Abstract

Recently, using various intelligent approaches to achieve the efficient inverse design of photonic nanostructures with predefined and appropriate functionalities has attracted considerable attention. We propose a method to design subwavelength metal-dielectric nanoantennas and optimize the scattering directionality using a Bayesian optimization approach. The nanoantennas consisted of three gold disks separated by two dielectric layers. The geometrical parameters were optimized in an intelligent and fully automatic process. We showed that with the aid of the machine learning method, strong forward scattering or backward scattering at a specific wavelength could be efficiently achieved. We further showed that unidirectional scattering in opposite directions at two separate wavelengths can be designed. Moreover, it is possible to exchange the forward and backward directionality at two target wavelengths. The multipole decomposition approach was applied to analyze the multipole moments of the scattering field up to the third order. In the optimized unidirectional nanoantennas the electric and magnetic dipole moments satisfied the Kerker or anti-Kerker conditions at the wavelengths of interest. Our results demonstrated the possibility of automatically designing nanoantennas for specific applications via a machine learning scheme.

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

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2019 (1)

E. A. Gurvitz, K. S. Ladutenko, P. A. Dergachev, A. B. Evlyukhin, A. E. Miroshnichenko, and A. S. Shalin, “All-dielectric nanophotonics: The high-order toroidal moments and anapole states in all-dielectric photonics,” Laser Photonics Rev. 13(5), 1970025 (2019).
[Crossref]

2018 (3)

A. F. Cihan, A. G. Curto, S. Raza, P. G. Kik, and M. L. Brongersma, “Silicon mie resonators for highly directional light emission from monolayer mos 2,” Nat. Photonics 12(5), 284–290 (2018).
[Crossref]

R. Li, X. Zhou, M. Panmai, J. Xiang, H. Liu, M. Ouyang, H. Fan, Q. Dai, and Z. Wei, “Broadband zero backward scattering by all-dielectric core-shell nanoparticles,” Opt. Express 26(22), 28891–28901 (2018).
[Crossref]

R. Alaee, C. Rockstuhl, and I. Fernandez-Corbaton, “An electromagnetic multipole expansion beyond the long-wavelength approximation,” Opt. Commun. 407, 17–21 (2018).
[Crossref]

2017 (3)

X. M. Zhang, J. J. Xiao, Q. Zhang, F. F. Qin, X. Cai, and F. Ye, “Dual-band unidirectional emission in a multilayered metal–dielectric nanoantenna,” ACS Omega 2(3), 774–783 (2017).
[Crossref]

P. D. Terekhov, K. V. Baryshnikova, Y. A. Artemyev, A. Karabchevsky, A. S. Shalin, and A. B. Evlyukhin, “Multipolar response of nonspherical silicon nanoparticles in the visible and near-infrared spectral ranges,” Phys. Rev. B 96(3), 035443 (2017).
[Crossref]

P. D. Terekhov, K. V. Baryshnikova, A. S. Shalin, K. Alina, and A. B. Evlyukhin, “Resonant forward scattering of light by high-refractive-index dielectric nanoparticles with toroidal dipole contribution,” Opt. Lett. 42(4), 835–838 (2017).
[Crossref]

2016 (2)

B. Shahriari, K. Swersky, Z. Wang, R. P. Adams, and N. De Freitas, “Taking the human out of the loop: A review of bayesian optimization,” Proc. IEEE 104(1), 148–175 (2016).
[Crossref]

F. F. Qin, Q. Zhang, and J. J. Xiao, “Sub-wavelength unidirectional antenna realized by stacked spoof localized surface plasmon resonators,” Sci. Rep. 6(1), 29773 (2016).
[Crossref]

2015 (5)

A. Pors, S. K. Andersen, and S. I. Bozhevolnyi, “Unidirectional scattering by nanoparticles near substrates: generalized Kerker conditions,” Opt. Express 23(22), 28808–28828 (2015).
[Crossref]

Q. Zhang, J. J. Xiao, M. Li, D. Han, and L. Gao, “Coexistence of scattering enhancement and suppression by plasmonic cavity modes in loaded dimer gap-Antennas,” Sci. Rep. 5(1) 17234 (2015).
[Crossref]

X. M. Zhang, J. J. Xiao, Q. Zhang, L. M. Li, and Y. Yao, “Plasmonic tm-like cavity modes and the hybridization in multilayer metal-dielectric nanoantenna,” Opt. Express 23(12), 16122–16132 (2015).
[Crossref]

Q. Zhang, J. J. Xiao, X. M. Zhang, D. Han, and L. Gao, “Core–shell-structured dielectric–metal circular nanodisk antenna: gap plasmon assisted magnetic toroid-like cavity modes,” ACS Photonics 2(1), 60–65 (2015).
[Crossref]

P. Y. Chen, C. Argyropoulos, G. D’Aguanno, and A. Alù, “Enhanced second-harmonic generation by metasurface nanomixer and nanocavity,” ACS Photonics 2(8), 1000–1006 (2015).
[Crossref]

2014 (4)

