Abstract

In this paper we describe a methodology for tailoring the design of metamaterial dielectric resonators, which represent a promising path toward low-loss metamaterials at optical frequencies. We first describe a procedure to decompose the far field scattered by subwavelength resonators in terms of multipolar field components, providing explicit expressions for the multipolar far fields. We apply this formulation to confirm that an isolated high-permittivity dielectric cube resonator possesses frequency separated electric and magnetic dipole resonances, as well as a magnetic quadrupole resonance in close proximity to the electric dipole resonance. We then introduce multiple dielectric gaps to the resonator geometry in a manner suggested by perturbation theory, and demonstrate the ability to overlap the electric and magnetic dipole resonances, thereby enabling directional scattering by satisfying the first Kerker condition. We further demonstrate the ability to push the quadrupole resonance away from the degenerate dipole resonances to achieve local behavior. These properties are confirmed through the multipolar expansion and show that the use of geometries suggested by perturbation theory is a viable route to achieve purely dipole resonances for metamaterial applications such as wave-front manipulation with Huygens’ metasurfaces. Our results are fully scalable across any frequency bands where high-permittivity dielectric materials are available, including microwave, THz, and infrared frequencies.

© 2015 Optical Society of America

Full Article  |  PDF Article

Corrections

Salvatore Campione, Lorena I. Basilio, Larry K. Warne, and Michael B. Sinclair, "Tailoring dielectric resonator geometries for directional scattering and Huygens’ metasurfaces: erratum," Opt. Express 25, 7730-7730 (2017)
https://www.osapublishing.org/oe/abstract.cfm?uri=oe-25-7-7730

