Abstract

In this paper, we propose a novel, frequency- and angularly- broadband approach to achieve absorption rate enhancement in high-index dielectric nanostructures through the engineering of non-radiative anapole modes. We employ multipolar decomposition of numerically computed current distributions and analyze the far-field scattering power of multipole moments. By leveraging the destructive interference of electric dipole and toroidal dipole moments, we design non-radiating anapole modes and demonstrate significantly enhanced absorbed power in silicon and germanium nanostructures. We demonstrate wide wavelength tunability of the anapole-driven peak absorption enhancement for nano-disks and square nano-pixel geometries, which can be conveniently fabricated with current lithography. Finally, by combining nano-disks and nano-pixels of different sizes into functional surface units, we design nanostructured arrays with enhanced bandwidth and absorption rates that can be useful for the engineering of broadband semiconductor photodetectors driven by controllable anapole responses.

© 2016 Optical Society of America

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References

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2015 (5)

A. E. Miroshnichenko, A. B. Evlyukhin, Y. F. Yu, R. M. Bakker, A. Chipouline, A. I. Kuznetsov, B. Luk’yanchuk, B. N. Chichkov, and Y. S. Kivshar, “Nonradiating anapole modes in dielectric nanoparticles,” Nat. Commun. 6, 8069 (2015).
[Crossref] [PubMed]

W. Liu, J. Shi, B. Lei, H. Hu, and A. E. Miroshnichenko, “Efficient excitation and tuning of toroidal dipoles within individual homogenous nanoparticles,” Opt. Express 23(19), 24738–24747 (2015).
[Crossref] [PubMed]

A. A. Basharin, M. Kafesaki, E. N. Economou, C. M. Soukoulis, V. A. Fedotov, V. Savinov, and N. I. Zheludev, “Dielectric metamaterials with toroidal dipolar response,” Phys. Rev. X 5(1), 011036 (2015).
[Crossref]

Y. Bao, X. Zhu, and Z. Fang, “Plasmonic toroidal dipolar response under radially polarized excitation,” Sci. Rep. 5, 11793 (2015).
[Crossref] [PubMed]

A. Casadei, E. A. Llado, F. Amaduzzi, E. Russo-Averchi, D. Rüffer, M. Heiss, L. D. Negro, and A. F. Morral, “Polarization response of nanowires à la carte,” Sci. Rep. 5, 7651 (2015).
[Crossref] [PubMed]

2013 (3)

Z. Dong, J. Zhu, X. Yin, J. Li, C. Lu, and X. Zhang, “All-optical Hall effect by the dynamic toroidal moment in a cavity-based metamaterial,” Phys. Rev. B 87(24), 245429 (2013).
[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(9), 7824–7832 (2013).
[Crossref] [PubMed]

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).
[Crossref] [PubMed]

2012 (5)

W. Liu, A. E. Miroshnichenko, D. N. Neshev, and Y. S. Kivshar, “Broadband unidirectional scattering by magneto-electric core-shell nanoparticles,” ACS Nano 6(6), 5489–5497 (2012).
[Crossref] [PubMed]

J. M. Geffrin, B. García-Cámara, R. Gómez-Medina, P. Albella, L. S. Froufe-Pérez, C. Eyraud, A. Litman, R. Vaillon, F. González, M. Nieto-Vesperinas, J. J. Sáenz, and F. Moreno, “Magnetic and electric coherence in forward- and back-scattered electromagnetic waves by a single dielectric subwavelength sphere,” Nat. Commun. 3, 1171 (2012).
[Crossref] [PubMed]

B. Ögüt, N. Talebi, R. Vogelgesang, W. Sigle, and P. A. van Aken, “Toroidal plasmonic eigenmodes in oligomer nanocavities for the visible,” Nano Lett. 12(10), 5239–5244 (2012).
[Crossref] [PubMed]

Z. G. Dong, P. Ni, J. Zhu, X. Yin, and X. Zhang, “Toroidal dipole response in a multifold double-ring metamaterial,” Opt. Express 20(12), 13065–13070 (2012).
[Crossref] [PubMed]

Y.-W. Huang, W. T. Chen, P. C. Wu, V. Fedotov, V. Savinov, Y. Z. Ho, Y.-F. Chau, N. I. Zheludev, and D. P. Tsai, “Design of plasmonic toroidal metamaterials at optical frequencies,” Opt. Express 20(2), 1760–1768 (2012).
[Crossref] [PubMed]

2010 (3)

T. Kaelberer, V. A. Fedotov, N. Papasimakis, D. P. Tsai, and N. I. Zheludev, “Toroidal dipolar response in a metamaterial,” Science 330(6010), 1510–1512 (2010).
[Crossref] [PubMed]

J. Michel, J. Liu, and L. C. Kimerling, “High-performance Ge-on-Si photodetectors,” Nat. Photonics 4(8), 527–534 (2010).
[Crossref]

C. Forestiere, M. Donelli, G. F. Walsh, E. Zeni, G. Miano, and L. Dal Negro, “Particle-swarm optimization of broadband nanoplasmonic arrays,” Opt. Lett. 35(2), 133–135 (2010).
[Crossref] [PubMed]

2009 (1)

L. Cao, J. S. White, J. S. Park, J. A. Schuller, B. M. Clemens, and M. L. Brongersma, “Engineering light absorption in semiconductor nanowire devices,” Nat. Mater. 8(8), 643–647 (2009).
[Crossref] [PubMed]

2008 (2)

