie resonators,” Nat. Commun. 3, 692 (2012).
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A. E. Krasnok, A. E. Miroshnichenko, P. A. Belov, and Y. S. Kivshar, “All-dielectric optical nanoantennas,” Opt. Express 20, 20599–20604 (2012).
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A. Moreau, C. Ciraci, J. J. Mock, R. T. Hill, Q. Wang, B. J. Wiley, A. Chilkoti, and D. R. Smith, “Controlled-reflectance surfaces with film-coupled colloidal nanoantennas,” Nature 492, 86–89 (2012).
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A. B. Evlyukhin, S. M. Novikov, U. Zywietz, R. L. Eriksen, C. Reinhardt, S. I. Bozhevolnyi, and B. N. Chichkov, “Demonstration of magnetic dipole resonances of dielectric nanospheres in the visible region,” Nano Lett. 12, 3749–3755 (2012).
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H. Tan, R. Santbergen, A. H. M. Smets, and M. Zeman, “Plasmonic light trapping in thin-film silicon solar cells with improved self-assembled silver nanoparticles,” Nano Lett. 12, 4070–4076 (2012).
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H.-T. Chen, “Interference theory of metamaterial perfect absorbers,” Opt. Express 20, 7165–7172 (2012).
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M. Albooyeh and C. R. Simovski, “Huge local field enhancement in perfect plasmonic absorbers,” Opt. Express 20, 21888–21895 (2012).
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M. Albooyeh, D. Morits, and S. A. Tretyakov, “Effective electric and magnetic properties of metasurfaces in transition from crystalline to amorphous state,” Phys. Rev. B 85, 205110 (2012).
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L. S. Slaughter, B. A. Willingham, W.-S. Chang, M. H. Chester, N. Ogden, and S. Link, “Toward plasmonic polymers,” Nano Lett. 12, 3967–3972 (2012).
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D. Solis, B. Willingham, S. L. Nauert, L. S. Slaughter, J. Olson, P. Swanglap, A. Paul, W.-S. Chang, and S. Link, “Electromagnetic energy transport in nanoparticle chains via dark plasmon modes,” Nano Lett. 12, 1349–1353 (2012).
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2011 (4)

M. Albooyeh, D. Morits, and C. R. Simovski, “Electromagnetic characterization of substrated metasurfaces,” Metamaterials 5, 178–205 (2011).
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M. Albooyeh and C. R. Simovski, “Substrate-induced bianisotropy in plasmonic grids,” J. Opt. 13, 105102 (2011).
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P. Spinelli, M. Hebbink, R. de Waele, L. Black, F. Lenzmann, and A. Polman, “Optical impedance matching using coupled plasmonic nanoparticle arrays,” Nano Lett. 11, 1760–1765 (2011).
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A. B. Evlyukhin, C. Reinhardt, and B. N. Chichkov, “Multipole light scattering by nonspherical nanoparticles in the discrete dipole approximation,” Phys. Rev. B 84, 235429 (2011).
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2010 (2)

H. A. Atwater and A. Polman, “Plasmonics for improved photovoltaic devices,” Nat. Mater. 9, 205–213 (2010).
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A. B. Evlyukhin, C. Reinhardt, A. Seidel, B. S. Luk’yanchuk, and B. N. Chichkov, “Optical response features of Si-nanoparticle arrays,” Phys. Rev. B 82, 045404 (2010).
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2008 (1)

H. Sai, H. Fujiwara, M. Kondo, and Y. Kanamori, “Enhancement of light trapping in thin-film hydrogenated microcrystalline Si solar cells using back reflectors with self-ordered dimple pattern,” Appl. Phys. Lett. 93, 143501 (2008).
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2002 (1)

1983 (1)

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M. Naffouti, T. David, A. Benkouider, L. Favre, A. Ronda, I. Berbezier, S. Bidault, N. Bonod, and M. Abbarchi, “Fabrication of poly-crystalline Si-based Mie resonators via amorphous Si on SiO2 dewetting,” Nanoscale 8, 2844–2849 (2016).
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M. Abbarchi, M. Naffouti, B. Vial, A. Benkouider, L. Lermusiaux, L. Favre, A. Ronda, S. Bidault, I. Berbezier, and N. Bonod, “Wafer scale formation of monocrystalline silicon-based Mie resonators via silicon-on-insulator dewetting,” ACS Nano 8, 11181–11190 (2014).
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Aizpurua, J.