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References

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  1. A. Ahmadi and H. Mosallaei, “Physical configuration and performance modeling of all-dielectric metamaterials,” Phys. Rev. B 77(4), 045104 (2008).
    [Crossref]
  2. M. Kerker, D. S. Wang, and C. L. Giles, “Electromagnetic scattering by magnetic spheres,” J. Opt. Soc. Am. 73(6), 765–767 (1983).
    [Crossref]
  3. J. M. Geffrin, B. García-Cámara, R. Gómez-Medina, P. Albella, L. S. Froufe-Pérez, C. Eyraud, A. Litman, R. Vaillon, F. González, M. Nieto-Vesperinas, J. J. Sáenz, and F. Moreno, “Magnetic and electric coherence in forward- and back-scattered electromagnetic waves by a single dielectric subwavelength sphere,” Nat Commun 3, 1171 (2012).
    [Crossref] [PubMed]
  4. Y. H. Fu, A. I. Kuznetsov, A. E. Miroshnichenko, Y. F. Yu, and B. Luk’yanchuk, “Directional visible light scattering by silicon nanoparticles,” Nat Commun 4, 1527 (2013).
    [Crossref] [PubMed]
  5. I. Staude, A. E. Miroshnichenko, M. Decker, N. T. Fofang, S. Liu, E. Gonzales, J. Dominguez, T. S. Luk, D. N. Neshev, I. Brener, and Y. Kivshar, “Tailoring Directional Scattering through Magnetic and Electric Resonances in Subwavelength Silicon Nanodisks,” ACS Nano 7(9), 7824–7832 (2013).
    [Crossref] [PubMed]
  6. R. E. Collin, Field Theory of Guided Waves (McGraw Hill, 1960).
  7. M. G. Silveirinha, “Generalized Lorentz-Lorenz formulas for microstructured materials,” Phys. Rev. B 76(24), 245117 (2007).
    [Crossref]
  8. C. R. Simovski, “Material parameters of metamaterials (a Review),” Opt. Spectrosc. 107(5), 726–753 (2009).
    [Crossref]
  9. A. Alù, “Restoring the physical meaning of metamaterial constitutive parameters,” Phys. Rev. B 83(8), 081102 (2011).
    [Crossref]
  10. R. Shore and A. D. Yaghjian, “Complex waves on periodic arrays of lossy and lossless permeable spheres. Part 1: Theory,” Radio Sci. 47, RS2014 (2012).
  11. J. C. Ginn, I. Brener, D. W. Peters, J. R. Wendt, J. O. Stevens, P. F. Hines, L. I. Basilio, L. K. Warne, J. F. Ihlefeld, P. G. Clem, and M. B. Sinclair, “Realizing Optical Magnetism from Dielectric Metamaterials,” Phys. Rev. Lett. 108(9), 097402 (2012).
    [Crossref] [PubMed]
  12. H. Alaeian and J. A. Dionne, “Plasmon nanoparticle superlattices as optical-frequency magnetic metamaterials,” Opt. Express 20(14), 15781–15796 (2012).
    [Crossref] [PubMed]
  13. S. Campione, M. B. Sinclair, and F. Capolino, “Effective medium representation and complex modes in 3D periodic metamaterials made of cubic resonators with large permittivity at mid-infrared frequencies,” Phot. Nano. Fund. Appl. 11(4), 423–435 (2013).
    [Crossref]
  14. C. Menzel, E. Hebestreit, R. Alaee, M. Albooyeh, S. Mühlig, S. Burger, C. Rockstuhl, C. Simovski, S. Tretyakov, F. Lederer, and T. Pertsch, “Extreme coupling: A route towards local magnetic metamaterials,” Phys. Rev. B 89(15), 155125 (2014).
    [Crossref]
  15. L. K. Warne, L. I. Basilio, W. L. Langston, W. A. Johnson, and M. B. Sinclair, “Perturbation Theory in the Design of Degenerate Spherical Dielectric Resonators,” IEEE Trans. Antenn. Propag. 61(4), 2130–2141 (2013).
    [Crossref]
  16. L. K. Warne, L. I. Basilio, W. L. Langston, W. A. Johnson, and M. B. Sinclair, “Perturbation theory in the design of degenerate rectangular dielectric resonators,” Prog. Electromagn. Res. B 44, 1–29 (2012).
    [Crossref]
  17. C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (John Wiley & Sons, Inc., 1983).
  18. J. D. Jackson, Classical Electrodynamics (Wiley, 1999).
  19. C. H. Papas, Theory of Electromagnetic Wave Propagation (Dover Publications, Inc., 1995).
  20. P. Grahn, A. Shevchenko, and M. Kaivola, “Electromagnetic multipole theory for optical nanomaterials,” New J. Phys. 14(9), 093033 (2012).
    [Crossref]
  21. A. B. Evlyukhin, C. Reinhardt, E. Evlyukhin, and B. N. Chichkov, “Multipole analysis of light scattering by arbitrary-shaped nanoparticles on a plane surface,” J. Opt. Soc. Am. B 30(10), 2589–2598 (2013).
    [Crossref]
  22. J. Chen, J. Ng, Z. Lin, and C. T. Chan, “Optical pulling force,” Nat. Photonics 5(9), 531–534 (2011).
    [Crossref]
  23. S. Mühlig, C. Menzel, C. Rockstuhl, and F. Lederer, “Multipole analysis of meta-atoms,” Metamaterials (Amst.) 5(2-3), 64–73 (2011).
    [Crossref]
  24. M. Decker, I. Staude, M. Falkner, J. Dominguez, D. N. Neshev, I. Brener, T. Pertsch, and Y. S. Kivshar, “High-efficiency light-wave control with all-dielectric optical Huygens’ metasurfaces,” arXiv:1405.5038 (2014).
  25. C. Pfeiffer and A. Grbic, “Metamaterial Huygens’ Surfaces: Tailoring Wave Fronts with Reflectionless Sheets,” Phys. Rev. Lett. 110(19), 197401 (2013).
    [Crossref] [PubMed]
  26. F. Monticone, N. M. Estakhri, and A. Alù, “Full Control of Nanoscale Optical Transmission with a Composite Metascreen,” Phys. Rev. Lett. 110(20), 203903 (2013).
    [Crossref] [PubMed]
  27. L. I. Basilio, L. K. Warne, W. L. Langston, W. A. Johnson, and M. B. Sinclair, “A Quick and Easy Simulation Procedure to Aid in Metamaterial Unit-Cell Design,” IEEE Antennas Wirel. Propag. Lett. 10, 1567–1570 (2011).
    [Crossref]
  28. C. Rockstuhl, C. Menzel, S. Mühlig, J. Petschulat, C. Helgert, C. Etrich, A. Chipouline, T. Pertsch, and F. Lederer, “Scattering properties of meta-atoms,” Phys. Rev. B 83(24), 245119 (2011).
    [Crossref]
  29. S. Liu, M. B. Sinclair, T. S. Mahony, Y. C. Jun, S. Campione, J. Ginn, D. A. Bender, J. R. Wendt, J. F. Ihlefeld, P. G. Clem, J. B. Wright, and I. Brener, “Optical magnetic mirrors without metals,” Optica 1(4), 250–256 (2014).
    [Crossref]
  30. A. Alu and N. Engheta, “Polarizabilities and effective parameters for collections of spherical nanoparticles formed by pairs of concentric double-negative, single-negative, and/or double-positive metamaterial layers,” J. Appl. Phys. 97(9), 094310 (2005).
    [Crossref]
  31. N. Yu, P. Genevet, M. A. Kats, F. Aieta, J.-P. Tetienne, F. Capasso, and Z. Gaburro, “Light Propagation with Phase Discontinuities: Generalized Laws of Reflection and Refraction,” Science 334(6054), 333–337 (2011).
    [Crossref] [PubMed]
  32. X. Ni, N. K. Emani, A. V. Kildishev, A. Boltasseva, and V. M. Shalaev, “Broadband Light Bending with Plasmonic Nanoantennas,” Science 335(6067), 427 (2012).
    [Crossref] [PubMed]

2014 (2)

C. Menzel, E. Hebestreit, R. Alaee, M. Albooyeh, S. Mühlig, S. Burger, C. Rockstuhl, C. Simovski, S. Tretyakov, F. Lederer, and T. Pertsch, “Extreme coupling: A route towards local magnetic metamaterials,” Phys. Rev. B 89(15), 155125 (2014).
[Crossref]