N. A. Spaldin, M. Fiebig, and M. Mostovoy, “The toroidal moment in condensed-matter physics and its relation to the magnetoelectric effect,” J. Phys. Condens. Matter 20(43), 434203 (2008).
[Crossref]

L. Tang, S. E. Kocabas, S. Latif, A. K. Okyay, D. Ly-Gagnon, K. C. Saraswat, and D. A. B. Miller, “Nanometre-scale germanium photodetector enhanced by a near-infrared dipole antenna,” Nat. Photonics 2(4), 226–229 (2008).
[Crossref]

2005 (1)

A. D. Boardman, K. Marinov, N. Zheludev, and V. A. Fedotov, “Nonradiating toroidal structures,” Proc. SPIE 5955, 595504 (2005).
[Crossref]

2004 (1)

E. A. Marengo and A. J. Devaney, “Nonradiating sources with connections to the adjoint problem,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 70(3), 037601 (2004).
[Crossref] [PubMed]

2002 (1)

E. E. Radescu and G. Vaman, “Exact calculation of the angular momentum loss, recoil force, and radiation intensity for an arbitrary source in terms of electric, magnetic, and toroid multipoles,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 65(4), 046609 (2002).
[Crossref] [PubMed]

2001 (1)

G. N. Afanasiev, “Simplest sources of electromagnetic fields as a tool for testing the reciprocity-like theorems,” J. Phys. D Appl. Phys. 34(4), 539–559 (2001).
[Crossref]

2000 (1)

V. M. Dubovik, M. A. Martsenyuk, and B. Saha, “Material equations for electromagnetism with toroidal polarizations,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 61(6), 7087–7097 (2000).
[Crossref] [PubMed]

1998 (1)

G. N. Afanasiev and V. M. Dubovik, “Some remarkable charge-current configurations,” Phys. Part. Nucl. 29(4), 366–391 (1998).
[Crossref]

1994 (1)

G. N. Afanasiev, “Vector solutions of the Laplace equation and the influence of helicity on Aharonov-Bohm scattering,” J. Phys. Math. Gen. 27(6), 2143–2160 (1994).
[Crossref]

1993 (1)

G. N. Afanasiev, “Toroidal solenoids in an electromagnetic field and toroidal Aharonov-Casher effect,” Phys. Scr. 48(4), 385–392 (1993).
[Crossref]

1990 (1)

V. M. Dubovik and V. V. Tugushev, “Toroid moments in electrodynamics and solid-state physics,” Phys. Rep. 187(4), 145–202 (1990).
[Crossref]

1986 (2)

V. M. Dubovik, L. A. Tosunyan, and V. V. Tugushev, “Axial toroidal moments in electrodynamics and solid-state physics,” Sov. Phys. JETP 63(2), 1-8 (1986).

K. Kim and E. Wolf, “Non-radiating monochromatic sources and their fields,” Opt. Commun. 59(1), 1–6 (1986).
[Crossref]

1983 (1)

1973 (1)

A. J. Devaney and E. Wolf, “Radiating and nonradiating classical current distributions and the fields they generate,” Phys. Rev. D Part. Fields 8(4), 1044–1047 (1973).
[Crossref]

1957 (1)

Y. Zel’dovich, “Electromagnetic interaction with parity violation,” Sov. Phys. JETP 6, 1184 (1957).

Afanasiev, G. N.

G. N. Afanasiev, “Simplest sources of electromagnetic fields as a tool for testing the reciprocity-like theorems,” J. Phys. D Appl. Phys. 34(4), 539–559 (2001).
[Crossref]

G. N. Afanasiev and V. M. Dubovik, “Some remarkable charge-current configurations,” Phys. Part. Nucl. 29(4), 366–391 (1998).
[Crossref]

G. N. Afanasiev, “Vector solutions of the Laplace equation and the influence of helicity on Aharonov-Bohm scattering,” J. Phys. Math. Gen. 27(6), 2143–2160 (1994).
[Crossref]

G. N. Afanasiev, “Toroidal solenoids in an electromagnetic field and toroidal Aharonov-Casher effect,” Phys. Scr. 48(4), 385–392 (1993).
[Crossref]

Albella, P.

J. M. Geffrin, B. García-Cámara, R. Gómez-Medina, P. Albella, L. S. Froufe-Pérez, C. Eyraud, A. Litman, R. Vaillon, F. González, M. Nieto-Vesperinas, J. J. Sáenz, and F. Moreno, “Magnetic and electric coherence in forward- and back-scattered electromagnetic waves by a single dielectric subwavelength sphere,” Nat. Commun. 3, 1171 (2012).
[Crossref] [PubMed]

Amaduzzi, F.

A. Casadei, E. A. Llado, F. Amaduzzi, E. Russo-Averchi, D. Rüffer, M. Heiss, L. D. Negro, and A. F. Morral, “Polarization response of nanowires à la carte,” Sci. Rep. 5, 7651 (2015).
[Crossref] [PubMed]

Bakker, R. M.

A. E. Miroshnichenko, A. B. Evlyukhin, Y. F. Yu, R. M. Bakker, A. Chipouline, A. I. Kuznetsov, B. Luk’yanchuk, B. N. Chichkov, and Y. S. Kivshar, “Nonradiating anapole modes in dielectric nanoparticles,” Nat. Commun. 6, 8069 (2015).
[Crossref] [PubMed]

Bao, Y.