U. Zywietz, M. K. Schmidt, A. B. Evlyukhin, C. Reinhardt, J. Aizpurua, and B. N. Chichkov, “Electromagnetic resonances of silicon nanoparticle dimers in the visible,” ACS Photon. 2, 913–920 (2015).
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Alaee, R.

R. Alaee, M. Albooyeh, A. Rahimzadegan, M. S. Mirmoosa, Y. S. Kivshar, and C. Rockstuhl, “All-dielectric reciprocal bianisotropic nanoparticles,” Phys. Rev. B 92, 245130 (2015).
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R. Alaee, R. Filter, D. Lehr, F. Lederer, and C. Rockstuhl, “A generalized Kerker condition for highly directive nanoantennas,” Opt. Lett. 40, 2645–2648 (2015).
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R. Alaee, M. Albooyeh, A. Rahimzadegan, M. S. Mirmoosa, Y. S. Kivshar, and C. Rockstuhl, “All-dielectric reciprocal bianisotropic nanoparticles,” Phys. Rev. B 92, 245130 (2015).
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M. Albooyeh, D. Morits, and S. A. Tretyakov, “Effective electric and magnetic properties of metasurfaces in transition from crystalline to amorphous state,” Phys. Rev. B 85, 205110 (2012).
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M. Albooyeh and C. R. Simovski, “Huge local field enhancement in perfect plasmonic absorbers,” Opt. Express 20, 21888–21895 (2012).
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M. Albooyeh, D. Morits, and C. R. Simovski, “Electromagnetic characterization of substrated metasurfaces,” Metamaterials 5, 178–205 (2011).
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M. Albooyeh and C. R. Simovski, “Substrate-induced bianisotropy in plasmonic grids,” J. Opt. 13, 105102 (2011).
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Almpanis, E.

E. Almpanis and N. Papanikolaou, “Designing photonic structures of nanosphere arrays on reflectors for total absorption,” J. Appl. Phys. 114, 083106 (2013).
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A. Andryieuski, A. V. Lavrinenko, M. Petrov, and S. A. Tretyakov, “Homogenization of metasurfaces formed by random resonant particles in periodical lattices,” Phys. Rev. B 93, 205127 (2016).
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H. A. Atwater and A. Polman, “Plasmonics for improved photovoltaic devices,” Nat. Mater. 9, 205–213 (2010).
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K. V. Baryshnikova, M. I. Petrov, V. E. Babicheva, and P. A. Belov, “Plasmonic and silicon nanoparticle anti-reflective coatings,” Sci. Rep. 6, 22136 (2016).
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Baranov, D. G.

P. A. Dmitriev, D. G. Baranov, V. A. Milichko, S. V. Makarov, I. S. Mukhin, A. K. Samusev, A. E. Krasnok, P. A. Belov, and Y. S. Kivshar, “Resonant Raman,” Nanoscale 8, 9721–9726 (2016).
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Barnes, W. L.

N. Meinzer, W. L. Barnes, and I. R. Hooper, “Plasmonic meta-atoms and metasurfaces,” Nat. Photonics 8, 889–898 (2014).
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D. Markovich, K. Baryshnikova, A. Shalin, A. Samusev, A. Krasnok, P. Belov, and P. Ginzburg, “Enhancement of artificial magnetism via resonant bianisotropy,” Sci. Rep. 6, 22546 (2016).
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K. V. Baryshnikova, M. I. Petrov, V. E. Babicheva, and P. A. Belov, “Plasmonic and silicon nanoparticle anti-reflective coatings,” Sci. Rep. 6, 22136 (2016).
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Bedu, F.

J. Proust, A.-L. Fehrembach, F. Bedu, I. Ozerov, and N. Bonod, “Optimized 2D array of thin silicon pillars for efficient antireflective coatings in the visible spectrum,” Sci. Rep. 6, 24947 (2016).
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Belov, P.

