Abstract

Relating the electromagnetic scattering and absorption properties of an individual particle to the reflection and transmission coefficients of a two-dimensional material composed of these particles is a crucial concept that has driven both fundamental and applied physics. It is at the heart of both the characterization of material properties as well as the phase and amplitude engineering of a wave. Here we propose a multipolar description of the reflection and transmission coefficients across a monolayer of particles using a vector spherical harmonic decomposition. This enables us to provide a generalized condition for perfect absorption which occurs when both the so-called generalized Kerker condition is reached and when the superposition of odd and even multipoles reaches a critical value. Using these conditions, we are able to propose two very different designs of two-dimensional materials that perfectly absorb a plane electromagnetic wave under normal incidence. One is an infinite array of silica microspheres that operates at mid-infrared frequencies, while the other is an infinite array of germanium nano-clusters that operates at visible frequencies. Both systems operate in a deeply multipolar regime. Our findings are important to the metamaterials and metasurfaces communities who design materials mainly restricted to the dipolar behavior of individual resonators, as well as the self-assembly and nanochemistry communities who separate the individual particle synthesis from the materials assembly.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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2019 (2)

R. Alaee, C. Rockstuhl, and I. Fernandez-Corbaton, “Exact multipolar decompositions with applications in nanophotonics,” Adv. Opt. Mater. 7, 1800783 (2019).
[Crossref]

P. D. Terekhov, V. E. Babicheva, K. V. Baryshnikova, A. S. Shalin, A. Karabchevsky, and A. B. Evlyukhin, “Multipole analysis of dielectric metasurfaces composed of nonspherical nanoparticles and lattice invisibility effect,” Phys. Rev. B 99, 045424 (2019).
[Crossref]

2018 (2)

W. Liu and Y. S. Kivshar, “Generalized kerker effects in nanophotonics and meta-optics,” Opt. Express 26, 13085–13105 (2018).
[Crossref] [PubMed]

J. Tian, H. Luo, Q. Li, X. Pei, K. Du, and M. Qiu, “Near-infrared super-absorbing all-dielectric metasurface based on single-layer germanium nanostructures,” Laser Photon. Rev. 12, 1800076 (2018).
[Crossref]

2017 (9)

N. Odebo Lank, R. Verre, P. Johansson, and M. Kall, “Large-scale silicon nanophotonic metasurfaces with polarization independent near-perfect absorption,” Nano Lett. 17, 3054–3060 (2017).
[Crossref] [PubMed]

X. Ming, X. Liu, L. Sun, and W. J. Padilla, “Degenerate critical coupling in all-dielectric metasurface absorbers,” Opt. Express 25, 24658–24669 (2017).
[Crossref] [PubMed]

R. Dezert, P. Richetti, and A. Baron, “Isotropic huygens dipoles and multipoles with colloidal particles,” Phys. Rev. B 96, 180201 (2017).
[Crossref]

V. Ponsinet, A. Baron, E. Pouget, Y. Okazaki, R. Oda, and P. Barois, “Self-assembled nanostructured metamaterials,” EPL 119, 14004 (2017).
[Crossref]

W. Liu, “Generalized magnetic mirrors,” Phys. Rev. Let. 119, 123902 (2017).
[Crossref]

X. Liu, K. Fan, I. V. Shadrivov, and W. J. Padilla, “Experimental realization of a terahertz all-dielectric metasurface absorber,” Opt. Express 25, 191–201 (2017).
[Crossref] [PubMed]

P. Bowen, A. Baron, and D. Smith, “Effective-medium description of a metasurface composed of a periodic array of nanoantennas coupled to a metallic film,” Phys. Rev. A 95, 033822 (2017).
[Crossref]

R. Alaee, M. Albooyeh, and C. Rockstuhl, “Theory of metasurface based perfect absorbers,” J. Phys. D Appl. Phys. 50, 503002 (2017).
[Crossref]

M. Khorasaninejad and F. Capasso, “Metalenses: Versatile multifunctional photonic components,” Science 358, eaam8100 (2017).
[Crossref] [PubMed]

