Abstract

In this work, we first derive the nonradiating anapole condition with a straightforward theoretical demonstration exploiting one of the Devaney-Wolf theorems for nonradiating currents. Based on the equivalent volumetric and surface electromagnetic sources, it is possible to establish a unique compact conditions directly from Maxwell’s Equations in order to ensure nonradiating anapole state. In addition, we support our theoretical findings with a numerical investigation on a broken-symmetry dielectric particle, building block of a metamaterial structure, demonstrating through a detailed multiple expansion the nonradiating anapole condition behind these peculiar destructive interactions.

© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

Full Article  |  PDF Article
OSA Recommended Articles
Invisibility and cloaking structures as weak or strong solutions of Devaney-Wolf theorem

Giuseppe Labate and Ladislau Matekovits
Opt. Express 24(17) 19245-19253 (2016)

Broken symmetry theta-shaped dielectric arrays for a high Q-factor Fano resonance with anapole excitation and magnetic field tunability

Wudeng Wang, Xin Zhao, Li Xiong, Li Zheng, Ying Shi, Yujie Liu, and Jianguang Qi
OSA Continuum 2(2) 507-517 (2019)

Optical radiation manipulation of Si-Ge2Sb2Te5 hybrid metasurfaces

Chaobiao Zhou, Shiyu Li, Menghui Fan, Xinfeng Wang, Yanli Xu, Weiwei Xu, Shuyuan Xiao, Mingzhe Hu, and Jiangtao Liu
Opt. Express 28(7) 9690-9701 (2020)

References

  • View by:
  • |
  • |
  • |

  1. A. Sommerfeld, “Zur elektronentheorie. I. Allgemeine untersuchung des feldes eines beliebig bewegten elektrons,” Akad. der Wiss. (Gott.), Math. Phys. Klasse, Nach., 99–130 (1904).
  2. A. Sommerfeld, “Zur elektronentheorie. II. Grundlagen fur eine allgemeine dynamik des elektrons,” Akad. der Wiss. (Gott.), Math. Phys. Klasse, Nach.363–439 (1904).
  3. P. Ehrenfest, “Ungleichformige Elektrizitätsbewegungen ohne Magnet-und Strahlungsfeld,” Physik. Zeit. 11, 708–709 (1910).
  4. G. A. Schott, “The electromagnetic field of a moving uniformly and rigidly electrified sphere and its radiationless orbits,” Phil. Mag. 15(100), 752–761 (1933).
    [Crossref]
  5. G. A. Schott, “The uniform circular motion with invariable normal spin of a rigidly and uniformly electrified sphere, IV,” Proc. Roy. Soc. A 159(899), 570–591 (1937).
    [Crossref]
  6. D. Bohm and M. Weinstein, “The self-oscillations of a charged particle,” Phys. Rev. 74(12), 1789–1798 (1948).
    [Crossref]
  7. G. H. Goedecke, “Classically radiationless motions and possible implications for quantum theory,” Phys. Rev. 135(1B), B281–B288 (1964).
    [Crossref]
  8. A. J. Devaney and E. Wolf, “Radiating and nonradiating classical current distributions and the fields they generate,” Phys. Rev. D 8(4), 1044–1047 (1973).
    [Crossref]
  9. K. Kim and E. Wolf, “Non-radiating monochromatic sources and their fields,” Opt. Commun. 59(1), 1–6 (1986).
    [Crossref]
  10. M. Berry, J. T. Foley, G. Gbur, and E. Wolf, “A simple explanation of simple non- radiating sources in one dimension comment on nonpropagating string excitations,” Am. J. Phys. 66(2), 121–123 (1998).
    [Crossref]
  11. B. J. Hoenders and H. A. Ferwerda, “The nonradiating component of the field generated by a finite monochromatic scalar source distribution,” Pure Appl. Opt. 7(5), 1201–1211 (1998).
    [Crossref]
  12. E. Marengo and R. Ziolkowski, “On the radiating and nonradiating components of scalar, electromagnetic, and weak gravitational sources,” Phys. Rev. Lett. 83(17), 3345–3349 (1999).
    [Crossref]
  13. B. J. Hoenders and H. A. Ferwerda, “Identification of the radiative and nonradiative parts of a wave field,” Phys. Rev. Lett. 87(6), 060401 (2001).
    [Crossref]
  14. G. Gbur, Nonradiating Sources and the Inverse Source Problem, University of Rochester Rochester, New York, 2001 (available at: www.maxwell.uncc.edu/gjgbur ).
  15. A. J. Devaney, “Nonradiating surface sources,” J. Opt. Soc. Am. A 21(11), 2216–2222 (2004).
    [Crossref]
  16. G. Gbur, “Nonradiating sources and other invisible objects,” Chap. 5 in E. Wolf (Ed.), Prog. in Optics (Elsevier, 2003), 273–315.
  17. G. Gbur, “Invisibility physics: past, present, and future,” Prog. Opt. 58, 65–114 (2013).
    [Crossref]
  18. E. Hurwitz and G. Gbur, “Null-field radiationless sources,” Opt. Lett. 39(22), 6529 (2014).
    [Crossref]
  19. F. Monticone and A. Alú, “Embedded Photonic Eigenvalues in 3D Nanostructures,” Phys. Rev. Lett. 112(21), 213903 (2014).
    [Crossref]
  20. V. A. Fedotov, A. V. Rogacheva, V. Savinov, D. P. Tsai, and N. I. Zheludev, “Resonant Transparency and Non-Trivial Non-Radiating Excitations in Toroidal Metamaterials,” Sci. Rep. 3(1), 2967 (2013).
    [Crossref]
  21. 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(1), 8069 (2015).
    [Crossref]
  22. N. A. Nemkov, A. A. Basharin, and V. A. Fedotov, “Nonradiating sources, dynamic anapole, and Aharonov-Bohm effect,” Phys. Rev. B 95(16), 165134 (2017).
    [Crossref]
  23. N. A. Nemkov, I. V. Stenishchev, and A. A. Basharin, “Nontrivial nonradiating all-dielectric anapole,” Sci. Rep. 7(1), 1064 (2017).
    [Crossref]
  24. P. C. Wu, C. Y. Liao, V. Savinov, T. L. Chung, W. T. Chen, Y.-W. Huang, P. R. Wu, Y.-H. Chen, A.-Q. Liu, N. I. Zheludev, and D. P. Tsai, “Optical anapole metamaterial,” ACS Nano 12(2), 1920–1927 (2018).
    [Crossref]
  25. S.-D. Liu, Z.-X. Wang, W.-J. Wang, J.-D. Chen, and Z.-H. Chen, “High Q-factor with the excitation of anapole modes in dielectric split nanodisk arrays,” Opt. Express 25(19), 22375–22387 (2017).
    [Crossref]
  26. J. F. Algorri, D. C. Zografopoulos, A. Ferraro, B. Garcia-Cámara, R. Beccherelli, and J. M. Sánchez-Pena, “Ultrahigh-quality factor resonant dielectric metasurfaces based on hollow nanocuboids,” Opt. Express 27(5), 6320–6330 (2019).
    [Crossref]
  27. W. Wang, X. Zhao, L. Xiong, L. Zheng, Y. Shi, Y. Liu, and J. Qi, “Broken symmetry theta-shaped dielectric arrays for a high Q-factor Fano resonance with anapole excitation and magnetic field tunability,” OSA Continuum 2(2), 507–517 (2019).
    [Crossref]
  28. N. Papasimakis, V. A. Fedotov, V. Savinov, T. A. Raybould, and N. I. Zheludev, “Electromagnetic toroidal excitations in matter and free space,” Nat. Mater. 15(3), 263–271 (2016).
    [Crossref]
  29. G. N. Afanasiev and Y. P. Stepanovsky, “The electromagnetic field of elementary time-dependent toroidal sources,” J. Phys. A: Math. Gen. 28(16), 4565–4580 (1995).
    [Crossref]
  30. G. Labate and L. Matekovits, “Invisibility and cloaking structures as weak or strong solutions of Devaney-Wolf theorem,” Opt. Express 24(17), 19245–19253 (2016).
    [Crossref]
  31. A. Alù and N. Engheta, “Achieving transparency with plasmonic and metamaterial coatings,” Phys. Rev. E 72(1), 016623 (2005).
    [Crossref]
  32. A. Alù, “Mantle cloak: Invisibility induced by a surface,” Phys. Rev. B 80(24), 245115 (2009).
    [Crossref]
  33. U. Leonhardt and T. G. Philbin, Geometry and Light: The Science of Invisibility (Dover, 2010).
  34. S. Maci, “A Cloaking Metamaterial Based on an Inhomogeneous Linear Field Transformation,” IEEE Trans. Antennas Propag. 58(4), 1136–1143 (2010).
    [Crossref]
  35. M. Selvanayagam and G. V. Eleftheriades, “An Active Electromagnetic Cloak Using the Equivalence Principle,” IEEE Ant. and Wireless Prop. Lett. 11, 1226–1229 (2012).
    [Crossref]
  36. D. Sounas, R. Fleury, and A. Alù, “Unidirectional Cloaking Based on Metasurfaces with Balanced Loss and Gain,” Phys. Rev. Appl. 4(1), 014005 (2015).
    [Crossref]
  37. A. Monti, F. Bilotti, and A. Toscano, “Optical cloaking of cylindrical objects by using covers made of core–shell nanoparticles,” Opt. Lett. 36(23), 4479–4481 (2011).
    [Crossref]
  38. P. -Y. Chen and A. Alù, “Mantle cloaking using thin patterned metasurfaces,” Phys. Rev. B 84(20), 205110 (2011).
    [Crossref]
  39. E. Shokati, N. Granpayeh, and M. Danaeifar, “Wideband and multi-frequency infrared cloaking of spherical objects by using the graphene-based metasurface,” Appl. Opt. 56(11), 3053–3058 (2017).
    [Crossref]
  40. G. Labate, A. Alú, and L. Matekovits, “Surface-admittance equivalence principle for nonradiating and cloaking problems,” Phys. Rev. A 95(6), 063841 (2017).
    [Crossref]
  41. G. Labate, S. K. Podilchak, and L. Matekovits, “Closed-form harmonic contrast control with surface impedance coatings for conductive objects,” Appl. Opt. 56(36), 10055 (2017).
    [Crossref]
  42. J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312(5781), 1780–1782 (2006).
    [Crossref]
  43. F. Zolla, S. Guenneau, A. Nicolet, and J. B. Pendry, “Electromagnetic analysis of cylindrical invisibility cloaks and mirage effects,” Opt. Lett. 32(9), 1069–1071 (2007).
    [Crossref]
  44. R. G. Quarfoth and D. F. Sievenpiper, “Nonscattering waveguides based on tensor impedance surfaces,” IEEE Trans. Antennas Propag. 63(4), 1746–1755 (2015).
    [Crossref]
  45. G. Labate, L. Matekovits, and A. Alú, “Metamaterial and Metasurface Cloaking: Principles and Applications,” Chap. 10 in Surface Electromagnetics (with Applications in Antenna, Microwave, and Optical Engineering), F. Yang and Y. Rahmat-Samii, eds., Cambridge University Press, 2019.
  46. A. K. Ospanova, G. Labate, L. Matekovits, and A. A. Basharin, “Multipolar passive cloaking by nonradiating anapole excitation,” Sci. Rep. 8(1), 12514 (2018).
    [Crossref]
  47. G. Afanasiev and V. Dubovik, “Some remarkable charge-current configurations,” Phys. Part. Nucl. 29(4), 366 (1998).
    [Crossref]
  48. A. Ishimaru, Electromagnetic wave propagation, radiation and scattering (Prentice-Hall, 1991).
  49. J. Van Bladel, Singular Electromagnetic Fields and Sources, Chap. 2 (Oxford1991).
  50. C. H. Papas, Theory of Electromagnetic Wave Propagation (Dover Publications, Inc., 1965).
  51. L. Di Donato, T. Isernia, G. Labate, and L. Matekovits, “Towards Printable Natural Dielectric Cloaks via Inverse Scattering Techniques,” Sci. Rep. 7(1), 3680 (2017).
    [Crossref]
  52. C. F. Bohren and D. R. Huffman, (Wiley-Interscience, New York, 1983), 82–84.
  53. 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]
  54. 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]
  55. I. V. Stenishchev and A. A. Basharin, “Toroidal response in all-dielectric metamaterials based on water,” Sci. Rep. 7(1), 9468 (2017).
    [Crossref]
  56. Y. Fan, Z. Wei, H. H. Chen, and C. M. Soukoulis, “Low-loss and high-Q planar metamaterial with toroidal moment,” Phys. Rev. B 87(11), 115417 (2013).
    [Crossref]
  57. Z. Liu, S. Du, A. Cui, Z. Li, Y. Fan, S. Chen, W. Li, J. Li, and C. Gu, “High-Quality-Factor Mid-Infrared Toroidal Excitation in Folded 3D Metamaterials,” Adv. Mater. 29(17), 1606298 (2017).
    [Crossref]
  58. Y. Fan, F. Zhang, N.-H. Shen, Q. Fu, Z. Wei, H. Li, and C. M. Soukoulis, “Achieving a high-Q response in metamaterials by manipulating the toroidal excitations,” Phys. Rev. A 97(3), 033816 (2018).
    [Crossref]
  59. Microwave Studio, Computer Simulation Technology, 2016.
  60. Ansoft High Frequency Structure Simulation (HFSS), Ansoft Corporation, 2016.
  61. B. Luk’yanchuk, R. Paniagua-Dominguez, A. I. Kuznetsov, A. E. Miroshnichenko, and Y. S. Kivshar, “Hybrid anapole modes of high-index dielectric nanoparticles,” Phys. Rev. A 95(6), 063820 (2017).
    [Crossref]
  62. Y. Yang and S. I. Bozhevolnyi, “Nonradiating anapole states in nanophotonics: from fundamentals to applications,” Nanotechnology 30(20), 204001 (2019).
    [Crossref]
  63. K. V. Baryshnikova, D. A. Smirnova, B. S. Luk’yanchuk, and Y. S. Kivshar, “Optical Anapoles: Concepts and Applications,” Adv. Opt. Mater. 7(14), 1801350 (2019).
    [Crossref]

