Abstract

Despite the recent extensive study of the nonradiating (anapole) mode in the resonant light scattering by nanoparticles, the key questions, about the dynamics of its excitation at the leading front of the incident pulse and collapse behind the trailing edge, still remain open. We answer the questions, first, by direct numerical integration of the complete set of the Maxwell equations, describing the scattering of a rectangular laser pulse by a dielectric cylinder. The simulation shows that while the excitation and the collapse periods, both have the same characteristic time-scale, the dynamics of these processes are qualitatively different. The relaxation to the steady-state scattering at the leading front is accompanied by high-amplitude oscillatory modulations of the envelope of the basic electromagnetic oscillations, while behind the trailing edge the decay of the envelope is monotonic. Then, we present the general arguments showing that this is the case for the anapole excited in any classical system. Next, we introduce a simple, exactly integrable yet accurate, physically transparent model describing the dynamics of the anapole. The model admits generalization to a broad class of resonant phenomena and may be regarded as a compliment to the commonly used Temporal Coupled-Mode Theory.

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

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References

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  8. B. Luk’yanchuk, R. Paniagua-Domínguez, A. I. Kuznetsov, A. E. Miroshnichenko, and Y. S. Kivshar, “Hybrid anapole modes of high-index dielectric nanoparticles,” Phys. Rev. A 95, 063820 (2017).
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    [Crossref]
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    [Crossref]
  30. P. Kapitanova, V. Ternovski, A. Miroshnichenko, N. Pavlov, P. Belov, Y. Kivshar, and M. Tribelsky, “Giant field enhancement in high-index dielectric subwavelength particles,” Sci. Rep. 7, 731 (2017).
    [Crossref] [PubMed]
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2017 (4)

J. Gongora, A. Miroshnichenko, Y. Kivshar, and A. Fratalocchi, “Anapole nanolasers for mode-locking and ultrafast pulse generation,” Nat. Commun. 8, 15535 (2017).
[Crossref]

B. Luk’yanchuk, R. Paniagua-Domínguez, A. I. Kuznetsov, A. E. Miroshnichenko, and Y. S. Kivshar, “Hybrid anapole modes of high-index dielectric nanoparticles,” Phys. Rev. A 95, 063820 (2017).
[Crossref]

M. F. Limonov, M. V. Rybin, A. N. Poddubny, and Y. S. Kivshar, “Fano resonances in photonics,” Nat. Photon. 11, 543 (2017).
[Crossref]

P. Kapitanova, V. Ternovski, A. Miroshnichenko, N. Pavlov, P. Belov, Y. Kivshar, and M. Tribelsky, “Giant field enhancement in high-index dielectric subwavelength particles,” Sci. Rep. 7, 731 (2017).
[Crossref] [PubMed]

2016 (4)

N. Papasimakis, V. Fedotov, V. Savinov, T. Raybould, and N. Zheludev, “Electromagnetic toroidal excitations in matter and free space,” Nat. Mater. 15, 263–271 (2016).
[Crossref] [PubMed]

L. Wei, Z. Xi, N. Bhattacharya, and H. P. Urbach, “Excitation of the radiationless anapole mode,” Optica 3, 799–802 (2016).
[Crossref]

C. W. Hsu, B. Zhen, A. D. Stone, J. D. Joannopoulos, and M. Soljačić, “Bound states in the continuum,” Nat. Rev. Mater. 1, 16048 (2016).
[Crossref]

M. I. Tribelsky and A. E. Miroshnichenko, “Giant in-particle field concentration and fano resonances at light scattering by high-refractive-index particles,” Phys. Rev. A 93, 053837 (2016).
[Crossref]

2015 (2)

B. S. Luk’yanchuk, N. V. Voshchinnikov, R. Paniagua-Domínguez, and A. I. Kuznetsov, “Optimum forward light scattering by spherical and spheroidal dielectric nanoparticles with high refractive index,” ACS Photon. 2, 993–999 (2015).
[Crossref]

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]

2014 (3)

M. Rahmani, A. E. Miroshnichenko, D. Y. Lei, B. Luk’yanchuk, M. I. Tribelsky, A. I. Kuznetsov, Y. S. Kivshar, Y. Francescato, V. Giannini, and M. Hong et al., “Beyond the hybridization effects in plasmonic nanoclusters: diffraction-induced enhanced absorption and scattering,” Small 10, 576–583 (2014).
[Crossref]

C. W. Hsu, B. G. DeLacy, S. G. Johnson, J. D. Joannopoulos, and M. Soljačić, “Theoretical criteria for scattering dark states in nanostructured particles,” Nano Lett. 14, 2783–2788 (2014).
[Crossref] [PubMed]

M. G. Silveirinha, “Trapping light in open plasmonic nanostructures,” Phys. Rev. A 89, 023813 (2014).
[Crossref]

2010 (1)

Z. Ruan and S. Fan, “Temporal coupled-mode theory for fano resonance in light scattering by a single obstacle,” J. Phys. Chem. C 114, 7324–7329 (2010).
[Crossref]

2007 (2)

B. Luk’yanchuk, M. Tribelsky, V. Ternovsky, Z. Wang, M. Hong, L. Shi, and T. Chong, “Peculiarities of light scattering by nanoparticles and nanowires near plasmon resonance frequencies in weakly dissipating materials,” J. Opt. A: Pure Appl. Opt. 9, S294–S300 (2007).
[Crossref]