G. M. Akselrod, C. Argyropoulos, T. B. Hoang, C. Ciracì, C. Fang, J. Huang, D. R. Smith, and M. H. Mikkelsen, “enhancement in plasmonic nanoantennas,” Nat. Photonics 8(11), 835–840 (2014).
[Crossref]

Z. Xi, Y. Lu, W. Yu, P. Wang, and H. Ming, “Unidirectional surface plasmon launcher: rotating dipole mimicked by optical antennas,” J. Optics 16(10), 105002 (2014).
[Crossref]

M. R. Shcherbakov, D. N. Neshev, B. Hopkins, A. S. Shorokhov, I. Staude, E. V. Melik-Gaykazyan, and A. A. Fedyanin, “Enhanced third-harmonic generation in silicon nanoparticles driven by magnetic response,” Nano Lett. 14(11), 6488–6492 (2014).
[Crossref]

J. R. Gardner, M. J. Kusner, Z. E. Xu, K. Q. Weinberger, and J. P. Cunningham, “Bayesian Optimization with Inequality Constraints,” PMLR 32(2), 937–945 (2014).

2013 (3)

I. Staude, A. E. Miroshnichenko, M. Decker, N. T. Fofang, S. Liu, E. Gonzales, and Y. Kivshar, “Tailoring directional scattering through magnetic and electric resonances in subwavelength silicon nanodisks,” ACS Nano 7(9), 7824–7832 (2013).
[Crossref]

F. J. Rodríguez-Fortuño, G. Marino, P. Ginzburg, D. O’Connor, A. Martínez, G. A. Wurtz, and A. V. Zayats, “Near-field interference for the unidirectional excitation of electromagnetic guided modes,” Science 340(6130), 328–330 (2013).
[Crossref]

D. Sikdar, I. D. Rukhlenko, W. Cheng, and M. Premaratne, “Optimized gold nanoshell ensembles for biomedical applications,” Nanoscale Res. Lett. 8(1), 142 (2013).
[Crossref]

2012 (5)

X. J. Ni, N. K. Emani, A. V. Kildishev, A. Boltasseva, and V. M. Shalaev, “Broadband light bending with plasmonic nanoantennas,” Science 335(6067), 427 (2012).
[Crossref]

A. E. Miroshnichenko, B. Luk’yanchuk, S. A. Maier, and Y. S. Kivshar, “Optically induced interaction of magnetic moments in hybrid metamaterials,” ACS Nano 6(1), 837–842 (2012).
[Crossref]

I. Ament, J. Prasad, A. Henkel, S. Schmachtel, and C. Sönnichsen, “Single unlabeled protein detection on individual plasmonic nanoparticles,” Nano Lett. 12(2), 1092–1095 (2012).
[Crossref]

I. S. Maksymov, I. Staude, A. E. Miroshnichenko, and Y. S. Kivshar, “Optical Yagi-Uda nanoantennas,” Nanophotonics 1, 65–81 (2012).
[Crossref]

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]

2011 (4)

D. Dregely, R. Taubert, J. Dorfmüller, R. Vogelgesang, K. Kern, and H. Giessen, “3D optical Yagi–Uda nanoantenna array,” Nat. Commun. 2(1), 267 (2011).
[Crossref]

L. Novotny and N. van Hulst, “Antennas for light,” Nat. Photonics 5(2), 83–90 (2011).
[Crossref]

N. F. Yu, P. Genevet, M. A. Kats, F. Aieta, J. P. Tetienne, F. Capasso, and Z. Gaburro, “Light propagation with phase discontinuities: generalized laws of reflection and refraction,” Science 334(6054), 333–337 (2011).
[Crossref]

A. B. Evlyukhin, C. Reinhardt, and B. N. Chichkov, “Multipole light scattering by nonspherical nanoparticles in the discrete dipole approximation,” Phys. Rev. B 84(23), 235429 (2011).
[Crossref]

2010 (5)

A. G. Curto, G. Volpe, T. H. Taminiau, M. P. Kreuzer, R. Quidant, and N. F. Van Hulst, “Unidirectional emission of a quantum dot coupled to a nanoantenna,” Science, 329(5994) 930–933 (2010).
[Crossref]

Z. Ruan and S. Fan, “Superscattering of light from subwavelength nanostructures,” Phys. Rev. Lett. 105(1), 013901 (2010).
[Crossref]

H. A. Atwater and A. Polman, “Plasmonics for improved photovoltaic devices,” Nat. Mater. 9(3), 205–213 (2010).
[Crossref]

A. B. Evlyukhin, S. I. Bozhevolnyi, A. Pors, M. G. Nielsen, I. P. Radko, M. Willatzen, and O. Albrektsen, “Detuned electrical dipoles for plasmonic sensing,” Nano Lett. 10(11), 4571–4577 (2010).
[Crossref]

T. Kosako, Y. Kadoya, and H. F. Hofmann, “Directional control of light by a nano-optical Yagi-Uda antenna,” Nat. Photonics 4(5), 312–315 (2010).
[Crossref]

2009 (1)

T. Pakizeh and M. Käll, “Unidirectional ultracompact optical nanoantennas,” Nano Lett. 9(6), 2343–2349 (2009).
[Crossref]