S. Liu, M. B. Sinclair, T. S. Mahony, Y. C. Jun, S. Campione, J. Ginn, D. A. Bender, J. R. Wendt, J. F. Ihlefeld, P. G. Clem, J. B. Wright, and I. Brener, “Optical magnetic mirrors without metals,” Optica 1(4), 250–256 (2014).
[Crossref]

2013 (7)

A. B. Evlyukhin, C. Reinhardt, E. Evlyukhin, and B. N. Chichkov, “Multipole analysis of light scattering by arbitrary-shaped nanoparticles on a plane surface,” J. Opt. Soc. Am. B 30(10), 2589–2598 (2013).
[Crossref]

L. K. Warne, L. I. Basilio, W. L. Langston, W. A. Johnson, and M. B. Sinclair, “Perturbation Theory in the Design of Degenerate Spherical Dielectric Resonators,” IEEE Trans. Antenn. Propag. 61(4), 2130–2141 (2013).
[Crossref]

C. Pfeiffer and A. Grbic, “Metamaterial Huygens’ Surfaces: Tailoring Wave Fronts with Reflectionless Sheets,” Phys. Rev. Lett. 110(19), 197401 (2013).
[Crossref] [PubMed]

F. Monticone, N. M. Estakhri, and A. Alù, “Full Control of Nanoscale Optical Transmission with a Composite Metascreen,” Phys. Rev. Lett. 110(20), 203903 (2013).
[Crossref] [PubMed]

Y. H. Fu, A. I. Kuznetsov, A. E. Miroshnichenko, Y. F. Yu, and B. Luk’yanchuk, “Directional visible light scattering by silicon nanoparticles,” Nat Commun 4, 1527 (2013).
[Crossref] [PubMed]

I. Staude, A. E. Miroshnichenko, M. Decker, N. T. Fofang, S. Liu, E. Gonzales, J. Dominguez, T. S. Luk, D. N. Neshev, I. Brener, and Y. Kivshar, “Tailoring Directional Scattering through Magnetic and Electric Resonances in Subwavelength Silicon Nanodisks,” ACS Nano 7(9), 7824–7832 (2013).
[Crossref] [PubMed]

S. Campione, M. B. Sinclair, and F. Capolino, “Effective medium representation and complex modes in 3D periodic metamaterials made of cubic resonators with large permittivity at mid-infrared frequencies,” Phot. Nano. Fund. Appl. 11(4), 423–435 (2013).
[Crossref]

2012 (7)

R. Shore and A. D. Yaghjian, “Complex waves on periodic arrays of lossy and lossless permeable spheres. Part 1: Theory,” Radio Sci. 47, RS2014 (2012).

J. C. Ginn, I. Brener, D. W. Peters, J. R. Wendt, J. O. Stevens, P. F. Hines, L. I. Basilio, L. K. Warne, J. F. Ihlefeld, P. G. Clem, and M. B. Sinclair, “Realizing Optical Magnetism from Dielectric Metamaterials,” Phys. Rev. Lett. 108(9), 097402 (2012).
[Crossref] [PubMed]

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

L. K. Warne, L. I. Basilio, W. L. Langston, W. A. Johnson, and M. B. Sinclair, “Perturbation theory in the design of degenerate rectangular dielectric resonators,” Prog. Electromagn. Res. B 44, 1–29 (2012).
[Crossref]

P. Grahn, A. Shevchenko, and M. Kaivola, “Electromagnetic multipole theory for optical nanomaterials,” New J. Phys. 14(9), 093033 (2012).
[Crossref]

X. Ni, N. K. Emani, A. V. Kildishev, A. Boltasseva, and V. M. Shalaev, “Broadband Light Bending with Plasmonic Nanoantennas,” Science 335(6067), 427 (2012).
[Crossref] [PubMed]

H. Alaeian and J. A. Dionne, “Plasmon nanoparticle superlattices as optical-frequency magnetic metamaterials,” Opt. Express 20(14), 15781–15796 (2012).
[Crossref] [PubMed]

2011 (6)

N. Yu, P. Genevet, M. A. Kats, F. Aieta, J.-P. Tetienne, F. Capasso, and Z. Gaburro, “Light Propagation with Phase Discontinuities: Generalized Laws of Reflection and Refraction,” Science 334(6054), 333–337 (2011).
[Crossref] [PubMed]

J. Chen, J. Ng, Z. Lin, and C. T. Chan, “Optical pulling force,” Nat. Photonics 5(9), 531–534 (2011).
[Crossref]

S. Mühlig, C. Menzel, C. Rockstuhl, and F. Lederer, “Multipole analysis of meta-atoms,” Metamaterials (Amst.) 5(2-3), 64–73 (2011).
[Crossref]

L. I. Basilio, L. K. Warne, W. L. Langston, W. A. Johnson, and M. B. Sinclair, “A Quick and Easy Simulation Procedure to Aid in Metamaterial Unit-Cell Design,” IEEE Antennas Wirel. Propag. Lett. 10, 1567–1570 (2011).
[Crossref]