B. Luk’yanchuk, Z. Wang, M. Tribelsky, V. Ternovsky, M. Hong, and T. Chong, “Peculiarities of light scattering by nanoparticles and nanowires near plasmon resonance frequencies,” J. Phys. Conf. Ser. 59, 234–239 (2007).
[Crossref]

2006 (2)

Y. S. Joe, A. M. Satanin, and C. S. Kim, “Classical analogy of fano resonances,” Phys. Scripta 74, 259–266 (2006).
[Crossref]

B. Luk’yanchuk, M. Tribel’skii, and V. Ternovskii, “Light scattering at nanoparticles close to plasmon resonance frequencies,” J. Opt. Tech. 73, 371–377 (2006).
[Crossref]

1966 (1)

K. Yee, “Numerical solution of initial boundary value problems involving maxwell’s equations in isotropic media,” IEEE Transactions on antennas propagation 14, 302–307 (1966).
[Crossref]

1961 (1)

U. Fano, “Effects of configuration interaction on intensities and phase shifts,” Phys. Rev. 124, 1866–1878 (1961).
[Crossref]

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]

Belov, P.

P. Kapitanova, V. Ternovski, A. Miroshnichenko, N. Pavlov, P. Belov, Y. Kivshar, and M. Tribelsky, “Giant field enhancement in high-index dielectric subwavelength particles,” Sci. Rep. 7, 731 (2017).
[Crossref] [PubMed]

Bhattacharya, N.

Bohren, C. F.

C. F. Bohren and D. R. Huffman, “Absorption and scattering of light by small particles,” (Wiley, 2008), chap. 8.4.

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]

Chong, T.

B. Luk’yanchuk, Z. Wang, M. Tribelsky, V. Ternovsky, M. Hong, and T. Chong, “Peculiarities of light scattering by nanoparticles and nanowires near plasmon resonance frequencies,” J. Phys. Conf. Ser. 59, 234–239 (2007).
[Crossref]

B. Luk’yanchuk, M. Tribelsky, V. Ternovsky, Z. Wang, M. Hong, L. Shi, and T. Chong, “Peculiarities of light scattering by nanoparticles and nanowires near plasmon resonance frequencies in weakly dissipating materials,” J. Opt. A: Pure Appl. Opt. 9, S294–S300 (2007).
[Crossref]

DeLacy, B. G.

C. W. Hsu, B. G. DeLacy, S. G. Johnson, J. D. Joannopoulos, and M. Soljačić, “Theoretical criteria for scattering dark states in nanostructured particles,” Nano Lett. 14, 2783–2788 (2014).
[Crossref] [PubMed]

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]

Fan, S.

Z. Ruan and S. Fan, “Temporal coupled-mode theory for fano resonance in light scattering by a single obstacle,” J. Phys. Chem. C 114, 7324–7329 (2010).
[Crossref]

Fang, Y.

Y. Fang and Z. Ruan, “Temporal coupled-mode theory for light scattering and absorption by nanostructures,” in Fano Resonances in Optics and Microwaves, (Springer, 2018), pp. 157–183.
[Crossref]

Fano, U.

U. Fano, “Effects of configuration interaction on intensities and phase shifts,” Phys. Rev. 124, 1866–1878 (1961).
[Crossref]

Fedotov, V.

N. Papasimakis, V. Fedotov, V. Savinov, T. Raybould, and N. Zheludev, “Electromagnetic toroidal excitations in matter and free space,” Nat. Mater. 15, 263–271 (2016).
[Crossref] [PubMed]

Francescato, Y.

M. Rahmani, A. E. Miroshnichenko, D. Y. Lei, B. Luk’yanchuk, M. I. Tribelsky, A. I. Kuznetsov, Y. S. Kivshar, Y. Francescato, V. Giannini, and M. Hong et al., “Beyond the hybridization effects in plasmonic nanoclusters: diffraction-induced enhanced absorption and scattering,” Small 10, 576–583 (2014).
[Crossref]

Fratalocchi, A.

J. Gongora, A. Miroshnichenko, Y. Kivshar, and A. Fratalocchi, “Anapole nanolasers for mode-locking and ultrafast pulse generation,” Nat. Commun. 8, 15535 (2017).
[Crossref]

Giannini, V.

M. Rahmani, A. E. Miroshnichenko, D. Y. Lei, B. Luk’yanchuk, M. I. Tribelsky, A. I. Kuznetsov, Y. S. Kivshar, Y. Francescato, V. Giannini, and M. Hong et al., “Beyond the hybridization effects in plasmonic nanoclusters: diffraction-induced enhanced absorption and scattering,” Small 10, 576–583 (2014).
[Crossref]

Gongora, J.

J. Gongora, A. Miroshnichenko, Y. Kivshar, and A. Fratalocchi, “Anapole nanolasers for mode-locking and ultrafast pulse generation,” Nat. Commun. 8, 15535 (2017).
[Crossref]

Hagness, S. C.

A. Taflove and S. C. Hagness, Computational electrodynamics: the finite-difference time-domain method (Artech house, 2005).

Haus, H. A.

H. A. Haus, Waves and fields in optoelectronics (Prentice-Hall, 1984).

Hecht, B.