2008 (1)

N. Noginova, G. Zhu, M. Mavy, and A. Noginov, “Magnetic dipole based system for probing optical magnetism,” J. Appl. Phys. 103(7), 07E901 (2008).
[Crossref]

2006 (1)

S. Kühn, U. Håkanson, L. Rogobete, and V. Sandoghdar, “Enhancement of single-molecule fluorescence using a gold nanoparticle as an optical nanoantenna,” Phys. Rev. Lett. 97(1), 017402 (2006).
[Crossref]

2005 (1)

P. J. Schuck, D. P. Fromm, A. Sundaramurthy, G. S. Kino, and W. E. Moerner, “Improving the mismatch between light and nanoscale objects with gold bowtie nanoantennas,” Phys. Rev. Lett. 94(1), 017402 (2005).
[Crossref]

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,” Phys. Rev. E 65(4), 046609 (2002).
[Crossref]

2001 (1)

D. R. Jones, “A taxonomy of global optimization methods based on response surfaces,” J. Global Optim. 21(4), 345–383 (2001).
[Crossref]

1997 (2)

S. Nie and S. R. Emory, “Probing single molecules and single nanoparticles by surface-enhanced Raman scattering,” Science 275(5303), 1102–1106 (1997).
[Crossref]

E. A. Jones and W. T. Joines, “Design of Yagi-Uda antennas using genetic algorithms,” IEEE Trans. Antennas Propag. 45(9), 1386–1392 (1997).
[Crossref]

1983 (1)

1972 (1)

P. B. Johnson and R. W. Christy, “Optical constants of the noblemetals,” Phys. Rev. B 6(12), 4370–4379 (1972).
[Crossref]

Adams, R. P.

B. Shahriari, K. Swersky, Z. Wang, R. P. Adams, and N. De Freitas, “Taking the human out of the loop: A review of bayesian optimization,” Proc. IEEE 104(1), 148–175 (2016).
[Crossref]

Aieta, F.

N. F. Yu, P. Genevet, M. A. Kats, F. Aieta, J. P. Tetienne, F. Capasso, and Z. Gaburro, “Light propagation with phase discontinuities: generalized laws of reflection and refraction,” Science 334(6054), 333–337 (2011).
[Crossref]

Akselrod, G. M.

G. M. Akselrod, C. Argyropoulos, T. B. Hoang, C. Ciracì, C. Fang, J. Huang, D. R. Smith, and M. H. Mikkelsen, “enhancement in plasmonic nanoantennas,” Nat. Photonics 8(11), 835–840 (2014).
[Crossref]

Alaee, R.

R. Alaee, C. Rockstuhl, and I. Fernandez-Corbaton, “An electromagnetic multipole expansion beyond the long-wavelength approximation,” Opt. Commun. 407, 17–21 (2018).
[Crossref]

Albrektsen, O.

A. B. Evlyukhin, S. I. Bozhevolnyi, A. Pors, M. G. Nielsen, I. P. Radko, M. Willatzen, and O. Albrektsen, “Detuned electrical dipoles for plasmonic sensing,” Nano Lett. 10(11), 4571–4577 (2010).
[Crossref]

Alina, K.

Alù, A.

P. Y. Chen, C. Argyropoulos, G. D’Aguanno, and A. Alù, “Enhanced second-harmonic generation by metasurface nanomixer and nanocavity,” ACS Photonics 2(8), 1000–1006 (2015).
[Crossref]

Ament, I.

I. Ament, J. Prasad, A. Henkel, S. Schmachtel, and C. Sönnichsen, “Single unlabeled protein detection on individual plasmonic nanoparticles,” Nano Lett. 12(2), 1092–1095 (2012).
[Crossref]

Andersen, S. K.

Argyropoulos, C.

P. Y. Chen, C. Argyropoulos, G. D’Aguanno, and A. Alù, “Enhanced second-harmonic generation by metasurface nanomixer and nanocavity,” ACS Photonics 2(8), 1000–1006 (2015).
[Crossref]

G. M. Akselrod, C. Argyropoulos, T. B. Hoang, C. Ciracì, C. Fang, J. Huang, D. R. Smith, and M. H. Mikkelsen, “enhancement in plasmonic nanoantennas,” Nat. Photonics 8(11), 835–840 (2014).
[Crossref]

Artemyev, Y. A.

P. D. Terekhov, K. V. Baryshnikova, Y. A. Artemyev, A. Karabchevsky, A. S. Shalin, and A. B. Evlyukhin, “Multipolar response of nonspherical silicon nanoparticles in the visible and near-infrared spectral ranges,” Phys. Rev. B 96(3), 035443 (2017).
[Crossref]

Atwater, H. A.

H. A. Atwater and A. Polman, “Plasmonics for improved photovoltaic devices,” Nat. Mater. 9(3), 205–213 (2010).
[Crossref]

Baryshnikova, K. V.