2016 (4)

S. B. Glybovski, S. A. Tretyakov, P. A. Belov, Y. S. Kivshar, and C. R. Simovski, “Metasurfaces: From microwaves to visible,” Phys. Rep. 634, 1–72 (2016).
[Crossref]

S. Kruk, B. Hopkins, I. I. Kravchenko, A. Miroshnichenko, D. N. Neshev, and Y. S. Kivshar, “Invited article: Broadband highly efficient dielectric metadevices for polarization control,” APL Photonics 1, 030801 (2016).
[Crossref]

S. Gómez-Graña, A. Le Beulze, M. Treguer-Delapierre, S. Mornet, E. Duguet, E. Grana, E. Cloutet, G. Hadziioannou, J. Leng, and J.-B. Salmon et al., “Hierarchical self-assembly of a bulk metamaterial enables isotropic magnetic permeability at optical frequencies,” Mater. Horiz. 3, 596–601 (2016).
[Crossref]

A. Baron, A. Aradian, V. Ponsinet, and P. Barois, “Self-assembled optical metamaterials,” Opt. Laser Technol. 82, 94–100 (2016).
[Crossref]

2015 (6)

M. J. Rozin, D. A. Rosen, T. J. Dill, and A. R. Tao, “Colloidal metasurfaces displaying near-ideal and tunable light absorbance in the infrared,” Nat. Commun. 6, 7325 (2015).
[Crossref] [PubMed]

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

A. Arbabi, Y. Horie, M. Bagheri, and A. Faraon, “Dielectric metasurfaces for complete control of phase and polarization with subwavelength spatial resolution and high transmission,” Nat. Nanotechnol. 10, 937–943 (2015).
[Crossref] [PubMed]

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]

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

Y. Radi, V. S. Asadchy, S. U. Kosulnikov, M. M. Omelyanovich, D. Morits, A. V. Osipov, C. R. Simovski, and S. A. Tretyakov, “Full light absorption in single arrays of spherical nanoparticles,” ACS Photonics 2, 653–660 (2015).
[Crossref]

2014 (3)

E. Poutrina and A. Urbas, “Multipole analysis of unidirectional light scattering from plasmonic dimers,” J. Opt. 16, 114005 (2014).
[Crossref]

V. Savinov, V. Fedotov, and N. I. Zheludev, “Toroidal dipolar excitation and macroscopic electromagnetic properties of metamaterials,” Phys. Rev. B 89, 205112 (2014).
[Crossref]

C. A. Valagiannopoulos and S. A. Tretyakov, “Symmetric absorbers realized as gratings of pec cylinders covered by ordinary dielectrics,” IEEE Trans. Antennas Propag. 62, 5089–5098 (2014).
[Crossref]

2012 (2)

S. Thongrattanasiri, F. H. Koppens, and F. J. G. De Abajo, “Complete optical absorption in periodically patterned graphene,” Phys. Rev. Lett. 108, 047401 (2012).
[Crossref] [PubMed]

P. Grahn, A. Shevchenko, and M. Kaivola, “Electromagnetic multipole theory for optical nanomaterials,” New J. Phys. 14, 093033 (2012).
[Crossref]

2011 (1)

S. Mühlig, C. Menzel, C. Rockstuhl, and F. Lederer, “Multipole analysis of meta-atoms,” Metamaterials 5, 64–73 (2011).
[Crossref]

2010 (1)

A. B. Evlyukhin, C. Reinhardt, A. Seidel, B. S. Lukyanchuk, and B. N. Chichkov, “Optical response features of si-nanoparticle arrays,” Phys. Rev. B 82, 045404 (2010).
[Crossref]

2003 (1)

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

1995 (1)

Alaee, R.

R. Alaee, C. Rockstuhl, and I. Fernandez-Corbaton, “Exact multipolar decompositions with applications in nanophotonics,” Adv. Opt. Mater. 7, 1800783 (2019).
[Crossref]

R. Alaee, M. Albooyeh, and C. Rockstuhl, “Theory of metasurface based perfect absorbers,” J. Phys. D Appl. Phys. 50, 503002 (2017).
[Crossref]

Albooyeh, M.