L. Novotny and B. Hecht, Principles of nano-optics (Cambridge University, 2006).
[Crossref]

Hong, M.

M. Rahmani, A. E. Miroshnichenko, D. Y. Lei, B. Luk’yanchuk, M. I. Tribelsky, A. I. Kuznetsov, Y. S. Kivshar, Y. Francescato, V. Giannini, and M. Hong et al., “Beyond the hybridization effects in plasmonic nanoclusters: diffraction-induced enhanced absorption and scattering,” Small 10, 576–583 (2014).
[Crossref]

B. Luk’yanchuk, M. Tribelsky, V. Ternovsky, Z. Wang, M. Hong, L. Shi, and T. Chong, “Peculiarities of light scattering by nanoparticles and nanowires near plasmon resonance frequencies in weakly dissipating materials,” J. Opt. A: Pure Appl. Opt. 9, S294–S300 (2007).
[Crossref]

B. Luk’yanchuk, Z. Wang, M. Tribelsky, V. Ternovsky, M. Hong, and T. Chong, “Peculiarities of light scattering by nanoparticles and nanowires near plasmon resonance frequencies,” J. Phys. Conf. Ser. 59, 234–239 (2007).
[Crossref]

Hsu, C. W.

C. W. Hsu, B. Zhen, A. D. Stone, J. D. Joannopoulos, and M. Soljačić, “Bound states in the continuum,” Nat. Rev. Mater. 1, 16048 (2016).
[Crossref]

C. W. Hsu, B. G. DeLacy, S. G. Johnson, J. D. Joannopoulos, and M. Soljačić, “Theoretical criteria for scattering dark states in nanostructured particles,” Nano Lett. 14, 2783–2788 (2014).
[Crossref] [PubMed]

Huffman, D. R.

C. F. Bohren and D. R. Huffman, “Absorption and scattering of light by small particles,” (Wiley, 2008), chap. 8.4.

Joannopoulos, J. D.

C. W. Hsu, B. Zhen, A. D. Stone, J. D. Joannopoulos, and M. Soljačić, “Bound states in the continuum,” Nat. Rev. Mater. 1, 16048 (2016).
[Crossref]

C. W. Hsu, B. G. DeLacy, S. G. Johnson, J. D. Joannopoulos, and M. Soljačić, “Theoretical criteria for scattering dark states in nanostructured particles,” Nano Lett. 14, 2783–2788 (2014).
[Crossref] [PubMed]

Joe, Y. S.

Y. S. Joe, A. M. Satanin, and C. S. Kim, “Classical analogy of fano resonances,” Phys. Scripta 74, 259–266 (2006).
[Crossref]

Johnson, S. G.

C. W. Hsu, B. G. DeLacy, S. G. Johnson, J. D. Joannopoulos, and M. Soljačić, “Theoretical criteria for scattering dark states in nanostructured particles,” Nano Lett. 14, 2783–2788 (2014).
[Crossref] [PubMed]

Kapitanova, P.

P. Kapitanova, V. Ternovski, A. Miroshnichenko, N. Pavlov, P. Belov, Y. Kivshar, and M. Tribelsky, “Giant field enhancement in high-index dielectric subwavelength particles,” Sci. Rep. 7, 731 (2017).
[Crossref] [PubMed]

Kerker, M.

M. Kerker, The Scattering of Light and Other Electromagnetic Radiation (Elsevier Science, 2013).

Kim, C. S.

Y. S. Joe, A. M. Satanin, and C. S. Kim, “Classical analogy of fano resonances,” Phys. Scripta 74, 259–266 (2006).
[Crossref]

Kivshar, Y.

P. Kapitanova, V. Ternovski, A. Miroshnichenko, N. Pavlov, P. Belov, Y. Kivshar, and M. Tribelsky, “Giant field enhancement in high-index dielectric subwavelength particles,” Sci. Rep. 7, 731 (2017).
[Crossref] [PubMed]

J. Gongora, A. Miroshnichenko, Y. Kivshar, and A. Fratalocchi, “Anapole nanolasers for mode-locking and ultrafast pulse generation,” Nat. Commun. 8, 15535 (2017).
[Crossref]

Kivshar, Y. S.

B. Luk’yanchuk, R. Paniagua-Domínguez, A. I. Kuznetsov, A. E. Miroshnichenko, and Y. S. Kivshar, “Hybrid anapole modes of high-index dielectric nanoparticles,” Phys. Rev. A 95, 063820 (2017).
[Crossref]

M. F. Limonov, M. V. Rybin, A. N. Poddubny, and Y. S. Kivshar, “Fano resonances in photonics,” Nat. Photon. 11, 543 (2017).
[Crossref]

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]

M. Rahmani, A. E. Miroshnichenko, D. Y. Lei, B. Luk’yanchuk, M. I. Tribelsky, A. I. Kuznetsov, Y. S. Kivshar, Y. Francescato, V. Giannini, and M. Hong et al., “Beyond the hybridization effects in plasmonic nanoclusters: diffraction-induced enhanced absorption and scattering,” Small 10, 576–583 (2014).
[Crossref]

Klimov, V.

V. Klimov, Nanoplasmonics (Pan Stanford, 2014).
[Crossref]

Kuznetsov, A. I.