D. Markovich, K. Baryshnikova, A. Shalin, A. Samusev, A. Krasnok, P. Belov, and P. Ginzburg, “Enhancement of artificial magnetism via resonant bianisotropy,” Sci. Rep. 6, 22546 (2016).
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A. Krasnok, S. Makarov, M. Petrov, R. Savelev, P. Belov, and Y. Kivshar, “Towards all-dielectric metamaterials and nanophotonics,” Proc. SPIE 9502, 950203 (2015).
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Belov, P. A.

P. A. Dmitriev, D. G. Baranov, V. A. Milichko, S. V. Makarov, I. S. Mukhin, A. K. Samusev, A. E. Krasnok, P. A. Belov, and Y. S. Kivshar, “Resonant Raman,” Nanoscale 8, 9721–9726 (2016).
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P. A. Dmitriev, S. V. Makarov, V. A. Milichko, I. S. Mukhin, A. S. Gudovskikh, A. A. Sitnikova, A. K. Samusev, A. E. Krasnok, and P. A. Belov, “Laser fabrication of crystalline silicon nanoresonators from an amorphous film for low-loss all-dielectric nanophotonics,” Nanoscale 8, 5043–5048 (2016).
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K. V. Baryshnikova, M. I. Petrov, V. E. Babicheva, and P. A. Belov, “Plasmonic and silicon nanoparticle anti-reflective coatings,” Sci. Rep. 6, 22136 (2016).
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A. E. Krasnok, C. R. Simovski, P. A. Belov, and Y. S. Kivshar, “Superdirective dielectric nanoantennas,” Nanoscale 6, 7354–7361 (2014).
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D. L. Markovich, P. Ginzburg, A. K. Samusev, P. A. Belov, and A. V. Zayats, “Magnetic dipole radiation tailored by substrates: numerical investigation,” Opt. Express 22, 10693–10702 (2014).
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A. E. Krasnok, A. E. Miroshnichenko, P. A. Belov, and Y. S. Kivshar, “All-dielectric optical nanoantennas,” Opt. Express 20, 20599–20604 (2012).
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M. Naffouti, T. David, A. Benkouider, L. Favre, A. Ronda, I. Berbezier, S. Bidault, N. Bonod, and M. Abbarchi, “Fabrication of poly-crystalline Si-based Mie resonators via amorphous Si on SiO2 dewetting,” Nanoscale 8, 2844–2849 (2016).
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M. Abbarchi, M. Naffouti, B. Vial, A. Benkouider, L. Lermusiaux, L. Favre, A. Ronda, S. Bidault, I. Berbezier, and N. Bonod, “Wafer scale formation of monocrystalline silicon-based Mie resonators via silicon-on-insulator dewetting,” ACS Nano 8, 11181–11190 (2014).
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Berbezier, I.

M. Naffouti, T. David, A. Benkouider, L. Favre, A. Ronda, I. Berbezier, S. Bidault, N. Bonod, and M. Abbarchi, “Fabrication of poly-crystalline Si-based Mie resonators via amorphous Si on SiO2 dewetting,” Nanoscale 8, 2844–2849 (2016).
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M. Abbarchi, M. Naffouti, B. Vial, A. Benkouider, L. Lermusiaux, L. Favre, A. Ronda, S. Bidault, I. Berbezier, and N. Bonod, “Wafer scale formation of monocrystalline silicon-based Mie resonators via silicon-on-insulator dewetting,” ACS Nano 8, 11181–11190 (2014).
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B. Slovick, Z. G. Yu, M. Berding, and S. Krishnamurthy, “Perfect dielectric-metamaterial reflector,” Phys. Rev. B 88, 165116 (2013).
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S. Tsoi, F. J. Bezares, A. Giles, J. P. Long, O. J. Glembocki, J. D. Caldwell, and J. Owrutsky, “Experimental demonstration of the optical lattice resonance in arrays of Si nanoresonators,” Appl. Phys. Lett. 108, 111101 (2016).
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F. J. Bezares, J. P. Long, O. J. Glembocki, J. Guo, R. W. Rendell, R. Kasica, L. Shirey, J. C. Owrutsky, and J. D. Caldwell, “Mie resonance-enhanced light absorption in periodic silicon nanopillar arrays,” Opt. Express 21, 27587–27601 (2013).
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Bidault, S.