C. Rockstuhl, C. Menzel, S. Mühlig, J. Petschulat, C. Helgert, C. Etrich, A. Chipouline, T. Pertsch, and F. Lederer, “Scattering properties of meta-atoms,” Phys. Rev. B 83(24), 245119 (2011).
[Crossref]

A. Alù, “Restoring the physical meaning of metamaterial constitutive parameters,” Phys. Rev. B 83(8), 081102 (2011).
[Crossref]

2009 (1)

C. R. Simovski, “Material parameters of metamaterials (a Review),” Opt. Spectrosc. 107(5), 726–753 (2009).
[Crossref]

2008 (1)

A. Ahmadi and H. Mosallaei, “Physical configuration and performance modeling of all-dielectric metamaterials,” Phys. Rev. B 77(4), 045104 (2008).
[Crossref]

2007 (1)

M. G. Silveirinha, “Generalized Lorentz-Lorenz formulas for microstructured materials,” Phys. Rev. B 76(24), 245117 (2007).
[Crossref]

2005 (1)

A. Alu and N. Engheta, “Polarizabilities and effective parameters for collections of spherical nanoparticles formed by pairs of concentric double-negative, single-negative, and/or double-positive metamaterial layers,” J. Appl. Phys. 97(9), 094310 (2005).
[Crossref]

1983 (1)

Ahmadi, A.

A. Ahmadi and H. Mosallaei, “Physical configuration and performance modeling of all-dielectric metamaterials,” Phys. Rev. B 77(4), 045104 (2008).
[Crossref]

Aieta, F.

N. Yu, P. Genevet, M. A. Kats, F. Aieta, J.-P. Tetienne, F. Capasso, and Z. Gaburro, “Light Propagation with Phase Discontinuities: Generalized Laws of Reflection and Refraction,” Science 334(6054), 333–337 (2011).
[Crossref] [PubMed]

Alaee, R.

C. Menzel, E. Hebestreit, R. Alaee, M. Albooyeh, S. Mühlig, S. Burger, C. Rockstuhl, C. Simovski, S. Tretyakov, F. Lederer, and T. Pertsch, “Extreme coupling: A route towards local magnetic metamaterials,” Phys. Rev. B 89(15), 155125 (2014).
[Crossref]

Alaeian, H.

Albella, P.

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

Albooyeh, M.

C. Menzel, E. Hebestreit, R. Alaee, M. Albooyeh, S. Mühlig, S. Burger, C. Rockstuhl, C. Simovski, S. Tretyakov, F. Lederer, and T. Pertsch, “Extreme coupling: A route towards local magnetic metamaterials,” Phys. Rev. B 89(15), 155125 (2014).
[Crossref]

Alu, A.

A. Alu and N. Engheta, “Polarizabilities and effective parameters for collections of spherical nanoparticles formed by pairs of concentric double-negative, single-negative, and/or double-positive metamaterial layers,” J. Appl. Phys. 97(9), 094310 (2005).
[Crossref]

Alù, A.

F. Monticone, N. M. Estakhri, and A. Alù, “Full Control of Nanoscale Optical Transmission with a Composite Metascreen,” Phys. Rev. Lett. 110(20), 203903 (2013).
[Crossref] [PubMed]

A. Alù, “Restoring the physical meaning of metamaterial constitutive parameters,” Phys. Rev. B 83(8), 081102 (2011).
[Crossref]

Basilio, L. I.

L. K. Warne, L. I. Basilio, W. L. Langston, W. A. Johnson, and M. B. Sinclair, “Perturbation Theory in the Design of Degenerate Spherical Dielectric Resonators,” IEEE Trans. Antenn. Propag. 61(4), 2130–2141 (2013).
[Crossref]

J. C. Ginn, I. Brener, D. W. Peters, J. R. Wendt, J. O. Stevens, P. F. Hines, L. I. Basilio, L. K. Warne, J. F. Ihlefeld, P. G. Clem, and M. B. Sinclair, “Realizing Optical Magnetism from Dielectric Metamaterials,” Phys. Rev. Lett. 108(9), 097402 (2012).
[Crossref] [PubMed]

L. K. Warne, L. I. Basilio, W. L. Langston, W. A. Johnson, and M. B. Sinclair, “Perturbation theory in the design of degenerate rectangular dielectric resonators,” Prog. Electromagn. Res. B 44, 1–29 (2012).
[Crossref]

L. I. Basilio, L. K. Warne, W. L. Langston, W. A. Johnson, and M. B. Sinclair, “A Quick and Easy Simulation Procedure to Aid in Metamaterial Unit-Cell Design,” IEEE Antennas Wirel. Propag. Lett. 10, 1567–1570 (2011).
[Crossref]

Bender, D. A.

Boltasseva, A.

X. Ni, N. K. Emani, A. V. Kildishev, A. Boltasseva, and V. M. Shalaev, “Broadband Light Bending with Plasmonic Nanoantennas,” Science 335(6067), 427 (2012).
[Crossref] [PubMed]

Brener, I.