2019 (4)

2018 (3)

Y. Fan, F. Zhang, N.-H. Shen, Q. Fu, Z. Wei, H. Li, and C. M. Soukoulis, “Achieving a high-Q response in metamaterials by manipulating the toroidal excitations,” Phys. Rev. A 97(3), 033816 (2018).
[Crossref]

A. K. Ospanova, G. Labate, L. Matekovits, and A. A. Basharin, “Multipolar passive cloaking by nonradiating anapole excitation,” Sci. Rep. 8(1), 12514 (2018).
[Crossref]

P. C. Wu, C. Y. Liao, V. Savinov, T. L. Chung, W. T. Chen, Y.-W. Huang, P. R. Wu, Y.-H. Chen, A.-Q. Liu, N. I. Zheludev, and D. P. Tsai, “Optical anapole metamaterial,” ACS Nano 12(2), 1920–1927 (2018).
[Crossref]

2017 (10)

S.-D. Liu, Z.-X. Wang, W.-J. Wang, J.-D. Chen, and Z.-H. Chen, “High Q-factor with the excitation of anapole modes in dielectric split nanodisk arrays,” Opt. Express 25(19), 22375–22387 (2017).
[Crossref]

N. A. Nemkov, A. A. Basharin, and V. A. Fedotov, “Nonradiating sources, dynamic anapole, and Aharonov-Bohm effect,” Phys. Rev. B 95(16), 165134 (2017).
[Crossref]

N. A. Nemkov, I. V. Stenishchev, and A. A. Basharin, “Nontrivial nonradiating all-dielectric anapole,” Sci. Rep. 7(1), 1064 (2017).
[Crossref]

E. Shokati, N. Granpayeh, and M. Danaeifar, “Wideband and multi-frequency infrared cloaking of spherical objects by using the graphene-based metasurface,” Appl. Opt. 56(11), 3053–3058 (2017).
[Crossref]

G. Labate, A. Alú, and L. Matekovits, “Surface-admittance equivalence principle for nonradiating and cloaking problems,” Phys. Rev. A 95(6), 063841 (2017).
[Crossref]

G. Labate, S. K. Podilchak, and L. Matekovits, “Closed-form harmonic contrast control with surface impedance coatings for conductive objects,” Appl. Opt. 56(36), 10055 (2017).
[Crossref]

L. Di Donato, T. Isernia, G. Labate, and L. Matekovits, “Towards Printable Natural Dielectric Cloaks via Inverse Scattering Techniques,” Sci. Rep. 7(1), 3680 (2017).
[Crossref]

B. Luk’yanchuk, R. Paniagua-Dominguez, A. I. Kuznetsov, A. E. Miroshnichenko, and Y. S. Kivshar, “Hybrid anapole modes of high-index dielectric nanoparticles,” Phys. Rev. A 95(6), 063820 (2017).
[Crossref]

I. V. Stenishchev and A. A. Basharin, “Toroidal response in all-dielectric metamaterials based on water,” Sci. Rep. 7(1), 9468 (2017).
[Crossref]