M. Naffouti, T. David, A. Benkouider, L. Favre, A. Ronda, I. Berbezier, S. Bidault, N. Bonod, and M. Abbarchi, “Fabrication of poly-crystalline Si-based Mie resonators via amorphous Si on SiO2 dewetting,” Nanoscale 8, 2844–2849 (2016).
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M. Abbarchi, M. Naffouti, B. Vial, A. Benkouider, L. Lermusiaux, L. Favre, A. Ronda, S. Bidault, I. Berbezier, and N. Bonod, “Wafer scale formation of monocrystalline silicon-based Mie resonators via silicon-on-insulator dewetting,” ACS Nano 8, 11181–11190 (2014).
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Biener, G.

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P. Spinelli, M. Hebbink, R. de Waele, L. Black, F. Lenzmann, and A. Polman, “Optical impedance matching using coupled plasmonic nanoparticle arrays,” Nano Lett. 11, 1760–1765 (2011).
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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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Bomzon, Z.

Bonod, N.

M. Naffouti, T. David, A. Benkouider, L. Favre, A. Ronda, I. Berbezier, S. Bidault, N. Bonod, and M. Abbarchi, “Fabrication of poly-crystalline Si-based Mie resonators via amorphous Si on SiO2 dewetting,” Nanoscale 8, 2844–2849 (2016).
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J. Proust, A.-L. Fehrembach, F. Bedu, I. Ozerov, and N. Bonod, “Optimized 2D array of thin silicon pillars for efficient antireflective coatings in the visible spectrum,” Sci. Rep. 6, 24947 (2016).
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M. Abbarchi, M. Naffouti, B. Vial, A. Benkouider, L. Lermusiaux, L. Favre, A. Ronda, S. Bidault, I. Berbezier, and N. Bonod, “Wafer scale formation of monocrystalline silicon-based Mie resonators via silicon-on-insulator dewetting,” ACS Nano 8, 11181–11190 (2014).
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A. B. Evlyukhin and S. I. Bozhevolnyi, “Resonant unidirectional and elastic scattering of surface plasmon polaritons by high refractive index dielectric nanoparticles,” Phys. Rev. B 92, 245419 (2015).
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A. Pors, S. K. H. Andersen, and S. I. Bozhevolnyi, “Unidirectional scattering by nanoparticles near substrates: generalized Kerker conditions,” Opt. Express 23, 28808–28828 (2015).
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A. B. Evlyukhin, S. M. Novikov, U. Zywietz, R. L. Eriksen, C. Reinhardt, S. I. Bozhevolnyi, and B. N. Chichkov, “Demonstration of magnetic dipole resonances of dielectric nanospheres in the visible region,” Nano Lett. 12, 3749–3755 (2012).
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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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I. Staude, A. E. Miroshnichenko, M. Decker, N. T. Fofang, S. Liu, E. Gonzales, J. Dominguez, T. S. Luk, D. N. Neshev, I. Brener, and Y. Kivshar, “Tailoring directional scattering through magnetic and electric resonances in subwavelength silicon nanodisks,” ACS Nano 7, 7824–7832 (2013).
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P. Moitra, B. A. Slovick, W. Li, I. I. Kravchencko, D. P. Briggs, S. Krishnamurthy, and J. Valentine, “Large-scale all-dielectric metamaterial perfect reflectors,” ACS Photon. 2, 692–698 (2015).
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D. Lin, P. Fan, E. Hasman, and M. Brongersma, “Dielectric gradient metasurface optical elements,” Science 345, 298–302 (2014).
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A. I. Kuznetsov, A. E. Miroshnichenko, M. L. Brongersma, Y. S. Kivshar, and B. Luk’yanchuk, “Optically resonant dielectric nanostructures,” Science 354, aag2472 (2016).
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M. L. Brongersma, Y. Cui, and S. Fan, “Light management for photovoltaics using high-index nanostructures,” Nat. Mater. 13, 451–460 (2014).
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T. Lewi, P. P. Iyer, N. A. Butakov, A. A. Mikhailovsky, and J. A. Schuller, “Widely tunable infrared antennas using free carrier refraction,” Nano Lett. 15, 8188–8193 (2015).
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S. Tsoi, F. J. Bezares, A. Giles, J. P. Long, O. J. Glembocki, J. D. Caldwell, and J. Owrutsky, “Experimental demonstration of the optical lattice resonance in arrays of Si nanoresonators,” Appl. Phys. Lett. 108, 111101 (2016).
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F. J. Bezares, J. P. Long, O. J. Glembocki, J. Guo, R. W. Rendell, R. Kasica, L. Shirey, J. C. Owrutsky, and J. D. Caldwell, “Mie resonance-enhanced light absorption in periodic silicon nanopillar arrays,” Opt. Express 21, 27587–27601 (2013).
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N. Yu and F. Capasso, “Flat optics with designer metasurfaces,” Nat. Mater. 13, 139–150 (2014).
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L. S. Slaughter, B. A. Willingham, W.-S. Chang, M. H. Chester, N. Ogden, and S. Link, “Toward plasmonic polymers,” Nano Lett. 12, 3967–3972 (2012).
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D. Solis, B. Willingham, S. L. Nauert, L. S. Slaughter, J. Olson, P. Swanglap, A. Paul, W.-S. Chang, and S. Link, “Electromagnetic energy transport in nanoparticle chains via dark plasmon modes,” Nano Lett. 12, 1349–1353 (2012).
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D. Sikdar, W. Cheng, and M. Premaratne, “Optically resonant magneto-electric cubic nanoantennas for ultra-directional light scattering,” J. Appl. Phys. 117, 083101 (2015).
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L. S. Slaughter, B. A. Willingham, W.-S. Chang, M. H. Chester, N. Ogden, and S. Link, “Toward plasmonic polymers,” Nano Lett. 12, 3967–3972 (2012).
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U. Zywietz, M. K. Schmidt, A. B. Evlyukhin, C. Reinhardt, J. Aizpurua, and B. N. Chichkov, “Electromagnetic resonances of silicon nanoparticle dimers in the visible,” ACS Photon. 2, 913–920 (2015).
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A. E. Miroshnichenko, A. B. Evlyukhin, Y. S. Kivshar, and B. N. Chichkov, “Substrate-induced resonant magnetoelectric effects for dielectric nanoparticles,” ACS Photon. 2, 1423–1428 (2015).
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U. Zywietz, A. B. Evlyukhin, C. Reinhardt, and B. N. Chichkov, “Laser printing of silicon nanoparticles with resonant optical electric and magnetic responses,” Nat. Commun. 5, 3402 (2014).
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A. B. Evlyukhin, C. Reinhardt, E. Evlyukhin, and B. N. Chichkov, “Multipole analysis of light scattering by arbitrary-shaped nanoparticles on a plane surface,” J. Opt. Soc. Am. B 30, 2589–2598 (2013).
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Zywietz, U.