S. Liu, M. B. Sinclair, T. S. Mahony, Y. C. Jun, S. Campione, J. Ginn, D. A. Bender, J. R. Wendt, J. F. Ihlefeld, P. G. Clem, J. B. Wright, and I. Brener, “Optical magnetic mirrors without metals,” Optica 1(4), 250–256 (2014).
[Crossref]

I. Staude, A. E. Miroshnichenko, M. Decker, N. T. Fofang, S. Liu, E. Gonzales, J. Dominguez, T. S. Luk, D. N. Neshev, I. Brener, and Y. Kivshar, “Tailoring Directional Scattering through Magnetic and Electric Resonances in Subwavelength Silicon Nanodisks,” ACS Nano 7(9), 7824–7832 (2013).
[Crossref] [PubMed]

J. C. Ginn, I. Brener, D. W. Peters, J. R. Wendt, J. O. Stevens, P. F. Hines, L. I. Basilio, L. K. Warne, J. F. Ihlefeld, P. G. Clem, and M. B. Sinclair, “Realizing Optical Magnetism from Dielectric Metamaterials,” Phys. Rev. Lett. 108(9), 097402 (2012).
[Crossref] [PubMed]

Burger, S.

C. Menzel, E. Hebestreit, R. Alaee, M. Albooyeh, S. Mühlig, S. Burger, C. Rockstuhl, C. Simovski, S. Tretyakov, F. Lederer, and T. Pertsch, “Extreme coupling: A route towards local magnetic metamaterials,” Phys. Rev. B 89(15), 155125 (2014).
[Crossref]

Campione, S.

S. Liu, M. B. Sinclair, T. S. Mahony, Y. C. Jun, S. Campione, J. Ginn, D. A. Bender, J. R. Wendt, J. F. Ihlefeld, P. G. Clem, J. B. Wright, and I. Brener, “Optical magnetic mirrors without metals,” Optica 1(4), 250–256 (2014).
[Crossref]

S. Campione, M. B. Sinclair, and F. Capolino, “Effective medium representation and complex modes in 3D periodic metamaterials made of cubic resonators with large permittivity at mid-infrared frequencies,” Phot. Nano. Fund. Appl. 11(4), 423–435 (2013).
[Crossref]

Capasso, F.

N. Yu, P. Genevet, M. A. Kats, F. Aieta, J.-P. Tetienne, F. Capasso, and Z. Gaburro, “Light Propagation with Phase Discontinuities: Generalized Laws of Reflection and Refraction,” Science 334(6054), 333–337 (2011).
[Crossref] [PubMed]

Capolino, F.

S. Campione, M. B. Sinclair, and F. Capolino, “Effective medium representation and complex modes in 3D periodic metamaterials made of cubic resonators with large permittivity at mid-infrared frequencies,” Phot. Nano. Fund. Appl. 11(4), 423–435 (2013).
[Crossref]

Chan, C. T.

J. Chen, J. Ng, Z. Lin, and C. T. Chan, “Optical pulling force,” Nat. Photonics 5(9), 531–534 (2011).
[Crossref]

Chen, J.

J. Chen, J. Ng, Z. Lin, and C. T. Chan, “Optical pulling force,” Nat. Photonics 5(9), 531–534 (2011).
[Crossref]

Chichkov, B. N.

Chipouline, A.

C. Rockstuhl, C. Menzel, S. Mühlig, J. Petschulat, C. Helgert, C. Etrich, A. Chipouline, T. Pertsch, and F. Lederer, “Scattering properties of meta-atoms,” Phys. Rev. B 83(24), 245119 (2011).
[Crossref]

Clem, P. G.

S. Liu, M. B. Sinclair, T. S. Mahony, Y. C. Jun, S. Campione, J. Ginn, D. A. Bender, J. R. Wendt, J. F. Ihlefeld, P. G. Clem, J. B. Wright, and I. Brener, “Optical magnetic mirrors without metals,” Optica 1(4), 250–256 (2014).
[Crossref]

J. C. Ginn, I. Brener, D. W. Peters, J. R. Wendt, J. O. Stevens, P. F. Hines, L. I. Basilio, L. K. Warne, J. F. Ihlefeld, P. G. Clem, and M. B. Sinclair, “Realizing Optical Magnetism from Dielectric Metamaterials,” Phys. Rev. Lett. 108(9), 097402 (2012).
[Crossref] [PubMed]

Decker, M.

I. Staude, A. E. Miroshnichenko, M. Decker, N. T. Fofang, S. Liu, E. Gonzales, J. Dominguez, T. S. Luk, D. N. Neshev, I. Brener, and Y. Kivshar, “Tailoring Directional Scattering through Magnetic and Electric Resonances in Subwavelength Silicon Nanodisks,” ACS Nano 7(9), 7824–7832 (2013).
[Crossref] [PubMed]

Dionne, J. A.

Dominguez, J.

I. Staude, A. E. Miroshnichenko, M. Decker, N. T. Fofang, S. Liu, E. Gonzales, J. Dominguez, T. S. Luk, D. N. Neshev, I. Brener, and Y. Kivshar, “Tailoring Directional Scattering through Magnetic and Electric Resonances in Subwavelength Silicon Nanodisks,” ACS Nano 7(9), 7824–7832 (2013).
[Crossref] [PubMed]

Emani, N. K.