P. D. Terekhov, K. V. Baryshnikova, Y. A. Artemyev, A. Karabchevsky, A. S. Shalin, and A. B. Evlyukhin, “Multipolar response of nonspherical silicon nanoparticles in the visible and near-infrared spectral ranges,” Phys. Rev. B 96(3), 035443 (2017).
[Crossref]

P. D. Terekhov, K. V. Baryshnikova, A. S. Shalin, K. Alina, and A. B. Evlyukhin, “Resonant forward scattering of light by high-refractive-index dielectric nanoparticles with toroidal dipole contribution,” Opt. Lett. 42(4), 835–838 (2017).
[Crossref]

Boltasseva, A.

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X. J. Ni, N. K. Emani, A. V. Kildishev, A. Boltasseva, and V. M. Shalaev, “Broadband light bending with plasmonic nanoantennas,” Science 335(6067), 427 (2012).
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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).
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A. E. Miroshnichenko, B. Luk’yanchuk, S. A. Maier, and Y. S. Kivshar, “Optically induced interaction of magnetic moments in hybrid metamaterials,” ACS Nano 6(1), 837–842 (2012).
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J. R. Gardner, M. J. Kusner, Z. E. Xu, K. Q. Weinberger, and J. P. Cunningham, “Bayesian Optimization with Inequality Constraints,” PMLR 32(2), 937–945 (2014).

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E. A. Gurvitz, K. S. Ladutenko, P. A. Dergachev, A. B. Evlyukhin, A. E. Miroshnichenko, and A. S. Shalin, “All-dielectric nanophotonics: The high-order toroidal moments and anapole states in all-dielectric photonics,” Laser Photonics Rev. 13(5), 1970025 (2019).
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Li, M.

Q. Zhang, J. J. Xiao, M. Li, D. Han, and L. Gao, “Coexistence of scattering enhancement and suppression by plasmonic cavity modes in loaded dimer gap-Antennas,” Sci. Rep. 5(1) 17234 (2015).
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Liu, H.

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I. Staude, A. E. Miroshnichenko, M. Decker, N. T. Fofang, S. Liu, E. Gonzales, 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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A. E. Miroshnichenko, B. Luk’yanchuk, S. A. Maier, and Y. S. Kivshar, “Optically induced interaction of magnetic moments in hybrid metamaterials,” ACS Nano 6(1), 837–842 (2012).
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G. M. Akselrod, C. Argyropoulos, T. B. Hoang, C. Ciracì, C. Fang, J. Huang, D. R. Smith, and M. H. Mikkelsen, “enhancement in plasmonic nanoantennas,” Nat. Photonics 8(11), 835–840 (2014).
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E. A. Gurvitz, K. S. Ladutenko, P. A. Dergachev, A. B. Evlyukhin, A. E. Miroshnichenko, and A. S. Shalin, “All-dielectric nanophotonics: The high-order toroidal moments and anapole states in all-dielectric photonics,” Laser Photonics Rev. 13(5), 1970025 (2019).
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M. R. Shcherbakov, D. N. Neshev, B. Hopkins, A. S. Shorokhov, I. Staude, E. V. Melik-Gaykazyan, and A. A. Fedyanin, “Enhanced third-harmonic generation in silicon nanoparticles driven by magnetic response,” Nano Lett. 14(11), 6488–6492 (2014).
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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]

Ni, X. J.

X. J. Ni, N. K. Emani, A. V. Kildishev, A. Boltasseva, and V. M. Shalaev, “Broadband light bending with plasmonic nanoantennas,” Science 335(6067), 427 (2012).
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S. Nie and S. R. Emory, “Probing single molecules and single nanoparticles by surface-enhanced Raman scattering,” Science 275(5303), 1102–1106 (1997).
[Crossref]

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A. B. Evlyukhin, S. I. Bozhevolnyi, A. Pors, M. G. Nielsen, I. P. Radko, M. Willatzen, and O. Albrektsen, “Detuned electrical dipoles for plasmonic sensing,” Nano Lett. 10(11), 4571–4577 (2010).
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F. J. Rodríguez-Fortuño, G. Marino, P. Ginzburg, D. O’Connor, A. Martínez, G. A. Wurtz, and A. V. Zayats, “Near-field interference for the unidirectional excitation of electromagnetic guided modes,” Science 340(6130), 328–330 (2013).
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T. Pakizeh and M. Käll, “Unidirectional ultracompact optical nanoantennas,” Nano Lett. 9(6), 2343–2349 (2009).
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H. A. Atwater and A. Polman, “Plasmonics for improved photovoltaic devices,” Nat. Mater. 9(3), 205–213 (2010).
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A. Pors, S. K. Andersen, and S. I. Bozhevolnyi, “Unidirectional scattering by nanoparticles near substrates: generalized Kerker conditions,” Opt. Express 23(22), 28808–28828 (2015).
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Prasad, J.