U. Zywietz, M. K. Schmidt, A. B. Evlyukhin, C. Reinhardt, J. Aizpurua, and B. N. Chichkov, “Electromagnetic resonances of silicon nanoparticle dimers in the visible,” ACS Photon. 2, 913–920 (2015).
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U. Zywietz, A. B. Evlyukhin, C. Reinhardt, and B. N. Chichkov, “Laser printing of silicon nanoparticles with resonant optical electric and magnetic responses,” Nat. Commun. 5, 3402 (2014).
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A. B. Evlyukhin, S. M. Novikov, U. Zywietz, R. L. Eriksen, C. Reinhardt, S. I. Bozhevolnyi, and B. N. Chichkov, “Demonstration of magnetic dipole resonances of dielectric nanospheres in the visible region,” Nano Lett. 12, 3749–3755 (2012).
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ACS Nano (4)

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]

I. Staude, A. E. Miroshnichenko, M. Decker, N. T. Fofang, S. Liu, E. Gonzales, J. Dominguez, T. S. Luk, D. N. Neshev, I. Brener, and Y. Kivshar, “Tailoring directional scattering through magnetic and electric resonances in subwavelength silicon nanodisks,” ACS Nano 7, 7824–7832 (2013).
[Crossref]

E. Xifré-Pérez, L. Shi, U. Tuzer, R. Fenollosa, F. Ramiro-Manzano, R. Quidant, and F. Meseguer, “Mirror-image-induced magnetic modes,” ACS Nano 7, 664–668 (2013).
[Crossref]

M. Abbarchi, M. Naffouti, B. Vial, A. Benkouider, L. Lermusiaux, L. Favre, A. Ronda, S. Bidault, I. Berbezier, and N. Bonod, “Wafer scale formation of monocrystalline silicon-based Mie resonators via silicon-on-insulator dewetting,” ACS Nano 8, 11181–11190 (2014).
[Crossref]