Z. Liu, S. Du, A. Cui, Z. Li, Y. Fan, S. Chen, W. Li, J. Li, and C. Gu, “High-Quality-Factor Mid-Infrared Toroidal Excitation in Folded 3D Metamaterials,” Adv. Mater. 29(17), 1606298 (2017).
[Crossref]

2016 (2)

G. Labate and L. Matekovits, “Invisibility and cloaking structures as weak or strong solutions of Devaney-Wolf theorem,” Opt. Express 24(17), 19245–19253 (2016).
[Crossref]

N. Papasimakis, V. A. Fedotov, V. Savinov, T. A. Raybould, and N. I. Zheludev, “Electromagnetic toroidal excitations in matter and free space,” Nat. Mater. 15(3), 263–271 (2016).
[Crossref]

2015 (4)

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(1), 8069 (2015).
[Crossref]

R. G. Quarfoth and D. F. Sievenpiper, “Nonscattering waveguides based on tensor impedance surfaces,” IEEE Trans. Antennas Propag. 63(4), 1746–1755 (2015).
[Crossref]

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]

D. Sounas, R. Fleury, and A. Alù, “Unidirectional Cloaking Based on Metasurfaces with Balanced Loss and Gain,” Phys. Rev. Appl. 4(1), 014005 (2015).
[Crossref]

2014 (2)

E. Hurwitz and G. Gbur, “Null-field radiationless sources,” Opt. Lett. 39(22), 6529 (2014).
[Crossref]

F. Monticone and A. Alú, “Embedded Photonic Eigenvalues in 3D Nanostructures,” Phys. Rev. Lett. 112(21), 213903 (2014).
[Crossref]

2013 (3)

V. A. Fedotov, A. V. Rogacheva, V. Savinov, D. P. Tsai, and N. I. Zheludev, “Resonant Transparency and Non-Trivial Non-Radiating Excitations in Toroidal Metamaterials,” Sci. Rep. 3(1), 2967 (2013).
[Crossref]

G. Gbur, “Invisibility physics: past, present, and future,” Prog. Opt. 58, 65–114 (2013).
[Crossref]

Y. Fan, Z. Wei, H. H. Chen, and C. M. Soukoulis, “Low-loss and high-Q planar metamaterial with toroidal moment,” Phys. Rev. B 87(11), 115417 (2013).
[Crossref]

2012 (1)

M. Selvanayagam and G. V. Eleftheriades, “An Active Electromagnetic Cloak Using the Equivalence Principle,” IEEE Ant. and Wireless Prop. Lett. 11, 1226–1229 (2012).
[Crossref]

2011 (2)

2010 (2)

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]

S. Maci, “A Cloaking Metamaterial Based on an Inhomogeneous Linear Field Transformation,” IEEE Trans. Antennas Propag. 58(4), 1136–1143 (2010).
[Crossref]

2009 (1)

A. Alù, “Mantle cloak: Invisibility induced by a surface,” Phys. Rev. B 80(24), 245115 (2009).
[Crossref]

2007 (1)

2006 (1)

J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312(5781), 1780–1782 (2006).
[Crossref]

2005 (1)

A. Alù and N. Engheta, “Achieving transparency with plasmonic and metamaterial coatings,” Phys. Rev. E 72(1), 016623 (2005).
[Crossref]

2004 (1)

2001 (1)

B. J. Hoenders and H. A. Ferwerda, “Identification of the radiative and nonradiative parts of a wave field,” Phys. Rev. Lett. 87(6), 060401 (2001).
[Crossref]

1999 (1)

E. Marengo and R. Ziolkowski, “On the radiating and nonradiating components of scalar, electromagnetic, and weak gravitational sources,” Phys. Rev. Lett. 83(17), 3345–3349 (1999).
[Crossref]

1998 (3)

M. Berry, J. T. Foley, G. Gbur, and E. Wolf, “A simple explanation of simple non- radiating sources in one dimension comment on nonpropagating string excitations,” Am. J. Phys. 66(2), 121–123 (1998).
[Crossref]

B. J. Hoenders and H. A. Ferwerda, “The nonradiating component of the field generated by a finite monochromatic scalar source distribution,” Pure Appl. Opt. 7(5), 1201–1211 (1998).
[Crossref]

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

1995 (1)

G. N. Afanasiev and Y. P. Stepanovsky, “The electromagnetic field of elementary time-dependent toroidal sources,” J. Phys. A: Math. Gen. 28(16), 4565–4580 (1995).
[Crossref]

1986 (1)

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

1973 (1)

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

1964 (1)

G. H. Goedecke, “Classically radiationless motions and possible implications for quantum theory,” Phys. Rev. 135(1B), B281–B288 (1964).
[Crossref]

1948 (1)

D. Bohm and M. Weinstein, “The self-oscillations of a charged particle,” Phys. Rev. 74(12), 1789–1798 (1948).
[Crossref]

1937 (1)

G. A. Schott, “The uniform circular motion with invariable normal spin of a rigidly and uniformly electrified sphere, IV,” Proc. Roy. Soc. A 159(899), 570–591 (1937).
[Crossref]

1933 (1)

G. A. Schott, “The electromagnetic field of a moving uniformly and rigidly electrified sphere and its radiationless orbits,” Phil. Mag. 15(100), 752–761 (1933).
[Crossref]

1910 (1)

P. Ehrenfest, “Ungleichformige Elektrizitätsbewegungen ohne Magnet-und Strahlungsfeld,” Physik. Zeit. 11, 708–709 (1910).

Afanasiev, G.

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

Afanasiev, G. N.

G. N. Afanasiev and Y. P. Stepanovsky, “The electromagnetic field of elementary time-dependent toroidal sources,” J. Phys. A: Math. Gen. 28(16), 4565–4580 (1995).
[Crossref]

Algorri, J. F.

Alú, A.

G. Labate, A. Alú, and L. Matekovits, “Surface-admittance equivalence principle for nonradiating and cloaking problems,” Phys. Rev. A 95(6), 063841 (2017).
[Crossref]

F. Monticone and A. Alú, “Embedded Photonic Eigenvalues in 3D Nanostructures,” Phys. Rev. Lett. 112(21), 213903 (2014).
[Crossref]

G. Labate, L. Matekovits, and A. Alú, “Metamaterial and Metasurface Cloaking: Principles and Applications,” Chap. 10 in Surface Electromagnetics (with Applications in Antenna, Microwave, and Optical Engineering), F. Yang and Y. Rahmat-Samii, eds., Cambridge University Press, 2019.

Alù, A.

D. Sounas, R. Fleury, and A. Alù, “Unidirectional Cloaking Based on Metasurfaces with Balanced Loss and Gain,” Phys. Rev. Appl. 4(1), 014005 (2015).
[Crossref]

P. -Y. Chen and A. Alù, “Mantle cloaking using thin patterned metasurfaces,” Phys. Rev. B 84(20), 205110 (2011).
[Crossref]

A. Alù, “Mantle cloak: Invisibility induced by a surface,” Phys. Rev. B 80(24), 245115 (2009).
[Crossref]

A. Alù and N. Engheta, “Achieving transparency with plasmonic and metamaterial coatings,” Phys. Rev. E 72(1), 016623 (2005).
[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(1), 8069 (2015).
[Crossref]

Baryshnikova, K. V.

K. V. Baryshnikova, D. A. Smirnova, B. S. Luk’yanchuk, and Y. S. Kivshar, “Optical Anapoles: Concepts and Applications,” Adv. Opt. Mater. 7(14), 1801350 (2019).
[Crossref]

Basharin, A. A.

A. K. Ospanova, G. Labate, L. Matekovits, and A. A. Basharin, “Multipolar passive cloaking by nonradiating anapole excitation,” Sci. Rep. 8(1), 12514 (2018).
[Crossref]

N. A. Nemkov, A. A. Basharin, and V. A. Fedotov, “Nonradiating sources, dynamic anapole, and Aharonov-Bohm effect,” Phys. Rev. B 95(16), 165134 (2017).
[Crossref]

N. A. Nemkov, I. V. Stenishchev, and A. A. Basharin, “Nontrivial nonradiating all-dielectric anapole,” Sci. Rep. 7(1), 1064 (2017).
[Crossref]

I. V. Stenishchev and A. A. Basharin, “Toroidal response in all-dielectric metamaterials based on water,” Sci. Rep. 7(1), 9468 (2017).
[Crossref]

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]

Beccherelli, R.

Berry, M.

M. Berry, J. T. Foley, G. Gbur, and E. Wolf, “A simple explanation of simple non- radiating sources in one dimension comment on nonpropagating string excitations,” Am. J. Phys. 66(2), 121–123 (1998).
[Crossref]

Bilotti, F.

Bohm, D.

D. Bohm and M. Weinstein, “The self-oscillations of a charged particle,” Phys. Rev. 74(12), 1789–1798 (1948).
[Crossref]

Bohren, C. F.