R. Alaee, M. Albooyeh, and C. Rockstuhl, “Theory of metasurface based perfect absorbers,” J. Phys. D Appl. Phys. 50, 503002 (2017).
[Crossref]

Aradian, A.

A. Baron, A. Aradian, V. Ponsinet, and P. Barois, “Self-assembled optical metamaterials,” Opt. Laser Technol. 82, 94–100 (2016).
[Crossref]

Arbabi, A.

A. Arbabi, Y. Horie, M. Bagheri, and A. Faraon, “Dielectric metasurfaces for complete control of phase and polarization with subwavelength spatial resolution and high transmission,” Nat. Nanotechnol. 10, 937–943 (2015).
[Crossref] [PubMed]

Asadchy, V. S.

Y. Radi, V. S. Asadchy, S. U. Kosulnikov, M. M. Omelyanovich, D. Morits, A. V. Osipov, C. R. Simovski, and S. A. Tretyakov, “Full light absorption in single arrays of spherical nanoparticles,” ACS Photonics 2, 653–660 (2015).
[Crossref]

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

Babicheva, V. E.

P. D. Terekhov, V. E. Babicheva, K. V. Baryshnikova, A. S. Shalin, A. Karabchevsky, and A. B. Evlyukhin, “Multipole analysis of dielectric metasurfaces composed of nonspherical nanoparticles and lattice invisibility effect,” Phys. Rev. B 99, 045424 (2019).
[Crossref]

Bagheri, M.

A. Arbabi, Y. Horie, M. Bagheri, and A. Faraon, “Dielectric metasurfaces for complete control of phase and polarization with subwavelength spatial resolution and high transmission,” Nat. Nanotechnol. 10, 937–943 (2015).
[Crossref] [PubMed]

Barois, P.

V. Ponsinet, A. Baron, E. Pouget, Y. Okazaki, R. Oda, and P. Barois, “Self-assembled nanostructured metamaterials,” EPL 119, 14004 (2017).
[Crossref]

A. Baron, A. Aradian, V. Ponsinet, and P. Barois, “Self-assembled optical metamaterials,” Opt. Laser Technol. 82, 94–100 (2016).
[Crossref]

Baron, A.

V. Ponsinet, A. Baron, E. Pouget, Y. Okazaki, R. Oda, and P. Barois, “Self-assembled nanostructured metamaterials,” EPL 119, 14004 (2017).
[Crossref]

R. Dezert, P. Richetti, and A. Baron, “Isotropic huygens dipoles and multipoles with colloidal particles,” Phys. Rev. B 96, 180201 (2017).
[Crossref]

P. Bowen, A. Baron, and D. Smith, “Effective-medium description of a metasurface composed of a periodic array of nanoantennas coupled to a metallic film,” Phys. Rev. A 95, 033822 (2017).
[Crossref]

A. Baron, A. Aradian, V. Ponsinet, and P. Barois, “Self-assembled optical metamaterials,” Opt. Laser Technol. 82, 94–100 (2016).
[Crossref]

Baryshnikova, K. V.

P. D. Terekhov, V. E. Babicheva, K. V. Baryshnikova, A. S. Shalin, A. Karabchevsky, and A. B. Evlyukhin, “Multipole analysis of dielectric metasurfaces composed of nonspherical nanoparticles and lattice invisibility effect,” Phys. Rev. B 99, 045424 (2019).
[Crossref]

Belov, P. A.

S. B. Glybovski, S. A. Tretyakov, P. A. Belov, Y. S. Kivshar, and C. R. Simovski, “Metasurfaces: From microwaves to visible,” Phys. Rep. 634, 1–72 (2016).
[Crossref]

Bohren, C. F.

C. F. Bohren and D. R. Huffman, Absorption and scattering of light by small particles (John Wiley & Sons, 2008).

Bowen, P.