Y. Bao, X. Zhu, and Z. Fang, “Plasmonic toroidal dipolar response under radially polarized excitation,” Sci. Rep. 5, 11793 (2015).
[Crossref] [PubMed]

Basharin, A. A.

A. A. Basharin, M. Kafesaki, E. N. Economou, C. M. Soukoulis, V. A. Fedotov, V. Savinov, and N. I. Zheludev, “Dielectric metamaterials with toroidal dipolar response,” Phys. Rev. X 5(1), 011036 (2015).
[Crossref]

Boardman, A. D.

A. D. Boardman, K. Marinov, N. Zheludev, and V. A. Fedotov, “Nonradiating toroidal structures,” Proc. SPIE 5955, 595504 (2005).
[Crossref]

Brener, I.

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(9), 7824–7832 (2013).
[Crossref] [PubMed]

Brongersma, M. L.

L. Cao, J. S. White, J. S. Park, J. A. Schuller, B. M. Clemens, and M. L. Brongersma, “Engineering light absorption in semiconductor nanowire devices,” Nat. Mater. 8(8), 643–647 (2009).
[Crossref] [PubMed]

Cao, L.

L. Cao, J. S. White, J. S. Park, J. A. Schuller, B. M. Clemens, and M. L. Brongersma, “Engineering light absorption in semiconductor nanowire devices,” Nat. Mater. 8(8), 643–647 (2009).
[Crossref] [PubMed]

Casadei, A.

A. Casadei, E. A. Llado, F. Amaduzzi, E. Russo-Averchi, D. Rüffer, M. Heiss, L. D. Negro, and A. F. Morral, “Polarization response of nanowires à la carte,” Sci. Rep. 5, 7651 (2015).
[Crossref] [PubMed]

Chau, Y.-F.

Chen, W. T.

Chichkov, B. N.

A. E. Miroshnichenko, A. B. Evlyukhin, Y. F. Yu, R. M. Bakker, A. Chipouline, A. I. Kuznetsov, B. Luk’yanchuk, B. N. Chichkov, and Y. S. Kivshar, “Nonradiating anapole modes in dielectric nanoparticles,” Nat. Commun. 6, 8069 (2015).
[Crossref] [PubMed]

Chipouline, A.

A. E. Miroshnichenko, A. B. Evlyukhin, Y. F. Yu, R. M. Bakker, A. Chipouline, A. I. Kuznetsov, B. Luk’yanchuk, B. N. Chichkov, and Y. S. Kivshar, “Nonradiating anapole modes in dielectric nanoparticles,” Nat. Commun. 6, 8069 (2015).
[Crossref] [PubMed]

Clemens, B. M.

L. Cao, J. S. White, J. S. Park, J. A. Schuller, B. M. Clemens, and M. L. Brongersma, “Engineering light absorption in semiconductor nanowire devices,” Nat. Mater. 8(8), 643–647 (2009).
[Crossref] [PubMed]

Dal Negro, L.

Decker, M.

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(9), 7824–7832 (2013).
[Crossref] [PubMed]

Devaney, A. J.

E. A. Marengo and A. J. Devaney, “Nonradiating sources with connections to the adjoint problem,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 70(3), 037601 (2004).
[Crossref] [PubMed]

A. J. Devaney and E. Wolf, “Radiating and nonradiating classical current distributions and the fields they generate,” Phys. Rev. D Part. Fields 8(4), 1044–1047 (1973).
[Crossref]

Dominguez, J.

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(9), 7824–7832 (2013).
[Crossref] [PubMed]

Donelli, M.

Dong, Z.

Z. Dong, J. Zhu, X. Yin, J. Li, C. Lu, and X. Zhang, “All-optical Hall effect by the dynamic toroidal moment in a cavity-based metamaterial,” Phys. Rev. B 87(24), 245429 (2013).
[Crossref]

Dong, Z. G.

Dubovik, V. M.

V. M. Dubovik, M. A. Martsenyuk, and B. Saha, “Material equations for electromagnetism with toroidal polarizations,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 61(6), 7087–7097 (2000).
[Crossref] [PubMed]

G. N. Afanasiev and V. M. Dubovik, “Some remarkable charge-current configurations,” Phys. Part. Nucl. 29(4), 366–391 (1998).
[Crossref]

V. M. Dubovik and V. V. Tugushev, “Toroid moments in electrodynamics and solid-state physics,” Phys. Rep. 187(4), 145–202 (1990).
[Crossref]

V. M. Dubovik, L. A. Tosunyan, and V. V. Tugushev, “Axial toroidal moments in electrodynamics and solid-state physics,” Sov. Phys. JETP 63(2), 1-8 (1986).

Economou, E. N.

A. A. Basharin, M. Kafesaki, E. N. Economou, C. M. Soukoulis, V. A. Fedotov, V. Savinov, and N. I. Zheludev, “Dielectric metamaterials with toroidal dipolar response,” Phys. Rev. X 5(1), 011036 (2015).
[Crossref]

Evlyukhin, A. B.

A. E. Miroshnichenko, A. B. Evlyukhin, Y. F. Yu, R. M. Bakker, A. Chipouline, A. I. Kuznetsov, B. Luk’yanchuk, B. N. Chichkov, and Y. S. Kivshar, “Nonradiating anapole modes in dielectric nanoparticles,” Nat. Commun. 6, 8069 (2015).
[Crossref] [PubMed]

Eyraud, C.