ACS Photon. (3)

U. Zywietz, M. K. Schmidt, A. B. Evlyukhin, C. Reinhardt, J. Aizpurua, and B. N. Chichkov, “Electromagnetic resonances of silicon nanoparticle dimers in the visible,” ACS Photon. 2, 913–920 (2015).
[Crossref]

A. E. Miroshnichenko, A. B. Evlyukhin, Y. S. Kivshar, and B. N. Chichkov, “Substrate-induced resonant magnetoelectric effects for dielectric nanoparticles,” ACS Photon. 2, 1423–1428 (2015).
[Crossref]

P. Moitra, B. A. Slovick, W. Li, I. I. Kravchencko, D. P. Briggs, S. Krishnamurthy, and J. Valentine, “Large-scale all-dielectric metamaterial perfect reflectors,” ACS Photon. 2, 692–698 (2015).
[Crossref]

Adv. Mater. (1)

S. Zhang, R. Jiang, Y. M. Xie, Q. Ruan, B. Yang, J. Wang, and H. Q. Lin, “Colloidal moderate-refractive-index Cu2O nanospheres as visible-region nanoantennas with electromagnetic resonance and directional light-scattering properties,” Adv. Mater. 27, 7432–7439 (2015).
[Crossref]

Adv. Opt. Mater. (2)

A. Jain, P. Moitra, T. Koschny, J. Valentine, and C. M. Soukoulis, “Electric and magnetic response in dielectric dark states for low loss subwavelength optical meta atoms,” Adv. Opt. Mater. 3, 1431–1438 (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]

Appl. Phys. Lett. (2)

S. Tsoi, F. J. Bezares, A. Giles, J. P. Long, O. J. Glembocki, J. D. Caldwell, and J. Owrutsky, “Experimental demonstration of the optical lattice resonance in arrays of Si nanoresonators,” Appl. Phys. Lett. 108, 111101 (2016).
[Crossref]

H. Sai, H. Fujiwara, M. Kondo, and Y. Kanamori, “Enhancement of light trapping in thin-film hydrogenated microcrystalline Si solar cells using back reflectors with self-ordered dimple pattern,” Appl. Phys. Lett. 93, 143501 (2008).
[Crossref]

IEEE J. Photovolt. (1)

P. Spinelli and A. Polman, “Light trapping in thin crystalline Si solar cells using surface Mie scatterers,” IEEE J. Photovolt. 4, 554–559 (2014).
[Crossref]

J. Appl. Phys. (2)

D. Sikdar, W. Cheng, and M. Premaratne, “Optically resonant magneto-electric cubic nanoantennas for ultra-directional light scattering,” J. Appl. Phys. 117, 083101 (2015).
[Crossref]

E. Almpanis and N. Papanikolaou, “Designing photonic structures of nanosphere arrays on reflectors for total absorption,” J. Appl. Phys. 114, 083106 (2013).
[Crossref]

J. Opt. (1)

M. Albooyeh and C. R. Simovski, “Substrate-induced bianisotropy in plasmonic grids,” J. Opt. 13, 105102 (2011).
[Crossref]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. B (1)

Laser Photon. Rev. (1)

Y. F. Yu, A. Y. Zhu, R. Paniagua-Domınguez, 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]

Metamaterials (1)

M. Albooyeh, D. Morits, and C. R. Simovski, “Electromagnetic characterization of substrated metasurfaces,” Metamaterials 5, 178–205 (2011).
[Crossref]

Nano Lett. (7)

P. Spinelli, M. Hebbink, R. de Waele, L. Black, F. Lenzmann, and A. Polman, “Optical impedance matching using coupled plasmonic nanoparticle arrays,” Nano Lett. 11, 1760–1765 (2011).
[Crossref]

A. B. Evlyukhin, S. M. Novikov, U. Zywietz, R. L. Eriksen, C. Reinhardt, S. I. Bozhevolnyi, and B. N. Chichkov, “Demonstration of magnetic dipole resonances of dielectric nanospheres in the visible region,” Nano Lett. 12, 3749–3755 (2012).
[Crossref]