C. F. Bohren and D. R. Huffman, (Wiley-Interscience, New York, 1983), 82–84.

Bozhevolnyi, S. I.

Y. Yang and S. I. Bozhevolnyi, “Nonradiating anapole states in nanophotonics: from fundamentals to applications,” Nanotechnology 30(20), 204001 (2019).
[Crossref]

Chen, H. H.

Y. Fan, Z. Wei, H. H. Chen, and C. M. Soukoulis, “Low-loss and high-Q planar metamaterial with toroidal moment,” Phys. Rev. B 87(11), 115417 (2013).
[Crossref]

Chen, J.-D.

Chen, S.

Z. Liu, S. Du, A. Cui, Z. Li, Y. Fan, S. Chen, W. Li, J. Li, and C. Gu, “High-Quality-Factor Mid-Infrared Toroidal Excitation in Folded 3D Metamaterials,” Adv. Mater. 29(17), 1606298 (2017).
[Crossref]

Chen, W. T.

P. C. Wu, C. Y. Liao, V. Savinov, T. L. Chung, W. T. Chen, Y.-W. Huang, P. R. Wu, Y.-H. Chen, A.-Q. Liu, N. I. Zheludev, and D. P. Tsai, “Optical anapole metamaterial,” ACS Nano 12(2), 1920–1927 (2018).
[Crossref]

Chen, Y.-H.

P. C. Wu, C. Y. Liao, V. Savinov, T. L. Chung, W. T. Chen, Y.-W. Huang, P. R. Wu, Y.-H. Chen, A.-Q. Liu, N. I. Zheludev, and D. P. Tsai, “Optical anapole metamaterial,” ACS Nano 12(2), 1920–1927 (2018).
[Crossref]

Chen, Z.-H.

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(1), 8069 (2015).
[Crossref]

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(1), 8069 (2015).
[Crossref]

Chung, T. L.

P. C. Wu, C. Y. Liao, V. Savinov, T. L. Chung, W. T. Chen, Y.-W. Huang, P. R. Wu, Y.-H. Chen, A.-Q. Liu, N. I. Zheludev, and D. P. Tsai, “Optical anapole metamaterial,” ACS Nano 12(2), 1920–1927 (2018).
[Crossref]

Cui, A.

Z. Liu, S. Du, A. Cui, Z. Li, Y. Fan, S. Chen, W. Li, J. Li, and C. Gu, “High-Quality-Factor Mid-Infrared Toroidal Excitation in Folded 3D Metamaterials,” Adv. Mater. 29(17), 1606298 (2017).
[Crossref]

Danaeifar, M.

Devaney, A. J.

A. J. Devaney, “Nonradiating surface sources,” J. Opt. Soc. Am. A 21(11), 2216–2222 (2004).
[Crossref]

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

Di Donato, L.

L. Di Donato, T. Isernia, G. Labate, and L. Matekovits, “Towards Printable Natural Dielectric Cloaks via Inverse Scattering Techniques,” Sci. Rep. 7(1), 3680 (2017).
[Crossref]

Du, S.

Z. Liu, S. Du, A. Cui, Z. Li, Y. Fan, S. Chen, W. Li, J. Li, and C. Gu, “High-Quality-Factor Mid-Infrared Toroidal Excitation in Folded 3D Metamaterials,” Adv. Mater. 29(17), 1606298 (2017).
[Crossref]

Dubovik, V.

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

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]

Ehrenfest, P.

P. Ehrenfest, “Ungleichformige Elektrizitätsbewegungen ohne Magnet-und Strahlungsfeld,” Physik. Zeit. 11, 708–709 (1910).

Eleftheriades, G. V.

M. Selvanayagam and G. V. Eleftheriades, “An Active Electromagnetic Cloak Using the Equivalence Principle,” IEEE Ant. and Wireless Prop. Lett. 11, 1226–1229 (2012).
[Crossref]

Engheta, N.

A. Alù and N. Engheta, “Achieving transparency with plasmonic and metamaterial coatings,” Phys. Rev. E 72(1), 016623 (2005).
[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(1), 8069 (2015).
[Crossref]

Fan, Y.

Y. Fan, F. Zhang, N.-H. Shen, Q. Fu, Z. Wei, H. Li, and C. M. Soukoulis, “Achieving a high-Q response in metamaterials by manipulating the toroidal excitations,” Phys. Rev. A 97(3), 033816 (2018).
[Crossref]

Z. Liu, S. Du, A. Cui, Z. Li, Y. Fan, S. Chen, W. Li, J. Li, and C. Gu, “High-Quality-Factor Mid-Infrared Toroidal Excitation in Folded 3D Metamaterials,” Adv. Mater. 29(17), 1606298 (2017).
[Crossref]

Y. Fan, Z. Wei, H. H. Chen, and C. M. Soukoulis, “Low-loss and high-Q planar metamaterial with toroidal moment,” Phys. Rev. B 87(11), 115417 (2013).
[Crossref]

Fedotov, V. A.

N. A. Nemkov, A. A. Basharin, and V. A. Fedotov, “Nonradiating sources, dynamic anapole, and Aharonov-Bohm effect,” Phys. Rev. B 95(16), 165134 (2017).
[Crossref]

N. Papasimakis, V. A. Fedotov, V. Savinov, T. A. Raybould, and N. I. Zheludev, “Electromagnetic toroidal excitations in matter and free space,” Nat. Mater. 15(3), 263–271 (2016).
[Crossref]

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]

V. A. Fedotov, A. V. Rogacheva, V. Savinov, D. P. Tsai, and N. I. Zheludev, “Resonant Transparency and Non-Trivial Non-Radiating Excitations in Toroidal Metamaterials,” Sci. Rep. 3(1), 2967 (2013).
[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).
[Crossref]

Ferraro, A.

Ferwerda, H. A.

B. J. Hoenders and H. A. Ferwerda, “Identification of the radiative and nonradiative parts of a wave field,” Phys. Rev. Lett. 87(6), 060401 (2001).
[Crossref]

B. J. Hoenders and H. A. Ferwerda, “The nonradiating component of the field generated by a finite monochromatic scalar source distribution,” Pure Appl. Opt. 7(5), 1201–1211 (1998).
[Crossref]

Fleury, R.

D. Sounas, R. Fleury, and A. Alù, “Unidirectional Cloaking Based on Metasurfaces with Balanced Loss and Gain,” Phys. Rev. Appl. 4(1), 014005 (2015).
[Crossref]

Foley, J. T.

M. Berry, J. T. Foley, G. Gbur, and E. Wolf, “A simple explanation of simple non- radiating sources in one dimension comment on nonpropagating string excitations,” Am. J. Phys. 66(2), 121–123 (1998).
[Crossref]

Fu, Q.

Y. Fan, F. Zhang, N.-H. Shen, Q. Fu, Z. Wei, H. Li, and C. M. Soukoulis, “Achieving a high-Q response in metamaterials by manipulating the toroidal excitations,” Phys. Rev. A 97(3), 033816 (2018).
[Crossref]

Garcia-Cámara, B.

Gbur, G.

E. Hurwitz and G. Gbur, “Null-field radiationless sources,” Opt. Lett. 39(22), 6529 (2014).
[Crossref]

G. Gbur, “Invisibility physics: past, present, and future,” Prog. Opt. 58, 65–114 (2013).
[Crossref]

M. Berry, J. T. Foley, G. Gbur, and E. Wolf, “A simple explanation of simple non- radiating sources in one dimension comment on nonpropagating string excitations,” Am. J. Phys. 66(2), 121–123 (1998).
[Crossref]

G. Gbur, Nonradiating Sources and the Inverse Source Problem, University of Rochester Rochester, New York, 2001 (available at: www.maxwell.uncc.edu/gjgbur ).

G. Gbur, “Nonradiating sources and other invisible objects,” Chap. 5 in E. Wolf (Ed.), Prog. in Optics (Elsevier, 2003), 273–315.

Goedecke, G. H.

G. H. Goedecke, “Classically radiationless motions and possible implications for quantum theory,” Phys. Rev. 135(1B), B281–B288 (1964).
[Crossref]

Granpayeh, N.

Gu, C.

Z. Liu, S. Du, A. Cui, Z. Li, Y. Fan, S. Chen, W. Li, J. Li, and C. Gu, “High-Quality-Factor Mid-Infrared Toroidal Excitation in Folded 3D Metamaterials,” Adv. Mater. 29(17), 1606298 (2017).
[Crossref]

Guenneau, S.

Hoenders, B. J.