J. M. Geffrin, B. García-Cámara, R. Gómez-Medina, P. Albella, L. S. Froufe-Pérez, C. Eyraud, A. Litman, R. Vaillon, F. González, M. Nieto-Vesperinas, J. J. Sáenz, and F. Moreno, “Magnetic and electric coherence in forward- and back-scattered electromagnetic waves by a single dielectric subwavelength sphere,” Nat. Commun. 3, 1171 (2012).
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Y. Bao, X. Zhu, and Z. Fang, “Plasmonic toroidal dipolar response under radially polarized excitation,” Sci. Rep. 5, 11793 (2015).
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Fedotov, V. A.

A. A. Basharin, M. Kafesaki, E. N. Economou, C. M. Soukoulis, V. A. Fedotov, V. Savinov, and N. I. Zheludev, “Dielectric metamaterials with toroidal dipolar response,” Phys. Rev. X 5(1), 011036 (2015).
[Crossref]

T. Kaelberer, V. A. Fedotov, N. Papasimakis, D. P. Tsai, and N. I. Zheludev, “Toroidal dipolar response in a metamaterial,” Science 330(6010), 1510–1512 (2010).
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A. D. Boardman, K. Marinov, N. Zheludev, and V. A. Fedotov, “Nonradiating toroidal structures,” Proc. SPIE 5955, 595504 (2005).
[Crossref]

Fiebig, M.

N. A. Spaldin, M. Fiebig, and M. Mostovoy, “The toroidal moment in condensed-matter physics and its relation to the magnetoelectric effect,” J. Phys. Condens. Matter 20(43), 434203 (2008).
[Crossref]

Fofang, N. T.

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(9), 7824–7832 (2013).
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Forestiere, C.

Froufe-Pérez, L. S.

J. M. Geffrin, B. García-Cámara, R. Gómez-Medina, P. Albella, L. S. Froufe-Pérez, C. Eyraud, A. Litman, R. Vaillon, F. González, M. Nieto-Vesperinas, J. J. Sáenz, and F. Moreno, “Magnetic and electric coherence in forward- and back-scattered electromagnetic waves by a single dielectric subwavelength sphere,” Nat. Commun. 3, 1171 (2012).
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Fu, Y. H.

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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García-Cámara, B.

J. M. Geffrin, B. García-Cámara, R. Gómez-Medina, P. Albella, L. S. Froufe-Pérez, C. Eyraud, A. Litman, R. Vaillon, F. González, M. Nieto-Vesperinas, J. J. Sáenz, and F. Moreno, “Magnetic and electric coherence in forward- and back-scattered electromagnetic waves by a single dielectric subwavelength sphere,” Nat. Commun. 3, 1171 (2012).
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J. M. Geffrin, B. García-Cámara, R. Gómez-Medina, P. Albella, L. S. Froufe-Pérez, C. Eyraud, A. Litman, R. Vaillon, F. González, M. Nieto-Vesperinas, J. J. Sáenz, and F. Moreno, “Magnetic and electric coherence in forward- and back-scattered electromagnetic waves by a single dielectric subwavelength sphere,” Nat. Commun. 3, 1171 (2012).
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Giles, C. L.

Gómez-Medina, R.

J. M. Geffrin, B. García-Cámara, R. Gómez-Medina, P. Albella, L. S. Froufe-Pérez, C. Eyraud, A. Litman, R. Vaillon, F. González, M. Nieto-Vesperinas, J. J. Sáenz, and F. Moreno, “Magnetic and electric coherence in forward- and back-scattered electromagnetic waves by a single dielectric subwavelength sphere,” Nat. Commun. 3, 1171 (2012).
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Gonzales, E.

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(9), 7824–7832 (2013).
[Crossref] [PubMed]

González, F.

J. M. Geffrin, B. García-Cámara, R. Gómez-Medina, P. Albella, L. S. Froufe-Pérez, C. Eyraud, A. Litman, R. Vaillon, F. González, M. Nieto-Vesperinas, J. J. Sáenz, and F. Moreno, “Magnetic and electric coherence in forward- and back-scattered electromagnetic waves by a single dielectric subwavelength sphere,” Nat. Commun. 3, 1171 (2012).
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Heiss, M.

A. Casadei, E. A. Llado, F. Amaduzzi, E. Russo-Averchi, D. Rüffer, M. Heiss, L. D. Negro, and A. F. Morral, “Polarization response of nanowires à la carte,” Sci. Rep. 5, 7651 (2015).
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Ho, Y. Z.

Hu, H.

Huang, Y.-W.

Kaelberer, T.

T. Kaelberer, V. A. Fedotov, N. Papasimakis, D. P. Tsai, and N. I. Zheludev, “Toroidal dipolar response in a metamaterial,” Science 330(6010), 1510–1512 (2010).
[Crossref] [PubMed]

Kafesaki, M.

A. A. Basharin, M. Kafesaki, E. N. Economou, C. M. Soukoulis, V. A. Fedotov, V. Savinov, and N. I. Zheludev, “Dielectric metamaterials with toroidal dipolar response,” Phys. Rev. X 5(1), 011036 (2015).
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Kerker, M.

Kim, K.

K. Kim and E. Wolf, “Non-radiating monochromatic sources and their fields,” Opt. Commun. 59(1), 1–6 (1986).
[Crossref]

Kimerling, L. C.

J. Michel, J. Liu, and L. C. Kimerling, “High-performance Ge-on-Si photodetectors,” Nat. Photonics 4(8), 527–534 (2010).
[Crossref]

Kivshar, Y.