S. Person, M. Jain, Z. Lapin, J. J. Sáenz, G. Wicks, and L. Novotny, “Demonstration of zero optical backscattering from single nanoparticles,” Nano Lett. 13, 1806–1809 (2013).
[Crossref]

H. Tan, R. Santbergen, A. H. M. Smets, and M. Zeman, “Plasmonic light trapping in thin-film silicon solar cells with improved self-assembled silver nanoparticles,” Nano Lett. 12, 4070–4076 (2012).
[Crossref]

T. Lewi, P. P. Iyer, N. A. Butakov, A. A. Mikhailovsky, and J. A. Schuller, “Widely tunable infrared antennas using free carrier refraction,” Nano Lett. 15, 8188–8193 (2015).
[Crossref]

L. S. Slaughter, B. A. Willingham, W.-S. Chang, M. H. Chester, N. Ogden, and S. Link, “Toward plasmonic polymers,” Nano Lett. 12, 3967–3972 (2012).
[Crossref]

D. Solis, B. Willingham, S. L. Nauert, L. S. Slaughter, J. Olson, P. Swanglap, A. Paul, W.-S. Chang, and S. Link, “Electromagnetic energy transport in nanoparticle chains via dark plasmon modes,” Nano Lett. 12, 1349–1353 (2012).
[Crossref]

Nanoscale (4)

M. Naffouti, T. David, A. Benkouider, L. Favre, A. Ronda, I. Berbezier, S. Bidault, N. Bonod, and M. Abbarchi, “Fabrication of poly-crystalline Si-based Mie resonators via amorphous Si on SiO2 dewetting,” Nanoscale 8, 2844–2849 (2016).
[Crossref]

P. A. Dmitriev, S. V. Makarov, V. A. Milichko, I. S. Mukhin, A. S. Gudovskikh, A. A. Sitnikova, A. K. Samusev, A. E. Krasnok, and P. A. Belov, “Laser fabrication of crystalline silicon nanoresonators from an amorphous film for low-loss all-dielectric nanophotonics,” Nanoscale 8, 5043–5048 (2016).
[Crossref]

A. E. Krasnok, C. R. Simovski, P. A. Belov, and Y. S. Kivshar, “Superdirective dielectric nanoantennas,” Nanoscale 6, 7354–7361 (2014).
[Crossref]

P. A. Dmitriev, D. G. Baranov, V. A. Milichko, S. V. Makarov, I. S. Mukhin, A. K. Samusev, A. E. Krasnok, P. A. Belov, and Y. S. Kivshar, “Resonant Raman,” Nanoscale 8, 9721–9726 (2016).
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Nanotechnology (1)

M. A. Cole, D. A. Powell, and I. V. Shadrivov, “Strong terahertz absorption in all-dielectric Huygens’ metasurfaces,” Nanotechnology 27, 424003 (2016).
[Crossref]

Nat. Commun. (5)

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Figures (7)

Fig. 1.
Fig. 1.

(a) Schematic view of the square periodic array of nanospheres on the substrate with permittivity εs. (b) Transmittance T=|tMS2| through the metasurface, that is, the case εs=1 (d=335  nm and R=60  nm). Between EDR and MDR, the transmittance is high (T0.8), and results of Eqs. (2) and (3) are similar to results obtained with Eq. (S2) of Ref. [51]. However, for the wavelength of resonances, this approximation does not give good results. (c) The absorbance of the sphere array for different substrate permittivity εs (results of the whole-structure numerical simulations, d=335  nm and R=60  nm). (d) The reflectance of the nanosphere metasurfaces for the same parameters as absorbance in (c). Each plot is shifted by 0.2 in respect to the previous one. Solid lines: numerical simulations. Two dips at λK1=559  nm and λK2=417  nm (εs=1) correspond to the wavelengths of near-zero reflectance where the first Kerker condition is satisfied. Dashed lines: calculations according to the model where contributions of bare substrates and nanoparticle array in the air [εs=1] calculated separately and added by Eq. (3). “s1” denotes substrate when reflectance between EDR and MDR is close to zero. Corresponding antiphase Kerker point is shown on (d) for εs=εs1=4 and λA=482  nm. The destructive interference occurs for 2.5<εs<6, and high reflectance is observed for the case of εs=εs2=20, where “s2” denotes the substrate with the highest reflectance between EDR and MDR.