B. Luk’yanchuk, R. Paniagua-Domínguez, A. I. Kuznetsov, A. E. Miroshnichenko, and Y. S. Kivshar, “Hybrid anapole modes of high-index dielectric nanoparticles,” Phys. Rev. A 95, 063820 (2017).
[Crossref]

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]

B. S. Luk’yanchuk, N. V. Voshchinnikov, R. Paniagua-Domínguez, and A. I. Kuznetsov, “Optimum forward light scattering by spherical and spheroidal dielectric nanoparticles with high refractive index,” ACS Photon. 2, 993–999 (2015).
[Crossref]

M. Rahmani, A. E. Miroshnichenko, D. Y. Lei, B. Luk’yanchuk, M. I. Tribelsky, A. I. Kuznetsov, Y. S. Kivshar, Y. Francescato, V. Giannini, and M. Hong et al., “Beyond the hybridization effects in plasmonic nanoclusters: diffraction-induced enhanced absorption and scattering,” Small 10, 576–583 (2014).
[Crossref]

Landau, L. D.

L. D. Landau and E. Lifshitz, Course of Theoretical Physics. Vol. 8: Electrodynamics of Continuous Media (Pergamon, 1984).

Lei, D. Y.

M. Rahmani, A. E. Miroshnichenko, D. Y. Lei, B. Luk’yanchuk, M. I. Tribelsky, A. I. Kuznetsov, Y. S. Kivshar, Y. Francescato, V. Giannini, and M. Hong et al., “Beyond the hybridization effects in plasmonic nanoclusters: diffraction-induced enhanced absorption and scattering,” Small 10, 576–583 (2014).
[Crossref]

Lifshitz, E.

L. D. Landau and E. Lifshitz, Course of Theoretical Physics. Vol. 8: Electrodynamics of Continuous Media (Pergamon, 1984).

Limonov, M. F.

M. F. Limonov, M. V. Rybin, A. N. Poddubny, and Y. S. Kivshar, “Fano resonances in photonics,” Nat. Photon. 11, 543 (2017).
[Crossref]

Louisell, W. H.

W. H. Louisell, Coupled mode and parametric electronics (Wiley, 1960).

Luk’yanchuk, B.

B. Luk’yanchuk, R. Paniagua-Domínguez, A. I. Kuznetsov, A. E. Miroshnichenko, and Y. S. Kivshar, “Hybrid anapole modes of high-index dielectric nanoparticles,” Phys. Rev. A 95, 063820 (2017).
[Crossref]

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]

M. Rahmani, A. E. Miroshnichenko, D. Y. Lei, B. Luk’yanchuk, M. I. Tribelsky, A. I. Kuznetsov, Y. S. Kivshar, Y. Francescato, V. Giannini, and M. Hong et al., “Beyond the hybridization effects in plasmonic nanoclusters: diffraction-induced enhanced absorption and scattering,” Small 10, 576–583 (2014).
[Crossref]

B. Luk’yanchuk, M. Tribelsky, V. Ternovsky, Z. Wang, M. Hong, L. Shi, and T. Chong, “Peculiarities of light scattering by nanoparticles and nanowires near plasmon resonance frequencies in weakly dissipating materials,” J. Opt. A: Pure Appl. Opt. 9, S294–S300 (2007).
[Crossref]

B. Luk’yanchuk, Z. Wang, M. Tribelsky, V. Ternovsky, M. Hong, and T. Chong, “Peculiarities of light scattering by nanoparticles and nanowires near plasmon resonance frequencies,” J. Phys. Conf. Ser. 59, 234–239 (2007).
[Crossref]

B. Luk’yanchuk, M. Tribel’skii, and V. Ternovskii, “Light scattering at nanoparticles close to plasmon resonance frequencies,” J. Opt. Tech. 73, 371–377 (2006).
[Crossref]

Luk’yanchuk, B. S.

B. S. Luk’yanchuk, N. V. Voshchinnikov, R. Paniagua-Domínguez, and A. I. Kuznetsov, “Optimum forward light scattering by spherical and spheroidal dielectric nanoparticles with high refractive index,” ACS Photon. 2, 993–999 (2015).
[Crossref]

M. I. Tribelsky and B. S. Luk’yanchuk, “Light scattering by small particles and their light heating: New aspects of the old problems in fundamentals of laser,” in Fundamentals of Laser-Asssted Micro- and Nanotechnologies,(Springer, 2014), Springer Series in Materials Science, vol. 195, pp. 125–146.
[Crossref]

Miroshnichenko, A.

J. Gongora, A. Miroshnichenko, Y. Kivshar, and A. Fratalocchi, “Anapole nanolasers for mode-locking and ultrafast pulse generation,” Nat. Commun. 8, 15535 (2017).
[Crossref]

P. Kapitanova, V. Ternovski, A. Miroshnichenko, N. Pavlov, P. Belov, Y. Kivshar, and M. Tribelsky, “Giant field enhancement in high-index dielectric subwavelength particles,” Sci. Rep. 7, 731 (2017).
[Crossref] [PubMed]

Miroshnichenko, A. E.