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(9), 7824–7832 (2013).
[Crossref] [PubMed]

Kivshar, Y. S.

A. E. Miroshnichenko, A. B. Evlyukhin, Y. F. Yu, R. M. Bakker, A. Chipouline, A. I. Kuznetsov, B. Luk’yanchuk, B. N. Chichkov, and Y. S. Kivshar, “Nonradiating anapole modes in dielectric nanoparticles,” Nat. Commun. 6, 8069 (2015).
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W. Liu, A. E. Miroshnichenko, D. N. Neshev, and Y. S. Kivshar, “Broadband unidirectional scattering by magneto-electric core-shell nanoparticles,” ACS Nano 6(6), 5489–5497 (2012).
[Crossref] [PubMed]

Kocabas, S. E.

L. Tang, S. E. Kocabas, S. Latif, A. K. Okyay, D. Ly-Gagnon, K. C. Saraswat, and D. A. B. Miller, “Nanometre-scale germanium photodetector enhanced by a near-infrared dipole antenna,” Nat. Photonics 2(4), 226–229 (2008).
[Crossref]

Kuznetsov, A. I.

A. E. Miroshnichenko, A. B. Evlyukhin, Y. F. Yu, R. M. Bakker, A. Chipouline, A. I. Kuznetsov, B. Luk’yanchuk, B. N. Chichkov, and Y. S. Kivshar, “Nonradiating anapole modes in dielectric nanoparticles,” Nat. Commun. 6, 8069 (2015).
[Crossref] [PubMed]

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).
[Crossref] [PubMed]

Latif, S.

L. Tang, S. E. Kocabas, S. Latif, A. K. Okyay, D. Ly-Gagnon, K. C. Saraswat, and D. A. B. Miller, “Nanometre-scale germanium photodetector enhanced by a near-infrared dipole antenna,” Nat. Photonics 2(4), 226–229 (2008).
[Crossref]

Lei, B.

Li, J.

Z. Dong, J. Zhu, X. Yin, J. Li, C. Lu, and X. Zhang, “All-optical Hall effect by the dynamic toroidal moment in a cavity-based metamaterial,” Phys. Rev. B 87(24), 245429 (2013).
[Crossref]

Litman, A.

J. M. Geffrin, B. García-Cámara, R. Gómez-Medina, P. Albella, L. S. Froufe-Pérez, C. Eyraud, A. Litman, R. Vaillon, F. González, M. Nieto-Vesperinas, J. J. Sáenz, and F. Moreno, “Magnetic and electric coherence in forward- and back-scattered electromagnetic waves by a single dielectric subwavelength sphere,” Nat. Commun. 3, 1171 (2012).
[Crossref] [PubMed]

Liu, J.

J. Michel, J. Liu, and L. C. Kimerling, “High-performance Ge-on-Si photodetectors,” Nat. Photonics 4(8), 527–534 (2010).
[Crossref]

Liu, S.

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(9), 7824–7832 (2013).
[Crossref] [PubMed]

Liu, W.

W. Liu, J. Shi, B. Lei, H. Hu, and A. E. Miroshnichenko, “Efficient excitation and tuning of toroidal dipoles within individual homogenous nanoparticles,” Opt. Express 23(19), 24738–24747 (2015).
[Crossref] [PubMed]

W. Liu, A. E. Miroshnichenko, D. N. Neshev, and Y. S. Kivshar, “Broadband unidirectional scattering by magneto-electric core-shell nanoparticles,” ACS Nano 6(6), 5489–5497 (2012).
[Crossref] [PubMed]

Llado, E. A.

A. Casadei, E. A. Llado, F. Amaduzzi, E. Russo-Averchi, D. Rüffer, M. Heiss, L. D. Negro, and A. F. Morral, “Polarization response of nanowires à la carte,” Sci. Rep. 5, 7651 (2015).
[Crossref] [PubMed]

Lu, C.

Z. Dong, J. Zhu, X. Yin, J. Li, C. Lu, and X. Zhang, “All-optical Hall effect by the dynamic toroidal moment in a cavity-based metamaterial,” Phys. Rev. B 87(24), 245429 (2013).
[Crossref]

Luk, T. S.

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(9), 7824–7832 (2013).
[Crossref] [PubMed]

Luk’yanchuk, B.

A. E. Miroshnichenko, A. B. Evlyukhin, Y. F. Yu, R. M. Bakker, A. Chipouline, A. I. Kuznetsov, B. Luk’yanchuk, B. N. Chichkov, and Y. S. Kivshar, “Nonradiating anapole modes in dielectric nanoparticles,” Nat. Commun. 6, 8069 (2015).
[Crossref] [PubMed]

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).
[Crossref] [PubMed]

Ly-Gagnon, D.

L. Tang, S. E. Kocabas, S. Latif, A. K. Okyay, D. Ly-Gagnon, K. C. Saraswat, and D. A. B. Miller, “Nanometre-scale germanium photodetector enhanced by a near-infrared dipole antenna,” Nat. Photonics 2(4), 226–229 (2008).
[Crossref]

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E. A. Marengo and A. J. Devaney, “Nonradiating sources with connections to the adjoint problem,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 70(3), 037601 (2004).
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Marinov, K.

A. D. Boardman, K. Marinov, N. Zheludev, and V. A. Fedotov, “Nonradiating toroidal structures,” Proc. SPIE 5955, 595504 (2005).
[Crossref]

Martsenyuk, M. A.