Fig. 2.
Fig. 2.

Ratio of backward to forward scattered energy of individual silicon nanoparticle with R=60  nm in the air compared to normalized absorption spectrum. Top inset: directivity plots for the different wavelengths of pronounced forward/backward scattering: the ratio is the highest in AK and the lowest in K1 and K2, as well as near the dipole resonances (EDR and MDR).

Fig. 3.
Fig. 3.

(a) Decomposition of the structure into the metasurface (i.e., nanoparticle array, left) and the substrate (right). (b, c) Artistic view of vector diagrams depicting electric field of the incident wave E0 and reflected field Esr at z=0 as well as decomposition of the metasurface-reflected field EMSr into contributions of electric and magnetic dipole moments EMS,er and EMS,mr, respectively, for two different cases: (b) εs=εs1=4, λA=482  nm (perfect match of reflected waves and near-zero reflectance) and (c) εs=εs2=20, λA=482  nm (non-zero reflectance).

Fig. 4.
Fig. 4.

Reflectance spectra of metasurfaces on Si substrate: (a) numerical simulations and (b) calculations according to the semi-analytical model (nanosphere array of R=60  nm and different array periods d=130400  nm). Being defined as a maximum of scattering cross section (see Fig. S7 in Ref. [51]), MDR and EDR of single nanosphere with R=60  nm are shown by the dashed lines: blue and light blue, respectively. Color bar is the same for (a) and (b). (c) The absorbance of the nanosphere array on the Si substrate. (d) The transmittance of metasurface (nanosphere array without substrate).

Fig. 5.
Fig. 5.

Reflectance spectra of metasurface on Si substrate for different angles of incidence α in TM polarization (nanosphere array of R=60  nm and d=335  nm). MDR and EDR of single nanosphere are shown by the dashed lines: blue and light blue, respectively. Diffraction effect defined as λd=d(1+sinα) is shown by the red solid line. Results for TE polarization and absorbance spectra can be found in Fig. S6 of Ref. [51].

Fig. 6.
Fig. 6.

Reflectance spectrum for a disordered array of silicon nanospheres on top of Si substrate (blue solid line) in comparison to reflectance from bare Si substrate (black dotted line) and from the 55 nm thick Si3N4 layer on top of the Si substrate (light blue solid line). Inset: top view of simulation domain with 49 nanospheres, radii R=5080  nm (approximately equal distribution), and the total area is 1.7×1.7μm2 (approximately 240×240  nm2 per nanoparticle). The 55 nm thick Si3N4 layer is chosen as an optimal single-layer antireflective coating that provides reflectance minimum at wavelength 470 nm and matches the reflection minimum of nanoparticle array under consideration.

Fig. 7.
Fig. 7.

(a) Schematic view of the square periodic array of nanodisks on top of the Si substrate with a thin intermediate layer of SiO2 (thickness s). (b) The transmittance of the metasurface without substrate and buffer layer (d=350  nm). (c) The absorbance of the nanodisk array on the substrate for different thickness of the buffer layer s=050  nm (results of the whole-structure numerical simulations, d=350  nm). (d)–(g) Nanoparticle modes in the absence (d),(f) and presence (e),(g) of the silica buffer layer (sc=15  nm): (d),(e) magnetic field amplitude at the wavelength of MDR (λMD=513  nm) in both cases with the same color map, and (f),(g) electric field amplitude at the wavelength of EDR (λED=448  nm) in both cases with the same color map. (h),(i) Reflectance spectra for nanodisk array on the SiO2 buffer layer and Si substrate for different thickness of the buffer layer: (h) numerical simulations and (i) calculations by transfer-matrix method (color bar is the same for both panels). Red dashed line corresponds to sc=15  nm, so that for s>sc both resonances are presented and semi-analytical model provides results that agree well with numerical simulations.

Equations (5)

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rMS=ik02d2(αeeffαmeff),tMS=1+ik02d2(αeeff+αmeff),
EMSr=EMS,er+EMS,mr,
EMS,er=ik02d2αeeffE0andEMS,mr=ik02d2αmeffE0
Esr=tMS2rse2ik0RE0+tMS2rMSrs2e4ik0RE0+=tMS2rse2ik0R/(1rMSrse2ik0R)E0.
Etotr=EMSr+Esr.

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