I. Ament, J. Prasad, A. Henkel, S. Schmachtel, and C. Sönnichsen, “Single unlabeled protein detection on individual plasmonic nanoparticles,” Nano Lett. 12(2), 1092–1095 (2012).
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D. Sikdar, I. D. Rukhlenko, W. Cheng, and M. Premaratne, “Optimized gold nanoshell ensembles for biomedical applications,” Nanoscale Res. Lett. 8(1), 142 (2013).
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X. M. Zhang, J. J. Xiao, Q. Zhang, F. F. Qin, X. Cai, and F. Ye, “Dual-band unidirectional emission in a multilayered metal–dielectric nanoantenna,” ACS Omega 2(3), 774–783 (2017).
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F. F. Qin, Q. Zhang, and J. J. Xiao, “Sub-wavelength unidirectional antenna realized by stacked spoof localized surface plasmon resonators,” Sci. Rep. 6(1), 29773 (2016).
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A. G. Curto, G. Volpe, T. H. Taminiau, M. P. Kreuzer, R. Quidant, and N. F. Van Hulst, “Unidirectional emission of a quantum dot coupled to a nanoantenna,” Science, 329(5994) 930–933 (2010).
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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,” Phys. Rev. E 65(4), 046609 (2002).
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A. B. Evlyukhin, S. I. Bozhevolnyi, A. Pors, M. G. Nielsen, I. P. Radko, M. Willatzen, and O. Albrektsen, “Detuned electrical dipoles for plasmonic sensing,” Nano Lett. 10(11), 4571–4577 (2010).
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C. E. Rasmussen and C. K. I. Williams, “Gaussian Processes for Machine Learning,” MIT Press: Cambridge, MA (2006).

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A. F. Cihan, A. G. Curto, S. Raza, P. G. Kik, and M. L. Brongersma, “Silicon mie resonators for highly directional light emission from monolayer mos 2,” Nat. Photonics 12(5), 284–290 (2018).
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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(23), 235429 (2011).
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R. Alaee, C. Rockstuhl, and I. Fernandez-Corbaton, “An electromagnetic multipole expansion beyond the long-wavelength approximation,” Opt. Commun. 407, 17–21 (2018).
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F. J. Rodríguez-Fortuño, G. Marino, P. Ginzburg, D. O’Connor, A. Martínez, G. A. Wurtz, and A. V. Zayats, “Near-field interference for the unidirectional excitation of electromagnetic guided modes,” Science 340(6130), 328–330 (2013).
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D. Sikdar, I. D. Rukhlenko, W. Cheng, and M. Premaratne, “Optimized gold nanoshell ensembles for biomedical applications,” Nanoscale Res. Lett. 8(1), 142 (2013).
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I. Ament, J. Prasad, A. Henkel, S. Schmachtel, and C. Sönnichsen, “Single unlabeled protein detection on individual plasmonic nanoparticles,” Nano Lett. 12(2), 1092–1095 (2012).
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P. J. Schuck, D. P. Fromm, A. Sundaramurthy, G. S. Kino, and W. E. Moerner, “Improving the mismatch between light and nanoscale objects with gold bowtie nanoantennas,” Phys. Rev. Lett. 94(1), 017402 (2005).
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P. D. Terekhov, K. V. Baryshnikova, Y. A. Artemyev, A. Karabchevsky, A. S. Shalin, and A. B. Evlyukhin, “Multipolar response of nonspherical silicon nanoparticles in the visible and near-infrared spectral ranges,” Phys. Rev. B 96(3), 035443 (2017).
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P. D. Terekhov, K. V. Baryshnikova, A. S. Shalin, K. Alina, and A. B. Evlyukhin, “Resonant forward scattering of light by high-refractive-index dielectric nanoparticles with toroidal dipole contribution,” Opt. Lett. 42(4), 835–838 (2017).
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D. Sikdar, I. D. Rukhlenko, W. Cheng, and M. Premaratne, “Optimized gold nanoshell ensembles for biomedical applications,” Nanoscale Res. Lett. 8(1), 142 (2013).
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G. M. Akselrod, C. Argyropoulos, T. B. Hoang, C. Ciracì, C. Fang, J. Huang, D. R. Smith, and M. H. Mikkelsen, “enhancement in plasmonic nanoantennas,” Nat. Photonics 8(11), 835–840 (2014).
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I. Ament, J. Prasad, A. Henkel, S. Schmachtel, and C. Sönnichsen, “Single unlabeled protein detection on individual plasmonic nanoparticles,” Nano Lett. 12(2), 1092–1095 (2012).
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M. R. Shcherbakov, D. N. Neshev, B. Hopkins, A. S. Shorokhov, I. Staude, E. V. Melik-Gaykazyan, and A. A. Fedyanin, “Enhanced third-harmonic generation in silicon nanoparticles driven by magnetic response,” Nano Lett. 14(11), 6488–6492 (2014).
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I. Staude, A. E. Miroshnichenko, M. Decker, N. T. Fofang, S. Liu, E. Gonzales, 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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I. S. Maksymov, I. Staude, A. E. Miroshnichenko, and Y. S. Kivshar, “Optical Yagi-Uda nanoantennas,” Nanophotonics 1, 65–81 (2012).
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P. J. Schuck, D. P. Fromm, A. Sundaramurthy, G. S. Kino, and W. E. Moerner, “Improving the mismatch between light and nanoscale objects with gold bowtie nanoantennas,” Phys. Rev. Lett. 94(1), 017402 (2005).
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B. Shahriari, K. Swersky, Z. Wang, R. P. Adams, and N. De Freitas, “Taking the human out of the loop: A review of bayesian optimization,” Proc. IEEE 104(1), 148–175 (2016).
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A. G. Curto, G. Volpe, T. H. Taminiau, M. P. Kreuzer, R. Quidant, and N. F. Van Hulst, “Unidirectional emission of a quantum dot coupled to a nanoantenna,” Science, 329(5994) 930–933 (2010).
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D. Dregely, R. Taubert, J. Dorfmüller, R. Vogelgesang, K. Kern, and H. Giessen, “3D optical Yagi–Uda nanoantenna array,” Nat. Commun. 2(1), 267 (2011).
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P. D. Terekhov, K. V. Baryshnikova, A. S. Shalin, K. Alina, and A. B. Evlyukhin, “Resonant forward scattering of light by high-refractive-index dielectric nanoparticles with toroidal dipole contribution,” Opt. Lett. 42(4), 835–838 (2017).
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P. D. Terekhov, K. V. Baryshnikova, Y. A. Artemyev, A. Karabchevsky, A. S. Shalin, and A. B. Evlyukhin, “Multipolar response of nonspherical silicon nanoparticles in the visible and near-infrared spectral ranges,” Phys. Rev. B 96(3), 035443 (2017).
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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,” Phys. Rev. E 65(4), 046609 (2002).
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L. Novotny and N. van Hulst, “Antennas for light,” Nat. Photonics 5(2), 83–90 (2011).
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A. G. Curto, G. Volpe, T. H. Taminiau, M. P. Kreuzer, R. Quidant, and N. F. Van Hulst, “Unidirectional emission of a quantum dot coupled to a nanoantenna,” Science, 329(5994) 930–933 (2010).
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A. G. Curto, G. Volpe, T. H. Taminiau, M. P. Kreuzer, R. Quidant, and N. F. Van Hulst, “Unidirectional emission of a quantum dot coupled to a nanoantenna,” Science, 329(5994) 930–933 (2010).
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Wang, D. S.