P. Bowen, A. Baron, and D. Smith, “Effective-medium description of a metasurface composed of a periodic array of nanoantennas coupled to a metallic film,” Phys. Rev. A 95, 033822 (2017).
[Crossref]

Brener, I.

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]

Capasso, F.

M. Khorasaninejad and F. Capasso, “Metalenses: Versatile multifunctional photonic components,” Science 358, eaam8100 (2017).
[Crossref] [PubMed]

Chichkov, B. N.

A. B. Evlyukhin, C. Reinhardt, A. Seidel, B. S. Lukyanchuk, and B. N. Chichkov, “Optical response features of si-nanoparticle arrays,” Phys. Rev. B 82, 045404 (2010).
[Crossref]

Cloutet, E.

S. Gómez-Graña, A. Le Beulze, M. Treguer-Delapierre, S. Mornet, E. Duguet, E. Grana, E. Cloutet, G. Hadziioannou, J. Leng, and J.-B. Salmon et al., “Hierarchical self-assembly of a bulk metamaterial enables isotropic magnetic permeability at optical frequencies,” Mater. Horiz. 3, 596–601 (2016).
[Crossref]

De Abajo, F. J. G.

S. Thongrattanasiri, F. H. Koppens, and F. J. G. De Abajo, “Complete optical absorption in periodically patterned graphene,” Phys. Rev. Lett. 108, 047401 (2012).
[Crossref] [PubMed]

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]

Dezert, R.

R. Dezert, P. Richetti, and A. Baron, “Isotropic huygens dipoles and multipoles with colloidal particles,” Phys. Rev. B 96, 180201 (2017).
[Crossref]

Dill, T. J.

M. J. Rozin, D. A. Rosen, T. J. Dill, and A. R. Tao, “Colloidal metasurfaces displaying near-ideal and tunable light absorbance in the infrared,” Nat. Commun. 6, 7325 (2015).
[Crossref] [PubMed]

Doicu, A.

A. Doicu, T. Wriedt, and Y. A. Eremin, Light scattering by systems of particles: null-field method with discrete sources: theory and programs, vol. 124 (Springer, 2006).
[Crossref]

Dominguez, J.

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]

Du, K.

J. Tian, H. Luo, Q. Li, X. Pei, K. Du, and M. Qiu, “Near-infrared super-absorbing all-dielectric metasurface based on single-layer germanium nanostructures,” Laser Photon. Rev. 12, 1800076 (2018).
[Crossref]

Duguet, E.

S. Gómez-Graña, A. Le Beulze, M. Treguer-Delapierre, S. Mornet, E. Duguet, E. Grana, E. Cloutet, G. Hadziioannou, J. Leng, and J.-B. Salmon et al., “Hierarchical self-assembly of a bulk metamaterial enables isotropic magnetic permeability at optical frequencies,” Mater. Horiz. 3, 596–601 (2016).
[Crossref]

Eremin, Y. A.

A. Doicu, T. Wriedt, and Y. A. Eremin, Light scattering by systems of particles: null-field method with discrete sources: theory and programs, vol. 124 (Springer, 2006).
[Crossref]

Evlyukhin, A. B.

P. D. Terekhov, V. E. Babicheva, K. V. Baryshnikova, A. S. Shalin, A. Karabchevsky, and A. B. Evlyukhin, “Multipole analysis of dielectric metasurfaces composed of nonspherical nanoparticles and lattice invisibility effect,” Phys. Rev. B 99, 045424 (2019).
[Crossref]

A. B. Evlyukhin, C. Reinhardt, A. Seidel, B. S. Lukyanchuk, and B. N. Chichkov, “Optical response features of si-nanoparticle arrays,” Phys. Rev. B 82, 045404 (2010).
[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, K.

Faniayeu, I. A.

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

Faraon, A.