B. J. Hoenders and H. A. Ferwerda, “Identification of the radiative and nonradiative parts of a wave field,” Phys. Rev. Lett. 87(6), 060401 (2001).
[Crossref]

B. J. Hoenders and H. A. Ferwerda, “The nonradiating component of the field generated by a finite monochromatic scalar source distribution,” Pure Appl. Opt. 7(5), 1201–1211 (1998).
[Crossref]

Huang, Y.-W.

P. C. Wu, C. Y. Liao, V. Savinov, T. L. Chung, W. T. Chen, Y.-W. Huang, P. R. Wu, Y.-H. Chen, A.-Q. Liu, N. I. Zheludev, and D. P. Tsai, “Optical anapole metamaterial,” ACS Nano 12(2), 1920–1927 (2018).
[Crossref]

Huffman, D. R.

C. F. Bohren and D. R. Huffman, (Wiley-Interscience, New York, 1983), 82–84.

Hurwitz, E.

Isernia, T.

L. Di Donato, T. Isernia, G. Labate, and L. Matekovits, “Towards Printable Natural Dielectric Cloaks via Inverse Scattering Techniques,” Sci. Rep. 7(1), 3680 (2017).
[Crossref]

Ishimaru, A.

A. Ishimaru, Electromagnetic wave propagation, radiation and scattering (Prentice-Hall, 1991).

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]

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).
[Crossref]

Kim, K.

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

Kivshar, Y. S.

K. V. Baryshnikova, D. A. Smirnova, B. S. Luk’yanchuk, and Y. S. Kivshar, “Optical Anapoles: Concepts and Applications,” Adv. Opt. Mater. 7(14), 1801350 (2019).
[Crossref]

B. Luk’yanchuk, R. Paniagua-Dominguez, A. I. Kuznetsov, A. E. Miroshnichenko, and Y. S. Kivshar, “Hybrid anapole modes of high-index dielectric nanoparticles,” Phys. Rev. A 95(6), 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(1), 8069 (2015).
[Crossref]

Kuznetsov, A. I.

B. Luk’yanchuk, R. Paniagua-Dominguez, A. I. Kuznetsov, A. E. Miroshnichenko, and Y. S. Kivshar, “Hybrid anapole modes of high-index dielectric nanoparticles,” Phys. Rev. A 95(6), 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(1), 8069 (2015).
[Crossref]

Labate, G.

A. K. Ospanova, G. Labate, L. Matekovits, and A. A. Basharin, “Multipolar passive cloaking by nonradiating anapole excitation,” Sci. Rep. 8(1), 12514 (2018).
[Crossref]

L. Di Donato, T. Isernia, G. Labate, and L. Matekovits, “Towards Printable Natural Dielectric Cloaks via Inverse Scattering Techniques,” Sci. Rep. 7(1), 3680 (2017).
[Crossref]

G. Labate, A. Alú, and L. Matekovits, “Surface-admittance equivalence principle for nonradiating and cloaking problems,” Phys. Rev. A 95(6), 063841 (2017).
[Crossref]

G. Labate, S. K. Podilchak, and L. Matekovits, “Closed-form harmonic contrast control with surface impedance coatings for conductive objects,” Appl. Opt. 56(36), 10055 (2017).
[Crossref]

G. Labate and L. Matekovits, “Invisibility and cloaking structures as weak or strong solutions of Devaney-Wolf theorem,” Opt. Express 24(17), 19245–19253 (2016).
[Crossref]

G. Labate, L. Matekovits, and A. Alú, “Metamaterial and Metasurface Cloaking: Principles and Applications,” Chap. 10 in Surface Electromagnetics (with Applications in Antenna, Microwave, and Optical Engineering), F. Yang and Y. Rahmat-Samii, eds., Cambridge University Press, 2019.

Leonhardt, U.

U. Leonhardt and T. G. Philbin, Geometry and Light: The Science of Invisibility (Dover, 2010).

Li, H.

Y. Fan, F. Zhang, N.-H. Shen, Q. Fu, Z. Wei, H. Li, and C. M. Soukoulis, “Achieving a high-Q response in metamaterials by manipulating the toroidal excitations,” Phys. Rev. A 97(3), 033816 (2018).
[Crossref]

Li, J.

Z. Liu, S. Du, A. Cui, Z. Li, Y. Fan, S. Chen, W. Li, J. Li, and C. Gu, “High-Quality-Factor Mid-Infrared Toroidal Excitation in Folded 3D Metamaterials,” Adv. Mater. 29(17), 1606298 (2017).
[Crossref]

Li, W.

Z. Liu, S. Du, A. Cui, Z. Li, Y. Fan, S. Chen, W. Li, J. Li, and C. Gu, “High-Quality-Factor Mid-Infrared Toroidal Excitation in Folded 3D Metamaterials,” Adv. Mater. 29(17), 1606298 (2017).
[Crossref]

Li, Z.

Z. Liu, S. Du, A. Cui, Z. Li, Y. Fan, S. Chen, W. Li, J. Li, and C. Gu, “High-Quality-Factor Mid-Infrared Toroidal Excitation in Folded 3D Metamaterials,” Adv. Mater. 29(17), 1606298 (2017).
[Crossref]

Liao, C. Y.

P. C. Wu, C. Y. Liao, V. Savinov, T. L. Chung, W. T. Chen, Y.-W. Huang, P. R. Wu, Y.-H. Chen, A.-Q. Liu, N. I. Zheludev, and D. P. Tsai, “Optical anapole metamaterial,” ACS Nano 12(2), 1920–1927 (2018).
[Crossref]

Liu, A.-Q.

P. C. Wu, C. Y. Liao, V. Savinov, T. L. Chung, W. T. Chen, Y.-W. Huang, P. R. Wu, Y.-H. Chen, A.-Q. Liu, N. I. Zheludev, and D. P. Tsai, “Optical anapole metamaterial,” ACS Nano 12(2), 1920–1927 (2018).
[Crossref]

Liu, S.-D.

Liu, Y.

Liu, Z.

Z. Liu, S. Du, A. Cui, Z. Li, Y. Fan, S. Chen, W. Li, J. Li, and C. Gu, “High-Quality-Factor Mid-Infrared Toroidal Excitation in Folded 3D Metamaterials,” Adv. Mater. 29(17), 1606298 (2017).
[Crossref]

Luk’yanchuk, B.

B. Luk’yanchuk, R. Paniagua-Dominguez, A. I. Kuznetsov, A. E. Miroshnichenko, and Y. S. Kivshar, “Hybrid anapole modes of high-index dielectric nanoparticles,” Phys. Rev. A 95(6), 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(1), 8069 (2015).
[Crossref]

Luk’yanchuk, B. S.

K. V. Baryshnikova, D. A. Smirnova, B. S. Luk’yanchuk, and Y. S. Kivshar, “Optical Anapoles: Concepts and Applications,” Adv. Opt. Mater. 7(14), 1801350 (2019).
[Crossref]

Maci, S.

S. Maci, “A Cloaking Metamaterial Based on an Inhomogeneous Linear Field Transformation,” IEEE Trans. Antennas Propag. 58(4), 1136–1143 (2010).
[Crossref]

Marengo, E.

E. Marengo and R. Ziolkowski, “On the radiating and nonradiating components of scalar, electromagnetic, and weak gravitational sources,” Phys. Rev. Lett. 83(17), 3345–3349 (1999).
[Crossref]

Matekovits, L.

A. K. Ospanova, G. Labate, L. Matekovits, and A. A. Basharin, “Multipolar passive cloaking by nonradiating anapole excitation,” Sci. Rep. 8(1), 12514 (2018).
[Crossref]

L. Di Donato, T. Isernia, G. Labate, and L. Matekovits, “Towards Printable Natural Dielectric Cloaks via Inverse Scattering Techniques,” Sci. Rep. 7(1), 3680 (2017).
[Crossref]

G. Labate, A. Alú, and L. Matekovits, “Surface-admittance equivalence principle for nonradiating and cloaking problems,” Phys. Rev. A 95(6), 063841 (2017).
[Crossref]

G. Labate, S. K. Podilchak, and L. Matekovits, “Closed-form harmonic contrast control with surface impedance coatings for conductive objects,” Appl. Opt. 56(36), 10055 (2017).
[Crossref]

G. Labate and L. Matekovits, “Invisibility and cloaking structures as weak or strong solutions of Devaney-Wolf theorem,” Opt. Express 24(17), 19245–19253 (2016).
[Crossref]

G. Labate, L. Matekovits, and A. Alú, “Metamaterial and Metasurface Cloaking: Principles and Applications,” Chap. 10 in Surface Electromagnetics (with Applications in Antenna, Microwave, and Optical Engineering), F. Yang and Y. Rahmat-Samii, eds., Cambridge University Press, 2019.

Miroshnichenko, A. E.