Wang, P.

Z. Xi, Y. Lu, W. Yu, P. Wang, and H. Ming, “Unidirectional surface plasmon launcher: rotating dipole mimicked by optical antennas,” J. Optics 16(10), 105002 (2014).
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B. Shahriari, K. Swersky, Z. Wang, R. P. Adams, and N. De Freitas, “Taking the human out of the loop: A review of bayesian optimization,” Proc. IEEE 104(1), 148–175 (2016).
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A. B. Evlyukhin, S. I. Bozhevolnyi, A. Pors, M. G. Nielsen, I. P. Radko, M. Willatzen, and O. Albrektsen, “Detuned electrical dipoles for plasmonic sensing,” Nano Lett. 10(11), 4571–4577 (2010).
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Z. Xi, Y. Lu, W. Yu, P. Wang, and H. Ming, “Unidirectional surface plasmon launcher: rotating dipole mimicked by optical antennas,” J. Optics 16(10), 105002 (2014).
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Xiang, J.

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X. M. Zhang, J. J. Xiao, Q. Zhang, F. F. Qin, X. Cai, and F. Ye, “Dual-band unidirectional emission in a multilayered metal–dielectric nanoantenna,” ACS Omega 2(3), 774–783 (2017).
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F. F. Qin, Q. Zhang, and J. J. Xiao, “Sub-wavelength unidirectional antenna realized by stacked spoof localized surface plasmon resonators,” Sci. Rep. 6(1), 29773 (2016).
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Q. Zhang, J. J. Xiao, X. M. Zhang, D. Han, and L. Gao, “Core–shell-structured dielectric–metal circular nanodisk antenna: gap plasmon assisted magnetic toroid-like cavity modes,” ACS Photonics 2(1), 60–65 (2015).
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X. M. Zhang, J. J. Xiao, Q. Zhang, L. M. Li, and Y. Yao, “Plasmonic tm-like cavity modes and the hybridization in multilayer metal-dielectric nanoantenna,” Opt. Express 23(12), 16122–16132 (2015).
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Q. Zhang, J. J. Xiao, M. Li, D. Han, and L. Gao, “Coexistence of scattering enhancement and suppression by plasmonic cavity modes in loaded dimer gap-Antennas,” Sci. Rep. 5(1) 17234 (2015).
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J. R. Gardner, M. J. Kusner, Z. E. Xu, K. Q. Weinberger, and J. P. Cunningham, “Bayesian Optimization with Inequality Constraints,” PMLR 32(2), 937–945 (2014).

Yao, Y.

Ye, F.