V. M. Dubovik, M. A. Martsenyuk, and B. Saha, “Material equations for electromagnetism with toroidal polarizations,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 61(6), 7087–7097 (2000).
[Crossref] [PubMed]

Miano, G.

Michel, J.

J. Michel, J. Liu, and L. C. Kimerling, “High-performance Ge-on-Si photodetectors,” Nat. Photonics 4(8), 527–534 (2010).
[Crossref]

Miller, D. A. B.

L. Tang, S. E. Kocabas, S. Latif, A. K. Okyay, D. Ly-Gagnon, K. C. Saraswat, and D. A. B. Miller, “Nanometre-scale germanium photodetector enhanced by a near-infrared dipole antenna,” Nat. Photonics 2(4), 226–229 (2008).
[Crossref]

Miroshnichenko, A. E.

A. E. Miroshnichenko, A. B. Evlyukhin, Y. F. Yu, R. M. Bakker, A. Chipouline, A. I. Kuznetsov, B. Luk’yanchuk, B. N. Chichkov, and Y. S. Kivshar, “Nonradiating anapole modes in dielectric nanoparticles,” Nat. Commun. 6, 8069 (2015).
[Crossref] [PubMed]

W. Liu, J. Shi, B. Lei, H. Hu, and A. E. Miroshnichenko, “Efficient excitation and tuning of toroidal dipoles within individual homogenous nanoparticles,” Opt. Express 23(19), 24738–24747 (2015).
[Crossref] [PubMed]

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(9), 7824–7832 (2013).
[Crossref] [PubMed]

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).
[Crossref] [PubMed]

W. Liu, A. E. Miroshnichenko, D. N. Neshev, and Y. S. Kivshar, “Broadband unidirectional scattering by magneto-electric core-shell nanoparticles,” ACS Nano 6(6), 5489–5497 (2012).
[Crossref] [PubMed]

Moreno, F.

J. M. Geffrin, B. García-Cámara, R. Gómez-Medina, P. Albella, L. S. Froufe-Pérez, C. Eyraud, A. Litman, R. Vaillon, F. González, M. Nieto-Vesperinas, J. J. Sáenz, and F. Moreno, “Magnetic and electric coherence in forward- and back-scattered electromagnetic waves by a single dielectric subwavelength sphere,” Nat. Commun. 3, 1171 (2012).
[Crossref] [PubMed]

Morral, A. F.

A. Casadei, E. A. Llado, F. Amaduzzi, E. Russo-Averchi, D. Rüffer, M. Heiss, L. D. Negro, and A. F. Morral, “Polarization response of nanowires à la carte,” Sci. Rep. 5, 7651 (2015).
[Crossref] [PubMed]

Mostovoy, M.

N. A. Spaldin, M. Fiebig, and M. Mostovoy, “The toroidal moment in condensed-matter physics and its relation to the magnetoelectric effect,” J. Phys. Condens. Matter 20(43), 434203 (2008).
[Crossref]

Negro, L. D.

A. Casadei, E. A. Llado, F. Amaduzzi, E. Russo-Averchi, D. Rüffer, M. Heiss, L. D. Negro, and A. F. Morral, “Polarization response of nanowires à la carte,” Sci. Rep. 5, 7651 (2015).
[Crossref] [PubMed]

Neshev, D. N.

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(9), 7824–7832 (2013).
[Crossref] [PubMed]

W. Liu, A. E. Miroshnichenko, D. N. Neshev, and Y. S. Kivshar, “Broadband unidirectional scattering by magneto-electric core-shell nanoparticles,” ACS Nano 6(6), 5489–5497 (2012).
[Crossref] [PubMed]

Ni, P.

Nieto-Vesperinas, M.

J. M. Geffrin, B. García-Cámara, R. Gómez-Medina, P. Albella, L. S. Froufe-Pérez, C. Eyraud, A. Litman, R. Vaillon, F. González, M. Nieto-Vesperinas, J. J. Sáenz, and F. Moreno, “Magnetic and electric coherence in forward- and back-scattered electromagnetic waves by a single dielectric subwavelength sphere,” Nat. Commun. 3, 1171 (2012).
[Crossref] [PubMed]

Ögüt, B.

B. Ögüt, N. Talebi, R. Vogelgesang, W. Sigle, and P. A. van Aken, “Toroidal plasmonic eigenmodes in oligomer nanocavities for the visible,” Nano Lett. 12(10), 5239–5244 (2012).
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Okyay, A. K.

L. Tang, S. E. Kocabas, S. Latif, A. K. Okyay, D. Ly-Gagnon, K. C. Saraswat, and D. A. B. Miller, “Nanometre-scale germanium photodetector enhanced by a near-infrared dipole antenna,” Nat. Photonics 2(4), 226–229 (2008).
[Crossref]

Papasimakis, N.

T. Kaelberer, V. A. Fedotov, N. Papasimakis, D. P. Tsai, and N. I. Zheludev, “Toroidal dipolar response in a metamaterial,” Science 330(6010), 1510–1512 (2010).
[Crossref] [PubMed]

Park, J. S.

L. Cao, J. S. White, J. S. Park, J. A. Schuller, B. M. Clemens, and M. L. Brongersma, “Engineering light absorption in semiconductor nanowire devices,” Nat. Mater. 8(8), 643–647 (2009).
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Radescu, E. E.

E. E. Radescu and G. Vaman, “Exact calculation of the angular momentum loss, recoil force, and radiation intensity for an arbitrary source in terms of electric, magnetic, and toroid multipoles,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 65(4), 046609 (2002).
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Rüffer, D.