B. Luk’yanchuk, R. Paniagua-Domínguez, A. I. Kuznetsov, A. E. Miroshnichenko, and Y. S. Kivshar, “Hybrid anapole modes of high-index dielectric nanoparticles,” Phys. Rev. A 95, 063820 (2017).
[Crossref]

M. I. Tribelsky and A. E. Miroshnichenko, “Giant in-particle field concentration and fano resonances at light scattering by high-refractive-index particles,” Phys. Rev. A 93, 053837 (2016).
[Crossref]

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]

M. Rahmani, A. E. Miroshnichenko, D. Y. Lei, B. Luk’yanchuk, M. I. Tribelsky, A. I. Kuznetsov, Y. S. Kivshar, Y. Francescato, V. Giannini, and M. Hong et al., “Beyond the hybridization effects in plasmonic nanoclusters: diffraction-induced enhanced absorption and scattering,” Small 10, 576–583 (2014).
[Crossref]

M. I. Tribelsky and A. E. Miroshnichenko, “Dynamic fano resonances: From toy model to resonant mie scattering,” arXiv preprint arXiv:1809.02474 (2018).

Novotny, L.

L. Novotny and B. Hecht, Principles of nano-optics (Cambridge University, 2006).
[Crossref]

Paniagua-Domínguez, R.

B. Luk’yanchuk, R. Paniagua-Domínguez, A. I. Kuznetsov, A. E. Miroshnichenko, and Y. S. Kivshar, “Hybrid anapole modes of high-index dielectric nanoparticles,” Phys. Rev. A 95, 063820 (2017).
[Crossref]

B. S. Luk’yanchuk, N. V. Voshchinnikov, R. Paniagua-Domínguez, and A. I. Kuznetsov, “Optimum forward light scattering by spherical and spheroidal dielectric nanoparticles with high refractive index,” ACS Photon. 2, 993–999 (2015).
[Crossref]

Papasimakis, N.

N. Papasimakis, V. Fedotov, V. Savinov, T. Raybould, and N. Zheludev, “Electromagnetic toroidal excitations in matter and free space,” Nat. Mater. 15, 263–271 (2016).
[Crossref] [PubMed]

Pavlov, N.

P. Kapitanova, V. Ternovski, A. Miroshnichenko, N. Pavlov, P. Belov, Y. Kivshar, and M. Tribelsky, “Giant field enhancement in high-index dielectric subwavelength particles,” Sci. Rep. 7, 731 (2017).
[Crossref] [PubMed]

Poddubny, A. N.

M. F. Limonov, M. V. Rybin, A. N. Poddubny, and Y. S. Kivshar, “Fano resonances in photonics,” Nat. Photon. 11, 543 (2017).
[Crossref]

Rahmani, M.

M. Rahmani, A. E. Miroshnichenko, D. Y. Lei, B. Luk’yanchuk, M. I. Tribelsky, A. I. Kuznetsov, Y. S. Kivshar, Y. Francescato, V. Giannini, and M. Hong et al., “Beyond the hybridization effects in plasmonic nanoclusters: diffraction-induced enhanced absorption and scattering,” Small 10, 576–583 (2014).
[Crossref]

Raybould, T.

N. Papasimakis, V. Fedotov, V. Savinov, T. Raybould, and N. Zheludev, “Electromagnetic toroidal excitations in matter and free space,” Nat. Mater. 15, 263–271 (2016).
[Crossref] [PubMed]

Ruan, Z.

Z. Ruan and S. Fan, “Temporal coupled-mode theory for fano resonance in light scattering by a single obstacle,” J. Phys. Chem. C 114, 7324–7329 (2010).
[Crossref]

Y. Fang and Z. Ruan, “Temporal coupled-mode theory for light scattering and absorption by nanostructures,” in Fano Resonances in Optics and Microwaves, (Springer, 2018), pp. 157–183.
[Crossref]

Rybin, M. V.

M. F. Limonov, M. V. Rybin, A. N. Poddubny, and Y. S. Kivshar, “Fano resonances in photonics,” Nat. Photon. 11, 543 (2017).
[Crossref]

Satanin, A. M.

Y. S. Joe, A. M. Satanin, and C. S. Kim, “Classical analogy of fano resonances,” Phys. Scripta 74, 259–266 (2006).
[Crossref]

Savinov, V.

N. Papasimakis, V. Fedotov, V. Savinov, T. Raybould, and N. Zheludev, “Electromagnetic toroidal excitations in matter and free space,” Nat. Mater. 15, 263–271 (2016).
[Crossref] [PubMed]

Shi, L.

B. Luk’yanchuk, M. Tribelsky, V. Ternovsky, Z. Wang, M. Hong, L. Shi, and T. Chong, “Peculiarities of light scattering by nanoparticles and nanowires near plasmon resonance frequencies in weakly dissipating materials,” J. Opt. A: Pure Appl. Opt. 9, S294–S300 (2007).
[Crossref]

Silveirinha, M. G.

M. G. Silveirinha, “Trapping light in open plasmonic nanostructures,” Phys. Rev. A 89, 023813 (2014).
[Crossref]

Soljacic, M.

C. W. Hsu, B. Zhen, A. D. Stone, J. D. Joannopoulos, and M. Soljačić, “Bound states in the continuum,” Nat. Rev. Mater. 1, 16048 (2016).
[Crossref]

C. W. Hsu, B. G. DeLacy, S. G. Johnson, J. D. Joannopoulos, and M. Soljačić, “Theoretical criteria for scattering dark states in nanostructured particles,” Nano Lett. 14, 2783–2788 (2014).
[Crossref] [PubMed]

Stone, A. D.