X. M. Zhang, J. J. Xiao, Q. Zhang, F. F. Qin, X. Cai, and F. Ye, “Dual-band unidirectional emission in a multilayered metal–dielectric nanoantenna,” ACS Omega 2(3), 774–783 (2017).
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N. F. Yu, P. Genevet, M. A. Kats, F. Aieta, J. P. Tetienne, F. Capasso, and Z. Gaburro, “Light propagation with phase discontinuities: generalized laws of reflection and refraction,” Science 334(6054), 333–337 (2011).
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Z. Xi, Y. Lu, W. Yu, P. Wang, and H. Ming, “Unidirectional surface plasmon launcher: rotating dipole mimicked by optical antennas,” J. Optics 16(10), 105002 (2014).
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F. J. Rodríguez-Fortuño, G. Marino, P. Ginzburg, D. O’Connor, A. Martínez, G. A. Wurtz, and A. V. Zayats, “Near-field interference for the unidirectional excitation of electromagnetic guided modes,” Science 340(6130), 328–330 (2013).
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X. M. Zhang, J. J. Xiao, Q. Zhang, F. F. Qin, X. Cai, and F. Ye, “Dual-band unidirectional emission in a multilayered metal–dielectric nanoantenna,” ACS Omega 2(3), 774–783 (2017).
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F. F. Qin, Q. Zhang, and J. J. Xiao, “Sub-wavelength unidirectional antenna realized by stacked spoof localized surface plasmon resonators,” Sci. Rep. 6(1), 29773 (2016).
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Q. Zhang, J. J. Xiao, X. M. Zhang, D. Han, and L. Gao, “Core–shell-structured dielectric–metal circular nanodisk antenna: gap plasmon assisted magnetic toroid-like cavity modes,” ACS Photonics 2(1), 60–65 (2015).
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X. M. Zhang, J. J. Xiao, Q. Zhang, L. M. Li, and Y. Yao, “Plasmonic tm-like cavity modes and the hybridization in multilayer metal-dielectric nanoantenna,” Opt. Express 23(12), 16122–16132 (2015).
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Q. Zhang, J. J. Xiao, X. M. Zhang, D. Han, and L. Gao, “Core–shell-structured dielectric–metal circular nanodisk antenna: gap plasmon assisted magnetic toroid-like cavity modes,” ACS Photonics 2(1), 60–65 (2015).
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X. M. Zhang, J. J. Xiao, Q. Zhang, L. M. Li, and Y. Yao, “Plasmonic tm-like cavity modes and the hybridization in multilayer metal-dielectric nanoantenna,” Opt. Express 23(12), 16122–16132 (2015).
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ACS Omega (1)

X. M. Zhang, J. J. Xiao, Q. Zhang, F. F. Qin, X. Cai, and F. Ye, “Dual-band unidirectional emission in a multilayered metal–dielectric nanoantenna,” ACS Omega 2(3), 774–783 (2017).
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ACS Photonics (2)

Q. Zhang, J. J. Xiao, X. M. Zhang, D. Han, and L. Gao, “Core–shell-structured dielectric–metal circular nanodisk antenna: gap plasmon assisted magnetic toroid-like cavity modes,” ACS Photonics 2(1), 60–65 (2015).
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E. A. Gurvitz, K. S. Ladutenko, P. A. Dergachev, A. B. Evlyukhin, A. E. Miroshnichenko, and A. S. Shalin, “All-dielectric nanophotonics: The high-order toroidal moments and anapole states in all-dielectric photonics,” Laser Photonics Rev. 13(5), 1970025 (2019).
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Nano Lett. (4)

I. Ament, J. Prasad, A. Henkel, S. Schmachtel, and C. Sönnichsen, “Single unlabeled protein detection on individual plasmonic nanoparticles,” Nano Lett. 12(2), 1092–1095 (2012).
[Crossref]

M. R. Shcherbakov, D. N. Neshev, B. Hopkins, A. S. Shorokhov, I. Staude, E. V. Melik-Gaykazyan, and A. A. Fedyanin, “Enhanced third-harmonic generation in silicon nanoparticles driven by magnetic response,” Nano Lett. 14(11), 6488–6492 (2014).
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A. B. Evlyukhin, S. I. Bozhevolnyi, A. Pors, M. G. Nielsen, I. P. Radko, M. Willatzen, and O. Albrektsen, “Detuned electrical dipoles for plasmonic sensing,” Nano Lett. 10(11), 4571–4577 (2010).
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T. Pakizeh and M. Käll, “Unidirectional ultracompact optical nanoantennas,” Nano Lett. 9(6), 2343–2349 (2009).
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Nanophotonics (1)

I. S. Maksymov, I. Staude, A. E. Miroshnichenko, and Y. S. Kivshar, “Optical Yagi-Uda nanoantennas,” Nanophotonics 1, 65–81 (2012).
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Nanoscale Res. Lett. (1)

D. Sikdar, I. D. Rukhlenko, W. Cheng, and M. Premaratne, “Optimized gold nanoshell ensembles for biomedical applications,” Nanoscale Res. Lett. 8(1), 142 (2013).
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Nat. Commun. (1)

D. Dregely, R. Taubert, J. Dorfmüller, R. Vogelgesang, K. Kern, and H. Giessen, “3D optical Yagi–Uda nanoantenna array,” Nat. Commun. 2(1), 267 (2011).
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Nat. Mater. (1)

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Opt. Lett. (1)

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[Crossref]

Phys. Rev. Lett. (3)

P. J. Schuck, D. P. Fromm, A. Sundaramurthy, G. S. Kino, and W. E. Moerner, “Improving the mismatch between light and nanoscale objects with gold bowtie nanoantennas,” Phys. Rev. Lett. 94(1), 017402 (2005).
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[Crossref]

PMLR (1)

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Proc. IEEE (1)

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[Crossref]

Sci. Rep. (2)

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[Crossref]

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[Crossref]

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[Crossref]

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[Crossref]

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[Crossref]

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http://www.comsol.com (accessed Jan 10, 2017).