B. Luk’yanchuk, R. Paniagua-Dominguez, A. I. Kuznetsov, A. E. Miroshnichenko, and Y. S. Kivshar, “Hybrid anapole modes of high-index dielectric nanoparticles,” Phys. Rev. A 95(6), 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(1), 8069 (2015).
[Crossref]

Monti, A.

Monticone, F.

F. Monticone and A. Alú, “Embedded Photonic Eigenvalues in 3D Nanostructures,” Phys. Rev. Lett. 112(21), 213903 (2014).
[Crossref]

Nemkov, N. A.

N. A. Nemkov, A. A. Basharin, and V. A. Fedotov, “Nonradiating sources, dynamic anapole, and Aharonov-Bohm effect,” Phys. Rev. B 95(16), 165134 (2017).
[Crossref]

N. A. Nemkov, I. V. Stenishchev, and A. A. Basharin, “Nontrivial nonradiating all-dielectric anapole,” Sci. Rep. 7(1), 1064 (2017).
[Crossref]

Nicolet, A.

Ospanova, A. K.

A. K. Ospanova, G. Labate, L. Matekovits, and A. A. Basharin, “Multipolar passive cloaking by nonradiating anapole excitation,” Sci. Rep. 8(1), 12514 (2018).
[Crossref]

Paniagua-Dominguez, R.

B. Luk’yanchuk, R. Paniagua-Dominguez, A. I. Kuznetsov, A. E. Miroshnichenko, and Y. S. Kivshar, “Hybrid anapole modes of high-index dielectric nanoparticles,” Phys. Rev. A 95(6), 063820 (2017).
[Crossref]

Papas, C. H.

C. H. Papas, Theory of Electromagnetic Wave Propagation (Dover Publications, Inc., 1965).

Papasimakis, N.

N. Papasimakis, V. A. Fedotov, V. Savinov, T. A. Raybould, and N. I. Zheludev, “Electromagnetic toroidal excitations in matter and free space,” Nat. Mater. 15(3), 263–271 (2016).
[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).
[Crossref]

Pendry, J. B.

Philbin, T. G.

U. Leonhardt and T. G. Philbin, Geometry and Light: The Science of Invisibility (Dover, 2010).

Podilchak, S. K.

Qi, J.

Quarfoth, R. G.

R. G. Quarfoth and D. F. Sievenpiper, “Nonscattering waveguides based on tensor impedance surfaces,” IEEE Trans. Antennas Propag. 63(4), 1746–1755 (2015).
[Crossref]

Raybould, T. A.

N. Papasimakis, V. A. Fedotov, V. Savinov, T. A. Raybould, and N. I. Zheludev, “Electromagnetic toroidal excitations in matter and free space,” Nat. Mater. 15(3), 263–271 (2016).
[Crossref]

Rogacheva, A. V.

V. A. Fedotov, A. V. Rogacheva, V. Savinov, D. P. Tsai, and N. I. Zheludev, “Resonant Transparency and Non-Trivial Non-Radiating Excitations in Toroidal Metamaterials,” Sci. Rep. 3(1), 2967 (2013).
[Crossref]

Sánchez-Pena, J. M.

Savinov, V.

P. C. Wu, C. Y. Liao, V. Savinov, T. L. Chung, W. T. Chen, Y.-W. Huang, P. R. Wu, Y.-H. Chen, A.-Q. Liu, N. I. Zheludev, and D. P. Tsai, “Optical anapole metamaterial,” ACS Nano 12(2), 1920–1927 (2018).
[Crossref]

N. Papasimakis, V. A. Fedotov, V. Savinov, T. A. Raybould, and N. I. Zheludev, “Electromagnetic toroidal excitations in matter and free space,” Nat. Mater. 15(3), 263–271 (2016).
[Crossref]

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]

V. A. Fedotov, A. V. Rogacheva, V. Savinov, D. P. Tsai, and N. I. Zheludev, “Resonant Transparency and Non-Trivial Non-Radiating Excitations in Toroidal Metamaterials,” Sci. Rep. 3(1), 2967 (2013).
[Crossref]

Schott, G. A.

G. A. Schott, “The uniform circular motion with invariable normal spin of a rigidly and uniformly electrified sphere, IV,” Proc. Roy. Soc. A 159(899), 570–591 (1937).
[Crossref]

G. A. Schott, “The electromagnetic field of a moving uniformly and rigidly electrified sphere and its radiationless orbits,” Phil. Mag. 15(100), 752–761 (1933).
[Crossref]

Schurig, D.

J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312(5781), 1780–1782 (2006).
[Crossref]

Selvanayagam, M.

M. Selvanayagam and G. V. Eleftheriades, “An Active Electromagnetic Cloak Using the Equivalence Principle,” IEEE Ant. and Wireless Prop. Lett. 11, 1226–1229 (2012).
[Crossref]

Shen, N.-H.

Y. Fan, F. Zhang, N.-H. Shen, Q. Fu, Z. Wei, H. Li, and C. M. Soukoulis, “Achieving a high-Q response in metamaterials by manipulating the toroidal excitations,” Phys. Rev. A 97(3), 033816 (2018).
[Crossref]

Shi, Y.

Shokati, E.

Sievenpiper, D. F.

R. G. Quarfoth and D. F. Sievenpiper, “Nonscattering waveguides based on tensor impedance surfaces,” IEEE Trans. Antennas Propag. 63(4), 1746–1755 (2015).
[Crossref]

Smirnova, D. A.

K. V. Baryshnikova, D. A. Smirnova, B. S. Luk’yanchuk, and Y. S. Kivshar, “Optical Anapoles: Concepts and Applications,” Adv. Opt. Mater. 7(14), 1801350 (2019).
[Crossref]

Smith, D. R.

J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312(5781), 1780–1782 (2006).
[Crossref]

Sommerfeld, A.

A. Sommerfeld, “Zur elektronentheorie. I. Allgemeine untersuchung des feldes eines beliebig bewegten elektrons,” Akad. der Wiss. (Gott.), Math. Phys. Klasse, Nach., 99–130 (1904).

A. Sommerfeld, “Zur elektronentheorie. II. Grundlagen fur eine allgemeine dynamik des elektrons,” Akad. der Wiss. (Gott.), Math. Phys. Klasse, Nach.363–439 (1904).

Soukoulis, C. M.

Y. Fan, F. Zhang, N.-H. Shen, Q. Fu, Z. Wei, H. Li, and C. M. Soukoulis, “Achieving a high-Q response in metamaterials by manipulating the toroidal excitations,” Phys. Rev. A 97(3), 033816 (2018).
[Crossref]

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. Fan, Z. Wei, H. H. Chen, and C. M. Soukoulis, “Low-loss and high-Q planar metamaterial with toroidal moment,” Phys. Rev. B 87(11), 115417 (2013).
[Crossref]

Sounas, D.

D. Sounas, R. Fleury, and A. Alù, “Unidirectional Cloaking Based on Metasurfaces with Balanced Loss and Gain,” Phys. Rev. Appl. 4(1), 014005 (2015).
[Crossref]

Stenishchev, I. V.

N. A. Nemkov, I. V. Stenishchev, and A. A. Basharin, “Nontrivial nonradiating all-dielectric anapole,” Sci. Rep. 7(1), 1064 (2017).
[Crossref]

I. V. Stenishchev and A. A. Basharin, “Toroidal response in all-dielectric metamaterials based on water,” Sci. Rep. 7(1), 9468 (2017).
[Crossref]

Stepanovsky, Y. P.

G. N. Afanasiev and Y. P. Stepanovsky, “The electromagnetic field of elementary time-dependent toroidal sources,” J. Phys. A: Math. Gen. 28(16), 4565–4580 (1995).
[Crossref]

Toscano, A.

Tsai, D. P.

P. C. Wu, C. Y. Liao, V. Savinov, T. L. Chung, W. T. Chen, Y.-W. Huang, P. R. Wu, Y.-H. Chen, A.-Q. Liu, N. I. Zheludev, and D. P. Tsai, “Optical anapole metamaterial,” ACS Nano 12(2), 1920–1927 (2018).
[Crossref]

V. A. Fedotov, A. V. Rogacheva, V. Savinov, D. P. Tsai, and N. I. Zheludev, “Resonant Transparency and Non-Trivial Non-Radiating Excitations in Toroidal Metamaterials,” Sci. Rep. 3(1), 2967 (2013).
[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).
[Crossref]

Van Bladel, J.

J. Van Bladel, Singular Electromagnetic Fields and Sources, Chap. 2 (Oxford1991).

Wang, W.

Wang, W.-J.

Wang, Z.-X.

Wei, Z.