C. W. Hsu, B. Zhen, A. D. Stone, J. D. Joannopoulos, and M. Soljačić, “Bound states in the continuum,” Nat. Rev. Mater. 1, 16048 (2016).
[Crossref]

Taflove, A.

A. Taflove and S. C. Hagness, Computational electrodynamics: the finite-difference time-domain method (Artech house, 2005).

Ternovski, V.

P. Kapitanova, V. Ternovski, A. Miroshnichenko, N. Pavlov, P. Belov, Y. Kivshar, and M. Tribelsky, “Giant field enhancement in high-index dielectric subwavelength particles,” Sci. Rep. 7, 731 (2017).
[Crossref] [PubMed]

Ternovskii, V.

B. Luk’yanchuk, M. Tribel’skii, and V. Ternovskii, “Light scattering at nanoparticles close to plasmon resonance frequencies,” J. Opt. Tech. 73, 371–377 (2006).
[Crossref]

Ternovsky, V.

B. Luk’yanchuk, Z. Wang, M. Tribelsky, V. Ternovsky, M. Hong, and T. Chong, “Peculiarities of light scattering by nanoparticles and nanowires near plasmon resonance frequencies,” J. Phys. Conf. Ser. 59, 234–239 (2007).
[Crossref]

B. Luk’yanchuk, M. Tribelsky, V. Ternovsky, Z. Wang, M. Hong, L. Shi, and T. Chong, “Peculiarities of light scattering by nanoparticles and nanowires near plasmon resonance frequencies in weakly dissipating materials,” J. Opt. A: Pure Appl. Opt. 9, S294–S300 (2007).
[Crossref]

Tribel’skii, M.

B. Luk’yanchuk, M. Tribel’skii, and V. Ternovskii, “Light scattering at nanoparticles close to plasmon resonance frequencies,” J. Opt. Tech. 73, 371–377 (2006).
[Crossref]

Tribelsky, M.

P. Kapitanova, V. Ternovski, A. Miroshnichenko, N. Pavlov, P. Belov, Y. Kivshar, and M. Tribelsky, “Giant field enhancement in high-index dielectric subwavelength particles,” Sci. Rep. 7, 731 (2017).
[Crossref] [PubMed]

B. Luk’yanchuk, Z. Wang, M. Tribelsky, V. Ternovsky, M. Hong, and T. Chong, “Peculiarities of light scattering by nanoparticles and nanowires near plasmon resonance frequencies,” J. Phys. Conf. Ser. 59, 234–239 (2007).
[Crossref]

B. Luk’yanchuk, M. Tribelsky, V. Ternovsky, Z. Wang, M. Hong, L. Shi, and T. Chong, “Peculiarities of light scattering by nanoparticles and nanowires near plasmon resonance frequencies in weakly dissipating materials,” J. Opt. A: Pure Appl. Opt. 9, S294–S300 (2007).
[Crossref]

Tribelsky, M. I.

M. I. Tribelsky and A. E. Miroshnichenko, “Giant in-particle field concentration and fano resonances at light scattering by high-refractive-index particles,” Phys. Rev. A 93, 053837 (2016).
[Crossref]

M. Rahmani, A. E. Miroshnichenko, D. Y. Lei, B. Luk’yanchuk, M. I. Tribelsky, A. I. Kuznetsov, Y. S. Kivshar, Y. Francescato, V. Giannini, and M. Hong et al., “Beyond the hybridization effects in plasmonic nanoclusters: diffraction-induced enhanced absorption and scattering,” Small 10, 576–583 (2014).
[Crossref]

M. I. Tribelsky and B. S. Luk’yanchuk, “Light scattering by small particles and their light heating: New aspects of the old problems in fundamentals of laser,” in Fundamentals of Laser-Asssted Micro- and Nanotechnologies,(Springer, 2014), Springer Series in Materials Science, vol. 195, pp. 125–146.
[Crossref]

M. I. Tribelsky and A. E. Miroshnichenko, “Dynamic fano resonances: From toy model to resonant mie scattering,” arXiv preprint arXiv:1809.02474 (2018).

Urbach, H. P.

Voshchinnikov, N. V.

B. S. Luk’yanchuk, N. V. Voshchinnikov, R. Paniagua-Domínguez, and A. I. Kuznetsov, “Optimum forward light scattering by spherical and spheroidal dielectric nanoparticles with high refractive index,” ACS Photon. 2, 993–999 (2015).
[Crossref]

Wang, Z.

B. Luk’yanchuk, Z. Wang, M. Tribelsky, V. Ternovsky, M. Hong, and T. Chong, “Peculiarities of light scattering by nanoparticles and nanowires near plasmon resonance frequencies,” J. Phys. Conf. Ser. 59, 234–239 (2007).
[Crossref]

B. Luk’yanchuk, M. Tribelsky, V. Ternovsky, Z. Wang, M. Hong, L. Shi, and T. Chong, “Peculiarities of light scattering by nanoparticles and nanowires near plasmon resonance frequencies in weakly dissipating materials,” J. Opt. A: Pure Appl. Opt. 9, S294–S300 (2007).
[Crossref]

Wei, L.

Xi, Z.

Yee, K.

K. Yee, “Numerical solution of initial boundary value problems involving maxwell’s equations in isotropic media,” IEEE Transactions on antennas propagation 14, 302–307 (1966).
[Crossref]

Yu, Y. F.