A. Casadei, E. A. Llado, F. Amaduzzi, E. Russo-Averchi, D. Rüffer, M. Heiss, L. D. Negro, and A. F. Morral, “Polarization response of nanowires à la carte,” Sci. Rep. 5, 7651 (2015).
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Russo-Averchi, E.

A. Casadei, E. A. Llado, F. Amaduzzi, E. Russo-Averchi, D. Rüffer, M. Heiss, L. D. Negro, and A. F. Morral, “Polarization response of nanowires à la carte,” Sci. Rep. 5, 7651 (2015).
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Sáenz, J. J.

J. M. Geffrin, B. García-Cámara, R. Gómez-Medina, P. Albella, L. S. Froufe-Pérez, C. Eyraud, A. Litman, R. Vaillon, F. González, M. Nieto-Vesperinas, J. J. Sáenz, and F. Moreno, “Magnetic and electric coherence in forward- and back-scattered electromagnetic waves by a single dielectric subwavelength sphere,” Nat. Commun. 3, 1171 (2012).
[Crossref] [PubMed]

Saha, B.

V. M. Dubovik, M. A. Martsenyuk, and B. Saha, “Material equations for electromagnetism with toroidal polarizations,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 61(6), 7087–7097 (2000).
[Crossref] [PubMed]

Saraswat, K. C.

L. Tang, S. E. Kocabas, S. Latif, A. K. Okyay, D. Ly-Gagnon, K. C. Saraswat, and D. A. B. Miller, “Nanometre-scale germanium photodetector enhanced by a near-infrared dipole antenna,” Nat. Photonics 2(4), 226–229 (2008).
[Crossref]

Savinov, V.

A. A. Basharin, M. Kafesaki, E. N. Economou, C. M. Soukoulis, V. A. Fedotov, V. Savinov, and N. I. Zheludev, “Dielectric metamaterials with toroidal dipolar response,” Phys. Rev. X 5(1), 011036 (2015).
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Y.-W. Huang, W. T. Chen, P. C. Wu, V. Fedotov, V. Savinov, Y. Z. Ho, Y.-F. Chau, N. I. Zheludev, and D. P. Tsai, “Design of plasmonic toroidal metamaterials at optical frequencies,” Opt. Express 20(2), 1760–1768 (2012).
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Schuller, J. A.

L. Cao, J. S. White, J. S. Park, J. A. Schuller, B. M. Clemens, and M. L. Brongersma, “Engineering light absorption in semiconductor nanowire devices,” Nat. Mater. 8(8), 643–647 (2009).
[Crossref] [PubMed]

Shi, J.

Sigle, W.

B. Ögüt, N. Talebi, R. Vogelgesang, W. Sigle, and P. A. van Aken, “Toroidal plasmonic eigenmodes in oligomer nanocavities for the visible,” Nano Lett. 12(10), 5239–5244 (2012).
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Soukoulis, C. M.

A. A. Basharin, M. Kafesaki, E. N. Economou, C. M. Soukoulis, V. A. Fedotov, V. Savinov, and N. I. Zheludev, “Dielectric metamaterials with toroidal dipolar response,” Phys. Rev. X 5(1), 011036 (2015).
[Crossref]

Spaldin, N. A.

N. A. Spaldin, M. Fiebig, and M. Mostovoy, “The toroidal moment in condensed-matter physics and its relation to the magnetoelectric effect,” J. Phys. Condens. Matter 20(43), 434203 (2008).
[Crossref]

Staude, I.

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(9), 7824–7832 (2013).
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Talebi, N.

B. Ögüt, N. Talebi, R. Vogelgesang, W. Sigle, and P. A. van Aken, “Toroidal plasmonic eigenmodes in oligomer nanocavities for the visible,” Nano Lett. 12(10), 5239–5244 (2012).
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Tang, L.

L. Tang, S. E. Kocabas, S. Latif, A. K. Okyay, D. Ly-Gagnon, K. C. Saraswat, and D. A. B. Miller, “Nanometre-scale germanium photodetector enhanced by a near-infrared dipole antenna,” Nat. Photonics 2(4), 226–229 (2008).
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V. M. Dubovik, L. A. Tosunyan, and V. V. Tugushev, “Axial toroidal moments in electrodynamics and solid-state physics,” Sov. Phys. JETP 63(2), 1-8 (1986).

Tsai, D. P.

Tugushev, V. V.

V. M. Dubovik and V. V. Tugushev, “Toroid moments in electrodynamics and solid-state physics,” Phys. Rep. 187(4), 145–202 (1990).
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V. M. Dubovik, L. A. Tosunyan, and V. V. Tugushev, “Axial toroidal moments in electrodynamics and solid-state physics,” Sov. Phys. JETP 63(2), 1-8 (1986).

Vaillon, R.

J. M. Geffrin, B. García-Cámara, R. Gómez-Medina, P. Albella, L. S. Froufe-Pérez, C. Eyraud, A. Litman, R. Vaillon, F. González, M. Nieto-Vesperinas, J. J. Sáenz, and F. Moreno, “Magnetic and electric coherence in forward- and back-scattered electromagnetic waves by a single dielectric subwavelength sphere,” Nat. Commun. 3, 1171 (2012).
[Crossref] [PubMed]

Vaman, G.