Y. Fan, F. Zhang, N.-H. Shen, Q. Fu, Z. Wei, H. Li, and C. M. Soukoulis, “Achieving a high-Q response in metamaterials by manipulating the toroidal excitations,” Phys. Rev. A 97(3), 033816 (2018).
[Crossref]

Y. Fan, Z. Wei, H. H. Chen, and C. M. Soukoulis, “Low-loss and high-Q planar metamaterial with toroidal moment,” Phys. Rev. B 87(11), 115417 (2013).
[Crossref]

Weinstein, M.

D. Bohm and M. Weinstein, “The self-oscillations of a charged particle,” Phys. Rev. 74(12), 1789–1798 (1948).
[Crossref]

Wolf, E.

M. Berry, J. T. Foley, G. Gbur, and E. Wolf, “A simple explanation of simple non- radiating sources in one dimension comment on nonpropagating string excitations,” Am. J. Phys. 66(2), 121–123 (1998).
[Crossref]

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

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

Wu, P. C.

P. C. Wu, C. Y. Liao, V. Savinov, T. L. Chung, W. T. Chen, Y.-W. Huang, P. R. Wu, Y.-H. Chen, A.-Q. Liu, N. I. Zheludev, and D. P. Tsai, “Optical anapole metamaterial,” ACS Nano 12(2), 1920–1927 (2018).
[Crossref]

Wu, P. R.

P. C. Wu, C. Y. Liao, V. Savinov, T. L. Chung, W. T. Chen, Y.-W. Huang, P. R. Wu, Y.-H. Chen, A.-Q. Liu, N. I. Zheludev, and D. P. Tsai, “Optical anapole metamaterial,” ACS Nano 12(2), 1920–1927 (2018).
[Crossref]

Xiong, L.

-Y. Chen, P.

P. -Y. Chen and A. Alù, “Mantle cloaking using thin patterned metasurfaces,” Phys. Rev. B 84(20), 205110 (2011).
[Crossref]

Yang, Y.

Y. Yang and S. I. Bozhevolnyi, “Nonradiating anapole states in nanophotonics: from fundamentals to applications,” Nanotechnology 30(20), 204001 (2019).
[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(1), 8069 (2015).
[Crossref]

Zhang, F.

Y. Fan, F. Zhang, N.-H. Shen, Q. Fu, Z. Wei, H. Li, and C. M. Soukoulis, “Achieving a high-Q response in metamaterials by manipulating the toroidal excitations,” Phys. Rev. A 97(3), 033816 (2018).
[Crossref]

Zhao, X.

Zheludev, N. I.

P. C. Wu, C. Y. Liao, V. Savinov, T. L. Chung, W. T. Chen, Y.-W. Huang, P. R. Wu, Y.-H. Chen, A.-Q. Liu, N. I. Zheludev, and D. P. Tsai, “Optical anapole metamaterial,” ACS Nano 12(2), 1920–1927 (2018).
[Crossref]

N. Papasimakis, V. A. Fedotov, V. Savinov, T. A. Raybould, and N. I. Zheludev, “Electromagnetic toroidal excitations in matter and free space,” Nat. Mater. 15(3), 263–271 (2016).
[Crossref]

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]

V. A. Fedotov, A. V. Rogacheva, V. Savinov, D. P. Tsai, and N. I. Zheludev, “Resonant Transparency and Non-Trivial Non-Radiating Excitations in Toroidal Metamaterials,” Sci. Rep. 3(1), 2967 (2013).
[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).
[Crossref]

Zheng, L.

Ziolkowski, R.

E. Marengo and R. Ziolkowski, “On the radiating and nonradiating components of scalar, electromagnetic, and weak gravitational sources,” Phys. Rev. Lett. 83(17), 3345–3349 (1999).
[Crossref]

Zografopoulos, D. C.

Zolla, F.

ACS Nano (1)

P. C. Wu, C. Y. Liao, V. Savinov, T. L. Chung, W. T. Chen, Y.-W. Huang, P. R. Wu, Y.-H. Chen, A.-Q. Liu, N. I. Zheludev, and D. P. Tsai, “Optical anapole metamaterial,” ACS Nano 12(2), 1920–1927 (2018).
[Crossref]

Adv. Mater. (1)

Z. Liu, S. Du, A. Cui, Z. Li, Y. Fan, S. Chen, W. Li, J. Li, and C. Gu, “High-Quality-Factor Mid-Infrared Toroidal Excitation in Folded 3D Metamaterials,” Adv. Mater. 29(17), 1606298 (2017).
[Crossref]

Adv. Opt. Mater. (1)

K. V. Baryshnikova, D. A. Smirnova, B. S. Luk’yanchuk, and Y. S. Kivshar, “Optical Anapoles: Concepts and Applications,” Adv. Opt. Mater. 7(14), 1801350 (2019).
[Crossref]

Am. J. Phys. (1)

M. Berry, J. T. Foley, G. Gbur, and E. Wolf, “A simple explanation of simple non- radiating sources in one dimension comment on nonpropagating string excitations,” Am. J. Phys. 66(2), 121–123 (1998).
[Crossref]

Appl. Opt. (2)

IEEE Ant. and Wireless Prop. Lett. (1)

M. Selvanayagam and G. V. Eleftheriades, “An Active Electromagnetic Cloak Using the Equivalence Principle,” IEEE Ant. and Wireless Prop. Lett. 11, 1226–1229 (2012).
[Crossref]

IEEE Trans. Antennas Propag. (2)

S. Maci, “A Cloaking Metamaterial Based on an Inhomogeneous Linear Field Transformation,” IEEE Trans. Antennas Propag. 58(4), 1136–1143 (2010).
[Crossref]

R. G. Quarfoth and D. F. Sievenpiper, “Nonscattering waveguides based on tensor impedance surfaces,” IEEE Trans. Antennas Propag. 63(4), 1746–1755 (2015).
[Crossref]

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

J. Phys. A: Math. Gen. (1)

G. N. Afanasiev and Y. P. Stepanovsky, “The electromagnetic field of elementary time-dependent toroidal sources,” J. Phys. A: Math. Gen. 28(16), 4565–4580 (1995).
[Crossref]

Nanotechnology (1)

Y. Yang and S. I. Bozhevolnyi, “Nonradiating anapole states in nanophotonics: from fundamentals to applications,” Nanotechnology 30(20), 204001 (2019).
[Crossref]

Nat. Commun. (1)

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(1), 8069 (2015).
[Crossref]

Nat. Mater. (1)

N. Papasimakis, V. A. Fedotov, V. Savinov, T. A. Raybould, and N. I. Zheludev, “Electromagnetic toroidal excitations in matter and free space,” Nat. Mater. 15(3), 263–271 (2016).
[Crossref]

Opt. Commun. (1)

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

Opt. Express (3)

Opt. Lett. (3)

OSA Continuum (1)

Phil. Mag. (1)

G. A. Schott, “The electromagnetic field of a moving uniformly and rigidly electrified sphere and its radiationless orbits,” Phil. Mag. 15(100), 752–761 (1933).
[Crossref]

Phys. Part. Nucl. (1)

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

Phys. Rev. (2)

D. Bohm and M. Weinstein, “The self-oscillations of a charged particle,” Phys. Rev. 74(12), 1789–1798 (1948).
[Crossref]

G. H. Goedecke, “Classically radiationless motions and possible implications for quantum theory,” Phys. Rev. 135(1B), B281–B288 (1964).
[Crossref]

Phys. Rev. A (3)

Y. Fan, F. Zhang, N.-H. Shen, Q. Fu, Z. Wei, H. Li, and C. M. Soukoulis, “Achieving a high-Q response in metamaterials by manipulating the toroidal excitations,” Phys. Rev. A 97(3), 033816 (2018).
[Crossref]

G. Labate, A. Alú, and L. Matekovits, “Surface-admittance equivalence principle for nonradiating and cloaking problems,” Phys. Rev. A 95(6), 063841 (2017).
[Crossref]

B. Luk’yanchuk, R. Paniagua-Dominguez, A. I. Kuznetsov, A. E. Miroshnichenko, and Y. S. Kivshar, “Hybrid anapole modes of high-index dielectric nanoparticles,” Phys. Rev. A 95(6), 063820 (2017).
[Crossref]

Phys. Rev. Appl. (1)

D. Sounas, R. Fleury, and A. Alù, “Unidirectional Cloaking Based on Metasurfaces with Balanced Loss and Gain,” Phys. Rev. Appl. 4(1), 014005 (2015).
[Crossref]

Phys. Rev. B (4)

P. -Y. Chen and A. Alù, “Mantle cloaking using thin patterned metasurfaces,” Phys. Rev. B 84(20), 205110 (2011).
[Crossref]

A. Alù, “Mantle cloak: Invisibility induced by a surface,” Phys. Rev. B 80(24), 245115 (2009).
[Crossref]

Y. Fan, Z. Wei, H. H. Chen, and C. M. Soukoulis, “Low-loss and high-Q planar metamaterial with toroidal moment,” Phys. Rev. B 87(11), 115417 (2013).
[Crossref]