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]

Zheludev, N.

N. Papasimakis, V. Fedotov, V. Savinov, T. Raybould, and N. Zheludev, “Electromagnetic toroidal excitations in matter and free space,” Nat. Mater. 15, 263–271 (2016).
[Crossref] [PubMed]

Zhen, B.

C. W. Hsu, B. Zhen, A. D. Stone, J. D. Joannopoulos, and M. Soljačić, “Bound states in the continuum,” Nat. Rev. Mater. 1, 16048 (2016).
[Crossref]

ACS Photon. (1)

B. S. Luk’yanchuk, N. V. Voshchinnikov, R. Paniagua-Domínguez, and A. I. Kuznetsov, “Optimum forward light scattering by spherical and spheroidal dielectric nanoparticles with high refractive index,” ACS Photon. 2, 993–999 (2015).
[Crossref]

IEEE Transactions on antennas propagation (1)

K. Yee, “Numerical solution of initial boundary value problems involving maxwell’s equations in isotropic media,” IEEE Transactions on antennas propagation 14, 302–307 (1966).
[Crossref]

J. Opt. A: Pure Appl. Opt. (1)

B. Luk’yanchuk, M. Tribelsky, V. Ternovsky, Z. Wang, M. Hong, L. Shi, and T. Chong, “Peculiarities of light scattering by nanoparticles and nanowires near plasmon resonance frequencies in weakly dissipating materials,” J. Opt. A: Pure Appl. Opt. 9, S294–S300 (2007).
[Crossref]

J. Opt. Tech. (1)

B. Luk’yanchuk, M. Tribel’skii, and V. Ternovskii, “Light scattering at nanoparticles close to plasmon resonance frequencies,” J. Opt. Tech. 73, 371–377 (2006).
[Crossref]

J. Phys. Chem. C (1)

Z. Ruan and S. Fan, “Temporal coupled-mode theory for fano resonance in light scattering by a single obstacle,” J. Phys. Chem. C 114, 7324–7329 (2010).
[Crossref]

J. Phys. Conf. Ser. (1)

B. Luk’yanchuk, Z. Wang, M. Tribelsky, V. Ternovsky, M. Hong, and T. Chong, “Peculiarities of light scattering by nanoparticles and nanowires near plasmon resonance frequencies,” J. Phys. Conf. Ser. 59, 234–239 (2007).
[Crossref]

Nano Lett. (1)

C. W. Hsu, B. G. DeLacy, S. G. Johnson, J. D. Joannopoulos, and M. Soljačić, “Theoretical criteria for scattering dark states in nanostructured particles,” Nano Lett. 14, 2783–2788 (2014).
[Crossref] [PubMed]

Nat. Commun. (2)

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]

J. Gongora, A. Miroshnichenko, Y. Kivshar, and A. Fratalocchi, “Anapole nanolasers for mode-locking and ultrafast pulse generation,” Nat. Commun. 8, 15535 (2017).
[Crossref]

Nat. Mater. (1)

N. Papasimakis, V. Fedotov, V. Savinov, T. Raybould, and N. Zheludev, “Electromagnetic toroidal excitations in matter and free space,” Nat. Mater. 15, 263–271 (2016).
[Crossref] [PubMed]

Nat. Photon. (1)

M. F. Limonov, M. V. Rybin, A. N. Poddubny, and Y. S. Kivshar, “Fano resonances in photonics,” Nat. Photon. 11, 543 (2017).
[Crossref]

Nat. Rev. Mater. (1)

C. W. Hsu, B. Zhen, A. D. Stone, J. D. Joannopoulos, and M. Soljačić, “Bound states in the continuum,” Nat. Rev. Mater. 1, 16048 (2016).
[Crossref]

Optica (1)

Phys. Rev. (1)

U. Fano, “Effects of configuration interaction on intensities and phase shifts,” Phys. Rev. 124, 1866–1878 (1961).
[Crossref]

Phys. Rev. A (3)

M. G. Silveirinha, “Trapping light in open plasmonic nanostructures,” Phys. Rev. A 89, 023813 (2014).
[Crossref]

B. Luk’yanchuk, R. Paniagua-Domínguez, A. I. Kuznetsov, A. E. Miroshnichenko, and Y. S. Kivshar, “Hybrid anapole modes of high-index dielectric nanoparticles,” Phys. Rev. A 95, 063820 (2017).
[Crossref]

M. I. Tribelsky and A. E. Miroshnichenko, “Giant in-particle field concentration and fano resonances at light scattering by high-refractive-index particles,” Phys. Rev. A 93, 053837 (2016).
[Crossref]

Phys. Scripta (1)

Y. S. Joe, A. M. Satanin, and C. S. Kim, “Classical analogy of fano resonances,” Phys. Scripta 74, 259–266 (2006).
[Crossref]

Sci. Rep. (1)

P. Kapitanova, V. Ternovski, A. Miroshnichenko, N. Pavlov, P. Belov, Y. Kivshar, and M. Tribelsky, “Giant field enhancement in high-index dielectric subwavelength particles,” Sci. Rep. 7, 731 (2017).
[Crossref] [PubMed]

Small (1)