A. Arbabi, Y. Horie, M. Bagheri, and A. Faraon, “Dielectric metasurfaces for complete control of phase and polarization with subwavelength spatial resolution and high transmission,” Nat. Nanotechnol. 10, 937–943 (2015).
[Crossref] [PubMed]

Fedotov, V.

V. Savinov, V. Fedotov, and N. I. Zheludev, “Toroidal dipolar excitation and macroscopic electromagnetic properties of metamaterials,” Phys. Rev. B 89, 205112 (2014).
[Crossref]

Fernandez-Corbaton, I.

R. Alaee, C. Rockstuhl, and I. Fernandez-Corbaton, “Exact multipolar decompositions with applications in nanophotonics,” Adv. Opt. Mater. 7, 1800783 (2019).
[Crossref]

Glybovski, S. B.

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N. Odebo Lank, R. Verre, P. Johansson, and M. Kall, “Large-scale silicon nanophotonic metasurfaces with polarization independent near-perfect absorption,” Nano Lett. 17, 3054–3060 (2017).
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N. Odebo Lank, R. Verre, P. Johansson, and M. Kall, “Large-scale silicon nanophotonic metasurfaces with polarization independent near-perfect absorption,” Nano Lett. 17, 3054–3060 (2017).
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S. Kruk, B. Hopkins, I. I. Kravchenko, A. Miroshnichenko, D. N. Neshev, and Y. S. Kivshar, “Invited article: Broadband highly efficient dielectric metadevices for polarization control,” APL Photonics 1, 030801 (2016).
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N. Odebo Lank, R. Verre, P. Johansson, and M. Kall, “Large-scale silicon nanophotonic metasurfaces with polarization independent near-perfect absorption,” Nano Lett. 17, 3054–3060 (2017).
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Pei, X.

J. Tian, H. Luo, Q. Li, X. Pei, K. Du, and M. Qiu, “Near-infrared super-absorbing all-dielectric metasurface based on single-layer germanium nanostructures,” Laser Photon. Rev. 12, 1800076 (2018).
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E. F. Kuester, M. A. Mohamed, M. Piket-May, and C. L. Holloway, “Averaged transition conditions for electromagnetic fields at a metafilm,” IEEE Trans. Antennas Propag. 51, 2641–2651 (2003).
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J. Tian, H. Luo, Q. Li, X. Pei, K. Du, and M. Qiu, “Near-infrared super-absorbing all-dielectric metasurface based on single-layer germanium nanostructures,” Laser Photon. Rev. 12, 1800076 (2018).
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Y. Radi, V. S. Asadchy, S. U. Kosulnikov, M. M. Omelyanovich, D. Morits, A. V. Osipov, C. R. Simovski, and S. A. Tretyakov, “Full light absorption in single arrays of spherical nanoparticles,” ACS Photonics 2, 653–660 (2015).
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V. S. Asadchy, I. A. Faniayeu, Y. Radi, S. Khakhomov, I. Semchenko, and S. Tretyakov, “Broadband reflectionless metasheets: frequency-selective transmission and perfect absorption,” Phys. Rev. X 5, 031005 (2015).

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A. B. Evlyukhin, C. Reinhardt, A. Seidel, B. S. Lukyanchuk, and B. N. Chichkov, “Optical response features of si-nanoparticle arrays,” Phys. Rev. B 82, 045404 (2010).
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Shalin, A. S.