X. Ni, N. K. Emani, A. V. Kildishev, A. Boltasseva, and V. M. Shalaev, “Broadband Light Bending with Plasmonic Nanoantennas,” Science 335(6067), 427 (2012).
[Crossref] [PubMed]

Engheta, N.

A. Alu and N. Engheta, “Polarizabilities and effective parameters for collections of spherical nanoparticles formed by pairs of concentric double-negative, single-negative, and/or double-positive metamaterial layers,” J. Appl. Phys. 97(9), 094310 (2005).
[Crossref]

Estakhri, N. M.

F. Monticone, N. M. Estakhri, and A. Alù, “Full Control of Nanoscale Optical Transmission with a Composite Metascreen,” Phys. Rev. Lett. 110(20), 203903 (2013).
[Crossref] [PubMed]

Etrich, C.

C. Rockstuhl, C. Menzel, S. Mühlig, J. Petschulat, C. Helgert, C. Etrich, A. Chipouline, T. Pertsch, and F. Lederer, “Scattering properties of meta-atoms,” Phys. Rev. B 83(24), 245119 (2011).
[Crossref]

Evlyukhin, A. B.

Evlyukhin, E.

Eyraud, C.

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

Fofang, N. T.

I. Staude, A. E. Miroshnichenko, M. Decker, N. T. Fofang, S. Liu, E. Gonzales, J. Dominguez, T. S. Luk, D. N. Neshev, I. Brener, and Y. Kivshar, “Tailoring Directional Scattering through Magnetic and Electric Resonances in Subwavelength Silicon Nanodisks,” ACS Nano 7(9), 7824–7832 (2013).
[Crossref] [PubMed]

Froufe-Pérez, L. S.

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

Fu, Y. H.

Y. H. Fu, A. I. Kuznetsov, A. E. Miroshnichenko, Y. F. Yu, and B. Luk’yanchuk, “Directional visible light scattering by silicon nanoparticles,” Nat Commun 4, 1527 (2013).
[Crossref] [PubMed]

Gaburro, Z.

N. Yu, P. Genevet, M. A. Kats, F. Aieta, J.-P. Tetienne, F. Capasso, and Z. Gaburro, “Light Propagation with Phase Discontinuities: Generalized Laws of Reflection and Refraction,” Science 334(6054), 333–337 (2011).
[Crossref] [PubMed]

García-Cámara, B.

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

Geffrin, J. M.

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

Genevet, P.

N. Yu, P. Genevet, M. A. Kats, F. Aieta, J.-P. Tetienne, F. Capasso, and Z. Gaburro, “Light Propagation with Phase Discontinuities: Generalized Laws of Reflection and Refraction,” Science 334(6054), 333–337 (2011).
[Crossref] [PubMed]

Giles, C. L.

Ginn, J.

Ginn, J. C.

J. C. Ginn, I. Brener, D. W. Peters, J. R. Wendt, J. O. Stevens, P. F. Hines, L. I. Basilio, L. K. Warne, J. F. Ihlefeld, P. G. Clem, and M. B. Sinclair, “Realizing Optical Magnetism from Dielectric Metamaterials,” Phys. Rev. Lett. 108(9), 097402 (2012).
[Crossref] [PubMed]

Gómez-Medina, R.

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

Gonzales, E.

I. Staude, A. E. Miroshnichenko, M. Decker, N. T. Fofang, S. Liu, E. Gonzales, J. Dominguez, T. S. Luk, D. N. Neshev, I. Brener, and Y. Kivshar, “Tailoring Directional Scattering through Magnetic and Electric Resonances in Subwavelength Silicon Nanodisks,” ACS Nano 7(9), 7824–7832 (2013).
[Crossref] [PubMed]

González, F.

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

Grahn, P.

P. Grahn, A. Shevchenko, and M. Kaivola, “Electromagnetic multipole theory for optical nanomaterials,” New J. Phys. 14(9), 093033 (2012).
[Crossref]

Grbic, A.

C. Pfeiffer and A. Grbic, “Metamaterial Huygens’ Surfaces: Tailoring Wave Fronts with Reflectionless Sheets,” Phys. Rev. Lett. 110(19), 197401 (2013).
[Crossref] [PubMed]

Hebestreit, E.

C. Menzel, E. Hebestreit, R. Alaee, M. Albooyeh, S. Mühlig, S. Burger, C. Rockstuhl, C. Simovski, S. Tretyakov, F. Lederer, and T. Pertsch, “Extreme coupling: A route towards local magnetic metamaterials,” Phys. Rev. B 89(15), 155125 (2014).
[Crossref]

Helgert, C.

C. Rockstuhl, C. Menzel, S. Mühlig, J. Petschulat, C. Helgert, C. Etrich, A. Chipouline, T. Pertsch, and F. Lederer, “Scattering properties of meta-atoms,” Phys. Rev. B 83(24), 245119 (2011).
[Crossref]

Hines, P. F.