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Figures (7)

Fig. 1.
Fig. 1. Flowchart for the design optimization of the unidirectional scattering nanoantenna. The dashed box labeled COMSOL shows the schematic of the nanoantenna consisting of three gold nanodisks with diameters $d$ and thicknesses $t$, and they are separated by two different layers with thicknesses ${t_1}$ and ${t_2}$. The FS (forward scattering) is along the wave vector of the incident light ${\bf k}$, and it is opposite for the BS (backward scattering).
Fig. 2.
Fig. 2. FS and BS structure optimization for wavelength $\lambda = 670$ nm. (a) 5 optimization runs with different initial choices of the candidate sets for the case of forward and backward unidirectional scattering, respectively. (b) Far-field directivity ${G_{FB}}$ of the two nanoantennas: nanoantenna-I corresponds to the structure for BS and II corresponds to the structure for FS. Three-dimensional (3D) radiation patterns for (c) nanoantenna-I and (d) nanoantenna-II at $\lambda = 670$ nm.
Fig. 3.
Fig. 3. Scattering cross-sections and the multipole decompositions of the scattering spectra, including ED, MD, EQ and MQ, for nanoantenna-(a) I and (b) II. “Total Scat (COMSOL)” is the result calculated by the FEM method and “Sum Scat” is the sum of ED, MD, EQ and MQ.
Fig. 4.
Fig. 4. Radiation patterns for different wavelengths. The wavelengths correspond to the black arrows in Figs.  3(a) and 3(b). The wave vector of the incident light ${\bf k}$ was along the $+ z$ direction.
Fig. 5.
Fig. 5. (a) Far-field directivity ${G_{FB}}$ for nanoantenna-III. The insets show the 3D radiation patterns for wavelength $\lambda = 650$ and 750 nm, respectively. (b) Corresponding scattering cross-section spectra and the multipole decompositions. The insets shows the 2D radiation pattern in the $xz$ plane for the peak wavelength. The black curve in the inset corresponds to the peak at $\lambda = 475$ nm and the red curve corresponds to the high peak at $\lambda = 700$ nm.
Fig. 6.
Fig. 6. (a) Far-field directivity ${G_{FB}}$ of nanoantenna-IV and V. Corresponding scattering cross-section spectra and the multipole decompositions for nanoantenna (b) IV and (c) V. The insets in (b) and (c) show the tion pattern in the $yz$ plane for $\lambda = 600$ and 725 nm. In the inset of (c) the black curve corresponds to $\lambda = 600$ nm and the red curve corresponds to $\lambda = 725$ nm.
Fig. 7.
Fig. 7. Radiation patterns for points “a”, “b”, “c”, “d” and “e” marked in Figs.  6(b) and 6(c). (a) $\lambda = 511$ nm, (b) $\lambda = 536$ nm, (c)$\lambda = 563$ nm, (d)$\lambda = 670$ nm, (e)$\lambda = 543$ nm. The wave vector of the incident light ${\bf k}$ was along the $+ z$ direction.

Tables (3)

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Table 1. The optimal parameters of the nanoantenna-I and II (unit: nm)

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Table 2. The optimal parameters of the nanoantenna-III (unit: nm)

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Table 3. The optimal parameters of the nanoantenna-IV and V (unit: nm)

Equations (6)

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p α = V { P α j 0 ( k r ) + k 2 [ 3 2 ( r P ) r α 1 2 r 2 P α ] j 2 ( k r ) k r } d r
m α = 3 i ω 2 v d V ( r × P ) α j 1 ( k r ) k r d r
Q α β = 3 V { [ ( r β P α + r α P β ) 2 3 ( r P ) δ α β ] j 1 ( k r ) k r + 2 3 k 2 [ 5 r α r β ( r P ) ( r β P α + r α P β ) r 2 r 2 ( r P ) δ α β ] j 3 ( k r ) k r } d r
M α β = 5 ω v d i V [ r α ( r × P ) β + r β ( r × P ) α ] j 2 ( k r ) k r d r
σ s c a = ( μ 0 / ε 0 ε d ) 1 / 2 4 π ε 0 | E i n c | 2 [ 2 ω 4 ε d 1 / 2 3 c 3 | p | 2 + 2 ω 4 ε d 1 / 2 3 c 3 | m | 2 + ω 6 ε d 3 / 2 5 c 5 | Q ^ | 2 + ω 6 ε d 3 / 2 20 c 5 | M ^ | 2 ]
f = i = 1 G F B λ i ( i = 1 , 2 )

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