P. D. Terekhov, V. E. Babicheva, K. V. Baryshnikova, A. S. Shalin, A. Karabchevsky, and A. B. Evlyukhin, “Multipole analysis of dielectric metasurfaces composed of nonspherical nanoparticles and lattice invisibility effect,” Phys. Rev. B 99, 045424 (2019).
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P. Grahn, A. Shevchenko, and M. Kaivola, “Electromagnetic multipole theory for optical nanomaterials,” New J. Phys. 14, 093033 (2012).
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Y. Ra’Di, C. Simovski, and S. Tretyakov, “Thin perfect absorbers for electromagnetic waves: theory, design, and realizations,” Phys. Rev. Appl. 3, 037001 (2015).
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S. B. Glybovski, S. A. Tretyakov, P. A. Belov, Y. S. Kivshar, and C. R. Simovski, “Metasurfaces: From microwaves to visible,” Phys. Rep. 634, 1–72 (2016).
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Y. Radi, V. S. Asadchy, S. U. Kosulnikov, M. M. Omelyanovich, D. Morits, A. V. Osipov, C. R. Simovski, and S. A. Tretyakov, “Full light absorption in single arrays of spherical nanoparticles,” ACS Photonics 2, 653–660 (2015).
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P. D. Terekhov, V. E. Babicheva, K. V. Baryshnikova, A. S. Shalin, A. Karabchevsky, and A. B. Evlyukhin, “Multipole analysis of dielectric metasurfaces composed of nonspherical nanoparticles and lattice invisibility effect,” Phys. Rev. B 99, 045424 (2019).
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S. Thongrattanasiri, F. H. Koppens, and F. J. G. De Abajo, “Complete optical absorption in periodically patterned graphene,” Phys. Rev. Lett. 108, 047401 (2012).
[Crossref] [PubMed]

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J. Tian, H. Luo, Q. Li, X. Pei, K. Du, and M. Qiu, “Near-infrared super-absorbing all-dielectric metasurface based on single-layer germanium nanostructures,” Laser Photon. Rev. 12, 1800076 (2018).
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V. S. Asadchy, I. A. Faniayeu, Y. Radi, S. Khakhomov, I. Semchenko, and S. Tretyakov, “Broadband reflectionless metasheets: frequency-selective transmission and perfect absorption,” Phys. Rev. X 5, 031005 (2015).

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[Crossref]

Y. Radi, V. S. Asadchy, S. U. Kosulnikov, M. M. Omelyanovich, D. Morits, A. V. Osipov, C. R. Simovski, and S. A. Tretyakov, “Full light absorption in single arrays of spherical nanoparticles,” ACS Photonics 2, 653–660 (2015).
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N. Odebo Lank, R. Verre, P. Johansson, and M. Kall, “Large-scale silicon nanophotonic metasurfaces with polarization independent near-perfect absorption,” Nano Lett. 17, 3054–3060 (2017).
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Zheludev, N. I.

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ACS Photonics (1)

Y. Radi, V. S. Asadchy, S. U. Kosulnikov, M. M. Omelyanovich, D. Morits, A. V. Osipov, C. R. Simovski, and S. A. Tretyakov, “Full light absorption in single arrays of spherical nanoparticles,” ACS Photonics 2, 653–660 (2015).
[Crossref]

Adv. Opt. Mater. (2)

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]

R. Alaee, C. Rockstuhl, and I. Fernandez-Corbaton, “Exact multipolar decompositions with applications in nanophotonics,” Adv. Opt. Mater. 7, 1800783 (2019).
[Crossref]

APL Photonics (1)

S. Kruk, B. Hopkins, I. I. Kravchenko, A. Miroshnichenko, D. N. Neshev, and Y. S. Kivshar, “Invited article: Broadband highly efficient dielectric metadevices for polarization control,” APL Photonics 1, 030801 (2016).
[Crossref]

Appl. Opt. (1)

EPL (1)

V. Ponsinet, A. Baron, E. Pouget, Y. Okazaki, R. Oda, and P. Barois, “Self-assembled nanostructured metamaterials,” EPL 119, 14004 (2017).
[Crossref]

IEEE Trans. Antennas Propag. (2)

C. A. Valagiannopoulos and S. A. Tretyakov, “Symmetric absorbers realized as gratings of pec cylinders covered by ordinary dielectrics,” IEEE Trans. Antennas Propag. 62, 5089–5098 (2014).
[Crossref]

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

J. Opt. (1)

E. Poutrina and A. Urbas, “Multipole analysis of unidirectional light scattering from plasmonic dimers,” J. Opt. 16, 114005 (2014).
[Crossref]