J. C. Ginn, I. Brener, D. W. Peters, J. R. Wendt, J. O. Stevens, P. F. Hines, L. I. Basilio, L. K. Warne, J. F. Ihlefeld, P. G. Clem, and M. B. Sinclair, “Realizing Optical Magnetism from Dielectric Metamaterials,” Phys. Rev. Lett. 108(9), 097402 (2012).
[Crossref] [PubMed]

Ihlefeld, J. F.

S. Liu, M. B. Sinclair, T. S. Mahony, Y. C. Jun, S. Campione, J. Ginn, D. A. Bender, J. R. Wendt, J. F. Ihlefeld, P. G. Clem, J. B. Wright, and I. Brener, “Optical magnetic mirrors without metals,” Optica 1(4), 250–256 (2014).
[Crossref]

J. C. Ginn, I. Brener, D. W. Peters, J. R. Wendt, J. O. Stevens, P. F. Hines, L. I. Basilio, L. K. Warne, J. F. Ihlefeld, P. G. Clem, and M. B. Sinclair, “Realizing Optical Magnetism from Dielectric Metamaterials,” Phys. Rev. Lett. 108(9), 097402 (2012).
[Crossref] [PubMed]

Johnson, W. A.

L. K. Warne, L. I. Basilio, W. L. Langston, W. A. Johnson, and M. B. Sinclair, “Perturbation Theory in the Design of Degenerate Spherical Dielectric Resonators,” IEEE Trans. Antenn. Propag. 61(4), 2130–2141 (2013).
[Crossref]

L. K. Warne, L. I. Basilio, W. L. Langston, W. A. Johnson, and M. B. Sinclair, “Perturbation theory in the design of degenerate rectangular dielectric resonators,” Prog. Electromagn. Res. B 44, 1–29 (2012).
[Crossref]

L. I. Basilio, L. K. Warne, W. L. Langston, W. A. Johnson, and M. B. Sinclair, “A Quick and Easy Simulation Procedure to Aid in Metamaterial Unit-Cell Design,” IEEE Antennas Wirel. Propag. Lett. 10, 1567–1570 (2011).
[Crossref]

Jun, Y. C.

Kaivola, M.

P. Grahn, A. Shevchenko, and M. Kaivola, “Electromagnetic multipole theory for optical nanomaterials,” New J. Phys. 14(9), 093033 (2012).
[Crossref]

Kats, M. A.

N. Yu, P. Genevet, M. A. Kats, F. Aieta, J.-P. Tetienne, F. Capasso, and Z. Gaburro, “Light Propagation with Phase Discontinuities: Generalized Laws of Reflection and Refraction,” Science 334(6054), 333–337 (2011).
[Crossref] [PubMed]

Kerker, M.

Kildishev, A. V.

X. Ni, N. K. Emani, A. V. Kildishev, A. Boltasseva, and V. M. Shalaev, “Broadband Light Bending with Plasmonic Nanoantennas,” Science 335(6067), 427 (2012).
[Crossref] [PubMed]

Kivshar, Y.

I. Staude, A. E. Miroshnichenko, M. Decker, N. T. Fofang, S. Liu, E. Gonzales, J. Dominguez, T. S. Luk, D. N. Neshev, I. Brener, and Y. Kivshar, “Tailoring Directional Scattering through Magnetic and Electric Resonances in Subwavelength Silicon Nanodisks,” ACS Nano 7(9), 7824–7832 (2013).
[Crossref] [PubMed]

Kuznetsov, A. I.

Y. H. Fu, A. I. Kuznetsov, A. E. Miroshnichenko, Y. F. Yu, and B. Luk’yanchuk, “Directional visible light scattering by silicon nanoparticles,” Nat Commun 4, 1527 (2013).
[Crossref] [PubMed]

Langston, W. L.

L. K. Warne, L. I. Basilio, W. L. Langston, W. A. Johnson, and M. B. Sinclair, “Perturbation Theory in the Design of Degenerate Spherical Dielectric Resonators,” IEEE Trans. Antenn. Propag. 61(4), 2130–2141 (2013).
[Crossref]

L. K. Warne, L. I. Basilio, W. L. Langston, W. A. Johnson, and M. B. Sinclair, “Perturbation theory in the design of degenerate rectangular dielectric resonators,” Prog. Electromagn. Res. B 44, 1–29 (2012).
[Crossref]

L. I. Basilio, L. K. Warne, W. L. Langston, W. A. Johnson, and M. B. Sinclair, “A Quick and Easy Simulation Procedure to Aid in Metamaterial Unit-Cell Design,” IEEE Antennas Wirel. Propag. Lett. 10, 1567–1570 (2011).
[Crossref]

Lederer, F.

C. Menzel, E. Hebestreit, R. Alaee, M. Albooyeh, S. Mühlig, S. Burger, C. Rockstuhl, C. Simovski, S. Tretyakov, F. Lederer, and T. Pertsch, “Extreme coupling: A route towards local magnetic metamaterials,” Phys. Rev. B 89(15), 155125 (2014).
[Crossref]

S. Mühlig, C. Menzel, C. Rockstuhl, and F. Lederer, “Multipole analysis of meta-atoms,” Metamaterials (Amst.) 5(2-3), 64–73 (2011).
[Crossref]

C. Rockstuhl, C. Menzel, S. Mühlig, J. Petschulat, C. Helgert, C. Etrich, A. Chipouline, T. Pertsch, and F. Lederer, “Scattering properties of meta-atoms,” Phys. Rev. B 83(24), 245119 (2011).
[Crossref]

Lin, Z.