N. A. Nemkov, A. A. Basharin, and V. A. Fedotov, “Nonradiating sources, dynamic anapole, and Aharonov-Bohm effect,” Phys. Rev. B 95(16), 165134 (2017).
[Crossref]

Phys. Rev. D (1)

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

Phys. Rev. E (1)

A. Alù and N. Engheta, “Achieving transparency with plasmonic and metamaterial coatings,” Phys. Rev. E 72(1), 016623 (2005).
[Crossref]

Phys. Rev. Lett. (3)

F. Monticone and A. Alú, “Embedded Photonic Eigenvalues in 3D Nanostructures,” Phys. Rev. Lett. 112(21), 213903 (2014).
[Crossref]

E. Marengo and R. Ziolkowski, “On the radiating and nonradiating components of scalar, electromagnetic, and weak gravitational sources,” Phys. Rev. Lett. 83(17), 3345–3349 (1999).
[Crossref]

B. J. Hoenders and H. A. Ferwerda, “Identification of the radiative and nonradiative parts of a wave field,” Phys. Rev. Lett. 87(6), 060401 (2001).
[Crossref]

Phys. Rev. X (1)

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]

Physik. Zeit. (1)

P. Ehrenfest, “Ungleichformige Elektrizitätsbewegungen ohne Magnet-und Strahlungsfeld,” Physik. Zeit. 11, 708–709 (1910).

Proc. Roy. Soc. A (1)

G. A. Schott, “The uniform circular motion with invariable normal spin of a rigidly and uniformly electrified sphere, IV,” Proc. Roy. Soc. A 159(899), 570–591 (1937).
[Crossref]

Prog. Opt. (1)

G. Gbur, “Invisibility physics: past, present, and future,” Prog. Opt. 58, 65–114 (2013).
[Crossref]

Pure Appl. Opt. (1)

B. J. Hoenders and H. A. Ferwerda, “The nonradiating component of the field generated by a finite monochromatic scalar source distribution,” Pure Appl. Opt. 7(5), 1201–1211 (1998).
[Crossref]

Sci. Rep. (5)

V. A. Fedotov, A. V. Rogacheva, V. Savinov, D. P. Tsai, and N. I. Zheludev, “Resonant Transparency and Non-Trivial Non-Radiating Excitations in Toroidal Metamaterials,” Sci. Rep. 3(1), 2967 (2013).
[Crossref]

N. A. Nemkov, I. V. Stenishchev, and A. A. Basharin, “Nontrivial nonradiating all-dielectric anapole,” Sci. Rep. 7(1), 1064 (2017).
[Crossref]

A. K. Ospanova, G. Labate, L. Matekovits, and A. A. Basharin, “Multipolar passive cloaking by nonradiating anapole excitation,” Sci. Rep. 8(1), 12514 (2018).
[Crossref]

I. V. Stenishchev and A. A. Basharin, “Toroidal response in all-dielectric metamaterials based on water,” Sci. Rep. 7(1), 9468 (2017).
[Crossref]

L. Di Donato, T. Isernia, G. Labate, and L. Matekovits, “Towards Printable Natural Dielectric Cloaks via Inverse Scattering Techniques,” Sci. Rep. 7(1), 3680 (2017).
[Crossref]

Science (2)

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]

J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312(5781), 1780–1782 (2006).
[Crossref]

Other (12)

U. Leonhardt and T. G. Philbin, Geometry and Light: The Science of Invisibility (Dover, 2010).

G. Gbur, “Nonradiating sources and other invisible objects,” Chap. 5 in E. Wolf (Ed.), Prog. in Optics (Elsevier, 2003), 273–315.

Microwave Studio, Computer Simulation Technology, 2016.

Ansoft High Frequency Structure Simulation (HFSS), Ansoft Corporation, 2016.

C. F. Bohren and D. R. Huffman, (Wiley-Interscience, New York, 1983), 82–84.

G. Labate, L. Matekovits, and A. Alú, “Metamaterial and Metasurface Cloaking: Principles and Applications,” Chap. 10 in Surface Electromagnetics (with Applications in Antenna, Microwave, and Optical Engineering), F. Yang and Y. Rahmat-Samii, eds., Cambridge University Press, 2019.

A. Ishimaru, Electromagnetic wave propagation, radiation and scattering (Prentice-Hall, 1991).

J. Van Bladel, Singular Electromagnetic Fields and Sources, Chap. 2 (Oxford1991).

C. H. Papas, Theory of Electromagnetic Wave Propagation (Dover Publications, Inc., 1965).

G. Gbur, Nonradiating Sources and the Inverse Source Problem, University of Rochester Rochester, New York, 2001 (available at: www.maxwell.uncc.edu/gjgbur ).

A. Sommerfeld, “Zur elektronentheorie. I. Allgemeine untersuchung des feldes eines beliebig bewegten elektrons,” Akad. der Wiss. (Gott.), Math. Phys. Klasse, Nach., 99–130 (1904).

A. Sommerfeld, “Zur elektronentheorie. II. Grundlagen fur eine allgemeine dynamik des elektrons,” Akad. der Wiss. (Gott.), Math. Phys. Klasse, Nach.363–439 (1904).

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (7)

Fig. 1.
Fig. 1. Top view of volume $V_1$ incorporating a generic cluster $V_2$ of volumetric dielectric scatterer (a). $\Gamma$ indicates the virtual boundary (surface) between the occupied volume $V$ and the external space. Side view with equivalent treatment (b) with volumetric dielectric sources $\vec {J}_1$ and $\vec {J}_2$.
Fig. 2.
Fig. 2. Illustration of subwavelength high-index dielectric cylinders in a periodic arrangement with symmetric (a) and asymmetric (b) hole. Here $\vec {J}$ denotes displacement currents, $\vec {m}$ magnetic moment, $\vec {P}$ and $\vec {T}$ is electric and toroidal dipole moments, respectively.
Fig. 3.
Fig. 3. Normalized power scattered by the multipoles excited in the dielectric particles at $1.1$ THz-$1.4$ THz frequency range for $d = 0 \mu$m (a), 2 $\mu$m (b), $3 \mu$m, (c) $3.5 \mu$m (d) and $4 \mu$m (e) hole displacements.
Fig. 4.
Fig. 4. CST [59] simulation for external electromagnetic fields, with colorbar saturated to $E_0=1$ V/m and $H_0=(120\pi )^{-1}$ A/m. Top view within the stand-alone asymmetric cylindrical particle: normalized (with respect to the maximum value) field maps of (a) absolute value of electric field and (b) absolute value of magnetic field intensities at $f=1.215$ THz.
Fig. 5.
Fig. 5. HFSS simulation [60] for highlighting internal electromagnetic fields, with colorbar normalized to $E_{max}=1$ V/m and $H_{max}=1$ A/m. Top view within the asymmetric cylindrical particle: field maps of (a) absolute value of electric field and (b) absolute value of magnetic field intensities (highlighting the formation of loop for the magnetic moment $m$) at $f=1.215$ THz.
Fig. 6.
Fig. 6. Total radiation of electric dipole $\vec {P}$ and toroidal dipole $\vec {T}$ moments, i.e. $|\vec {P}+ik_0\vec {T}|$ for hole displacement $d=3.5 \mu$m and transmission spectra at resonant frequency close to $f=1.215$ THz.
Fig. 7.
Fig. 7. Normalized power scattered by the multipoles excited in metamolecules at $1.1$ THz-$1.4$ THz frequency range $d=3.5 \mu m$ hole displacements for three axial components of each dipole moment in Cartesian coordinate system: $P_x$, $P_y$, $P_z$ for electric dipole, $M_x$, $M_y$, $M_z$ for magnetic dipole and $T_x$, $T_y$, $T_z$ for toroidal dipole moments. Inset shows zoom close to $f=1.215$ THz.

Equations (15)

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

× E = i ω μ 0 H
× H = i ω ε 0 E + J e q
J v e ( r ) = + i ω ε 0 P ( r ) with   r V
J v m ( r ) = Y 0 × M ( r ) with   r V
J s e = n ^ × [ H + H ] with   r Γ
J s m = n ^ × [ E + E ] with   r Γ
× × E k 0 2 E = i ω μ 0 J e q
× × H k 0 2 H = × J e q
J e q = 0 p with   r Γ
× J e q = 0 p with   r V
i ω ε 0 P Y 0 × M = 0 p .
M = × T
J e q × × T i k 0 P = 0 p
J N R = 1 4 π i ( c k 0 ) { × × F k 0 2 F }
P + i k 0 T = 0 p

Metrics