J. Phys. D Appl. Phys. (1)

R. Alaee, M. Albooyeh, and C. Rockstuhl, “Theory of metasurface based perfect absorbers,” J. Phys. D Appl. Phys. 50, 503002 (2017).
[Crossref]

Laser Photon. Rev. (1)

J. Tian, H. Luo, Q. Li, X. Pei, K. Du, and M. Qiu, “Near-infrared super-absorbing all-dielectric metasurface based on single-layer germanium nanostructures,” Laser Photon. Rev. 12, 1800076 (2018).
[Crossref]

Mater. Horiz. (1)

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Figures (5)

Fig. 1
Fig. 1 Artistic rendition of the multipolar decomposition of the field scattered by an array of particles. The particles are reprensented as spheres but the shape can be arbitrary. An electromagnetic plane wave Ei with wavevector k is incident on the metasurface. Current densities J are produced within the particles which radiate a scattered field Es in both the top and bottom directions. The interference of the incident field with the scattered field produces a reflected (Er) and transmitted field (Et). The current density within a single particle in the array is decomposed on a vector spherical harmonic basis which enables a determination of the multipole coefficients an,m and bn,m of the unit cell.
Fig. 2
Fig. 2 Test of the multipole decomposition. (a) Reflectance (R), transmittance (T) and absorption (A) spectra of an infinite square periodic array of period a composed of a spherical particle of index N = 4 + 0.05i shown in the inset. The surface fill fraction is 0.4. The continous lines are the spectra calculated from the input and output ports, while the dotted curves are computed from the current decompositions inside the particle and introduced in eqs. 2 and 3. The absorption is caculated directly from the currents. The green curve equal to 1 across the spectrum is R + T + A and ensures energy conservation. (b) Spectra of the magnitude of the multipolar coefficients. Continuous (dashed) lines represent the electric (magnetic) multipoles.
Fig. 3
Fig. 3 Design of perfect absorbers using the multipolar behavior of individual particles. (a) Wavelength dependence of the sum of even and odd multipole coefficients of an individual SiO2 microsphere in vacuum that is 4.12 μm in radius, calculated using Mie theory. (b) Wavelength dependence of the sum of even and odd multipole coefficients of the SiO2 microsphere in an infinite square array with a surface fill fraction of 0.7. (c) Spectra of R, T and A calculated for the square array of SiO2 microspheres, revealing the perfect absorption behavior calculated using the same methods as those used for Fig. 2. (d) Spectra of the modulus of the multipole coefficients retrieved from the current decomposition for the SiO2 microsphere array. (e–h) are respectively the same quantities as those reprensented on panels (a–d) but for a particle cluster composed of thirteen Ge particles that are 75 nm in redius and are pseudo-homgenously distributed in a sphere through repulsive interaction, with a volume fraction of 0.35. The square array made of these clusters has a surface fill fraction of 0.6. The individual cluster was calculated and explored using the T-matrix method.
Fig. 4
Fig. 4 Validation of the multipole decomposition with unsymmetrical particles. (a) Reflectance (R), transmittance (T) and absorption (A) spectra of an infinite square periodic array of period a composed of a 3 times truncated spherical particle. The continuous lines are the spectra of the specular reflection and transmission calculated from the input and output ports, while the dashed curves are computed from the extracted multipoles as introduced in eqs. 19 and 18. The green curve equal to 1 across the spectrum is R + T + A ensuring energy conservation. (b) Spectra of the magnitude of the multipole coefficients of order m = 1. Continuous (dashed) lines represents the electric (magnetic) multipoles.(c) Spectra of the magnitude of the multipole coefficients of order m = −1.
Fig. 5
Fig. 5 Cross section decomposition in terms of even and odd contributions apply to a cluster-based absorbing metasurface. Each cluster consist of thirteen Ge particles that are 75 nm in radius distributed in a sphere of radius R = 250nm. The square array has a surface fill fraction of 0.6.