M. Rahmani, A. E. Miroshnichenko, D. Y. Lei, B. Luk’yanchuk, M. I. Tribelsky, A. I. Kuznetsov, Y. S. Kivshar, Y. Francescato, V. Giannini, and M. Hong et al., “Beyond the hybridization effects in plasmonic nanoclusters: diffraction-induced enhanced absorption and scattering,” Small 10, 576–583 (2014).
[Crossref]

Other (11)

M. I. Tribelsky and B. S. Luk’yanchuk, “Light scattering by small particles and their light heating: New aspects of the old problems in fundamentals of laser,” in Fundamentals of Laser-Asssted Micro- and Nanotechnologies,(Springer, 2014), Springer Series in Materials Science, vol. 195, pp. 125–146.
[Crossref]

M. Kerker, The Scattering of Light and Other Electromagnetic Radiation (Elsevier Science, 2013).

L. Novotny and B. Hecht, Principles of nano-optics (Cambridge University, 2006).
[Crossref]

V. Klimov, Nanoplasmonics (Pan Stanford, 2014).
[Crossref]

C. F. Bohren and D. R. Huffman, “Absorption and scattering of light by small particles,” (Wiley, 2008), chap. 8.4.

W. H. Louisell, Coupled mode and parametric electronics (Wiley, 1960).

H. A. Haus, Waves and fields in optoelectronics (Prentice-Hall, 1984).

Y. Fang and Z. Ruan, “Temporal coupled-mode theory for light scattering and absorption by nanostructures,” in Fano Resonances in Optics and Microwaves, (Springer, 2018), pp. 157–183.
[Crossref]

A. Taflove and S. C. Hagness, Computational electrodynamics: the finite-difference time-domain method (Artech house, 2005).

M. I. Tribelsky and A. E. Miroshnichenko, “Dynamic fano resonances: From toy model to resonant mie scattering,” arXiv preprint arXiv:1809.02474 (2018).

L. D. Landau and E. Lifshitz, Course of Theoretical Physics. Vol. 8: Electrodynamics of Continuous Media (Pergamon, 1984).

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Figures (3)

Fig. 1
Fig. 1 The resonance lines |a1| and |d1| for the exact solution of the steady scattering problem (solid brown and dashed blue lines, respectively) and the fitting of |d1(Ω)| with the line for a harmonic oscillator (black dot-dashed line). Both profiles — for |d1| (actual and fitted) have the same linewidths (FWHM) and are normalized on the corresponding maximal values; Ω ≈ 1.14 (marked with the vertical line) is the anapole eigenfrequency. The inset shows the mutual orientation of the cylinder, coordinate frame, and the plane TE-polarized incident wave.
Fig. 2
Fig. 2 Temporal dependence of the normalized instant total energy stored in the irradiated cylinder, obtained by direct numerical integration of the complete set of the Maxwell equations (magenta) and the one for a simple harmonic oscillator model (blue) at Ω ≈ 1.14. The envelope of a rectangular incident (driving) pulse in a.u. is shown in green; θ = ω0t, see the text for details. The inset shows the tails of the decay processes, where two more curves for the actual problem with Ω ≈ 1.07 (dashed orange) and Ω = 1 (dotted black) are added.
Fig. 3
Fig. 3 Smoothed temporal dependence of the normalized instant total energy stored in the irradiated cylinder obtained by direct numerical integration of the complete set of the Maxwell equations (magenta, solid) and the one for a simple harmonic oscillator model (blue, dashed) at three different values of Ω (indicated in the plot), θ = ω0t, see the text for details.

Equations (13)

Equations on this page are rendered with MathJax. Learn more.

E ( TE ) E 0 = ( i ) + 1 e i φ d { i J ( m ρ ) m ρ , J ( m ρ ) , 0 } ,
H ( TE ) H 0 = m ( i ) e i φ d { 0 , 0 , J ( m ρ ) } ,
E ( TE , s ) E 0 = ( i ) + 1 e i φ a { i H ( 1 ) ( ρ ) ρ , H ( 1 ) ( ρ ) , 0 } ,
H ( TE , s ) H 0 = ( i ) e i φ a { 0 , 0 , H ( 1 ) ( ρ ) } .
a = F F + i G , d = i F + i G ,
F = π q 2 ( m J ( m q ) J ( q ) J ( m q ) J ( q ) ) ,
G = π q 2 ( m J ( m q ) N ( q ) J ( m q ) N ( q ) ) ,
W ( θ ) = 1 8 π 0 R r d r 0 2 π d ϕ ( ε E 2 + H 2 ) ,
a a ( PEC ) J ( m q ) H ( 1 ) ( q ) d .
| d 1 | 2 | d 1 ( max ) | 2 ( Γ / 2 ) 2 ( Γ / 2 ) 2 + ( Ω 1 ) 2 .
d θ θ + Γ d θ + d = A ( θ ) exp ( i Ω θ ) ,
d = A Ω 0 e i Ω θ e γ θ [ Ω 0 cos ( Ω 0 θ ) + ( γ i Ω ) sin ( Ω 0 θ ) ] Ω 0 ( 1 Ω 2 2 i γ Ω ) .
d = ( d θ ( τ ) + γ d ( τ ) Ω 0 sin [ Ω 0 ( θ τ ) ] + d ( τ ) cos [ Ω 0 ( θ τ ) ] ) exp [ γ ( θ τ ) ] ,

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