E. E. Radescu and G. Vaman, “Exact calculation of the angular momentum loss, recoil force, and radiation intensity for an arbitrary source in terms of electric, magnetic, and toroid multipoles,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 65(4), 046609 (2002).
[Crossref] [PubMed]

van Aken, P. A.

B. Ögüt, N. Talebi, R. Vogelgesang, W. Sigle, and P. A. van Aken, “Toroidal plasmonic eigenmodes in oligomer nanocavities for the visible,” Nano Lett. 12(10), 5239–5244 (2012).
[Crossref] [PubMed]

Vogelgesang, R.

B. Ögüt, N. Talebi, R. Vogelgesang, W. Sigle, and P. A. van Aken, “Toroidal plasmonic eigenmodes in oligomer nanocavities for the visible,” Nano Lett. 12(10), 5239–5244 (2012).
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Walsh, G. F.

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Figures (9)

Fig. 1
Fig. 1 For a single Si nano-disk in the anapole mode, (a) geometry of nano-disk and excitation condition for anapole mode, (b) and (c) are the E-field and H-field enhancement at anapole mode respectively, the superimposed arrows indicates the direction of the fields. (d) The full multipolar decomposition of the first contributing five multipole moments: electric dipole (p), magnetic dipole (m), toroidal dipole (T), electric quadrupole (Qe), magnetic quadrupole (Qm). The powers are normalized with respect to the maximum value by electric dipole in the investigated spectrum. (e) The far-field scattered power (green, in arbitrary units) as a sum of all intensity contribution from multipole moments in (d), as well and the actual scattering efficiency (blue) with normalization with respect to the geometrical cross-section area. In this case D = 350nm and H = 60nm.
Fig. 2
Fig. 2 For a single Si square nano-pixel in the anapole mode, (a) geometry of square nano-pixel and excitation condition for anapole mode. (b) The full multipolar decomposition of the first contributing five multipole moments: electric dipole (p), magnetic dipole (m), toroidal dipole (T), electric quadrupole (Qe), magnetic quadrupole (Qm), the interaction between p and T, which is proportional to the real part of their inner product <p, T>. The powers are normalized with k respect to the maximum value by electric dipole in the investigated spectrum. (c) and (d) are the E-field and H-field enhancement at anapole mode respectively, the superimposed arrows indicates the direction of the fields. For the simulated case D = 350nm and H = 60nm.
Fig. 3
Fig. 3 The effect of changing side length of Si square nano-pixels on various multipolar contributions, scattering cross-sections, and absorption rate enhancements. For fixed height of H = 100nm, (a) and (b) are for D = 500nm, (c) and (d) are for D = 700nm.
Fig. 4
Fig. 4 The effect of changing height of Si square nano-pixels on various multipolar contributions, scattering cross-sections, and absorption rate enhancements. For fixed side length D = 400nm, (a) and (b) are for H = 80nm, (c) and (d) are for H = 120nm.
Fig. 5
Fig. 5 (a) and (b) are the change multipolar decomposition for a single Ge nano-disk (D = 650nm, H = 1000nm) and square nano-pixel (D = 500nm, H = 100nm) respectively. (c) the absorption enhancement rates normalized to the thin-film cases for Si nano-disks with diameter D = 500nm and 600nm, as well as Si square nano-pixels with side length A = 500nm and 600nm. The height H are fixed as 100nm. (d) is shows counterpart cases with material in (c) replaced by Ge, and all geometric parameters unchanged.
Fig. 6
Fig. 6 (a) and (b) are the change in the wavelengths of anapole-induced absorption rate enhancement peaks depending on D and H respectively for Si nano-disks. In each panel, three representative fixed heights or diameters are shown. (c) and (d) are the similar study for Si square nano-pixels.
Fig. 7
Fig. 7 (a) and (b) are the change in the wavelengths of anapole-induced absorption rate enhancement peaks depending on D and H respectively for Ge nano-disks. In each panel, three representative fixed heights or diameters are shown. (c) and (d) are the similar study for Ge square nano-pixels.
Fig. 8
Fig. 8 (a) and (b) show the change in the wavelengths of anapole-induced absorption rate enhancement peaks for two linear polarizations at varying incident angles with respect to the normal to the surface, for Si nano-disk and square nano-pixel respectively (solid lines). Both have D = 350nm, and H = 60nm. The scattering efficiency Qsca is obtained by normalizing with the projected area of the square nano-pixel onto the plane of the wave front (dashed lines). (c) and (d) show the effect of absorption rate enhancement change for three representative cases with different thicknesses d of ITO (n = 1.8) coatings on both side of the Si nano-disk or square nano-pixel (insets) with the same geometries as in (a) and (b) respectively.
Fig. 9
Fig. 9 The absorption rate enhancements for a surface element formed by two Ge nano-disks with diameters D = 550nm and 700nm respectively (H = 100nm). (a) The absorption rate enhancements of each single Ge nano-disk. (b) shows the absorption rate enhancements of the combined element for three different separations, and the inset show that dimer elements are separated with distance d (center-to-center) in a combined surface element.. (c) shows the absorption rate enhancements of each single Ge square nano-pixel with D = 550nm and 700nm respectively (H = 100nm), and (d) shows the absorption rate enhancements of the combined element made of two Ge square nano-pixels.

Tables (1)

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Table 1 Current multipoles and corresponding far-field scattered power.

Equations (3)

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J(r)=iω ε 0 ( n 2 1)E(r)
γ abs = P abs / P abs 0
P abs = ω 2 ε'' | E(r) | 2 d 3 r

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