Equations (32)

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E a ( z ) = 2 π i | z | k S E s ( z )
r = π 2 k 2 S n = 1 [ n 𝒪 n ]
t = 1 π 2 k 2 S n = 1 [ n + 𝒪 n ]
n = m = 1 + 1 [ m ( 4 n + 1 ) a 2 n , m + ( 4 n 1 ) b 2 n 1 , m ]
𝒪 n = m = 1 + 1 [ m ( 4 n 1 ) a 2 n 1 , m + ( 4 n + 1 ) b 2 n , m ]
n = 1 + 𝒪 n = n = 1 + n = k 2 S π
σ s 𝒪 = σ s = σ a 2
E s ( θ , ϕ ) = i E 0 e i k r k r n = 1 m = n + n π ( 2 n + 1 ) n ( n + 1 ) 𝒬 n m × [ τ n m ( cos θ ) a n m + π n m ( cos θ ) b n m ] e i m ϕ
𝒬 n m = 2 n + 1 4 π ( n m ) ! ( n + m ) !
π n m ( cos θ ) = m sin θ P n m ( cos θ )
τ n m ( cos θ ) = d d θ P n m ( cos θ )
π n , m ( ± 1 ) = { ( ± 1 ) n 1 n ( n + 1 ) 2 m = 1 ( ± 1 ) n 1 2 m = 1 0 otherwise
τ n , m ( ± 1 ) = { ( ± 1 ) n n ( n + 1 ) 2 m = 1 ( ± 1 ) n 2 m = 1 0 otherwise
E s ( 0 , 0 ) = i E 0 4 e i k r k r n = 1 ( 2 n + 1 ) [ a n , 1 a n , 1 + b n , 1 + b n , 1 ]
E s ( π , π ) = i E 0 4 e i k r k r n = 1 ( 2 n + 1 ) ( 1 ) n + 1 [ a n , 1 a n , 1 b n , 1 b n , 1 ]
E a ( z + ) = π 2 k 2 S n = 1 ( 2 n + 1 ) ( a n , 1 a n , 1 + b n , 1 + b n , 1 ) E 0
E a ( z ) = π 2 k 2 S n = 1 ( 1 ) n + 1 ( 2 n + 1 ) ( a n , 1 a n , 1 b n , 1 b n , 1 ) E 0
t = 1 π 2 k 2 S n = 1 m = 1 , + 1 ( 2 n + 1 ) ( m a n , m + b n , m )
r = π 2 k 2 S n = 1 m = 1 , + 1 ( 1 ) n + 1 ( 2 n + 1 ) ( m a n , m b n , m )
a n , m = k 2 η E 0 i n 1 π ( 2 n + 1 ) O n m e im ϕ ( [ Ψ n ( k r ) + Ψ n ( k r ) ] P n m ( cos θ ) r J s ( r ) + Ψ n ( k r ) k r [ τ n m ( θ ) e θ J s ( r ) π n m ( θ ) e ϕ J s ( r ) ] ) d V
b n , m = k 2 η E 0 i n + 1 π ( 2 n + 1 ) O n m e i m ϕ j n ( k r ) [ i π n m ( θ ) e θ J s ( r ) + τ n m ( θ ) e ϕ J s ( r ) ] d V
σ s = π 2 2 k 4 S | n = 1 n | 2
σ s 𝒪 = π 2 2 k 4 S | n = 1 𝒪 n | 2
σ s 𝒪 = σ s = σ a 2
A = 2 ( π 2 k 2 S ) 2 [ | n = 1 n | 2 + | n = 1 𝒪 n | 2 ] + π k 2 S n = 1 R e ( n + 𝒪 n )
σ a = σ s + σ e x t
σ e x t = π k 2 n = 1 m = 1 , + 1 ( 2 n + 1 ) R e ( m a n , m + b n , m )
σ e x t = π k 2 n = 1 R e ( n )
σ e x t 𝒪 = π k 2 n = 1 R e ( 𝒪 n )
σ a 𝒪 = σ e x t 𝒪 σ s 𝒪
σ a = σ e x t σ s
{ σ s 𝒪 σ a 𝒪 σ 0 2 σ s σ a σ 0 2

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