J. Chen, J. Ng, Z. Lin, and C. T. Chan, “Optical pulling force,” Nat. Photonics 5(9), 531–534 (2011).
[Crossref]

Litman, A.

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

Liu, S.

S. Liu, M. B. Sinclair, T. S. Mahony, Y. C. Jun, S. Campione, J. Ginn, D. A. Bender, J. R. Wendt, J. F. Ihlefeld, P. G. Clem, J. B. Wright, and I. Brener, “Optical magnetic mirrors without metals,” Optica 1(4), 250–256 (2014).
[Crossref]

I. Staude, A. E. Miroshnichenko, M. Decker, N. T. Fofang, S. Liu, E. Gonzales, J. Dominguez, T. S. Luk, D. N. Neshev, I. Brener, and Y. Kivshar, “Tailoring Directional Scattering through Magnetic and Electric Resonances in Subwavelength Silicon Nanodisks,” ACS Nano 7(9), 7824–7832 (2013).
[Crossref] [PubMed]

Luk, T. S.

I. Staude, A. E. Miroshnichenko, M. Decker, N. T. Fofang, S. Liu, E. Gonzales, J. Dominguez, T. S. Luk, D. N. Neshev, I. Brener, and Y. Kivshar, “Tailoring Directional Scattering through Magnetic and Electric Resonances in Subwavelength Silicon Nanodisks,” ACS Nano 7(9), 7824–7832 (2013).
[Crossref] [PubMed]

Luk’yanchuk, B.

Y. H. Fu, A. I. Kuznetsov, A. E. Miroshnichenko, Y. F. Yu, and B. Luk’yanchuk, “Directional visible light scattering by silicon nanoparticles,” Nat Commun 4, 1527 (2013).
[Crossref] [PubMed]

Mahony, T. S.

Menzel, C.

C. Menzel, E. Hebestreit, R. Alaee, M. Albooyeh, S. Mühlig, S. Burger, C. Rockstuhl, C. Simovski, S. Tretyakov, F. Lederer, and T. Pertsch, “Extreme coupling: A route towards local magnetic metamaterials,” Phys. Rev. B 89(15), 155125 (2014).
[Crossref]

S. Mühlig, C. Menzel, C. Rockstuhl, and F. Lederer, “Multipole analysis of meta-atoms,” Metamaterials (Amst.) 5(2-3), 64–73 (2011).
[Crossref]

C. Rockstuhl, C. Menzel, S. Mühlig, J. Petschulat, C. Helgert, C. Etrich, A. Chipouline, T. Pertsch, and F. Lederer, “Scattering properties of meta-atoms,” Phys. Rev. B 83(24), 245119 (2011).
[Crossref]

Miroshnichenko, A. E.

I. Staude, A. E. Miroshnichenko, M. Decker, N. T. Fofang, S. Liu, E. Gonzales, J. Dominguez, T. S. Luk, D. N. Neshev, I. Brener, and Y. Kivshar, “Tailoring Directional Scattering through Magnetic and Electric Resonances in Subwavelength Silicon Nanodisks,” ACS Nano 7(9), 7824–7832 (2013).
[Crossref] [PubMed]

Y. H. Fu, A. I. Kuznetsov, A. E. Miroshnichenko, Y. F. Yu, and B. Luk’yanchuk, “Directional visible light scattering by silicon nanoparticles,” Nat Commun 4, 1527 (2013).
[Crossref] [PubMed]

Monticone, F.

F. Monticone, N. M. Estakhri, and A. Alù, “Full Control of Nanoscale Optical Transmission with a Composite Metascreen,” Phys. Rev. Lett. 110(20), 203903 (2013).
[Crossref] [PubMed]

Moreno, F.

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

Mosallaei, H.

A. Ahmadi and H. Mosallaei, “Physical configuration and performance modeling of all-dielectric metamaterials,” Phys. Rev. B 77(4), 045104 (2008).
[Crossref]

Mühlig, S.

C. Menzel, E. Hebestreit, R. Alaee, M. Albooyeh, S. Mühlig, S. Burger, C. Rockstuhl, C. Simovski, S. Tretyakov, F. Lederer, and T. Pertsch, “Extreme coupling: A route towards local magnetic metamaterials,” Phys. Rev. B 89(15), 155125 (2014).
[Crossref]

S. Mühlig, C. Menzel, C. Rockstuhl, and F. Lederer, “Multipole analysis of meta-atoms,” Metamaterials (Amst.) 5(2-3), 64–73 (2011).
[Crossref]

C. Rockstuhl, C. Menzel, S. Mühlig, J. Petschulat, C. Helgert, C. Etrich, A. Chipouline, T. Pertsch, and F. Lederer, “Scattering properties of meta-atoms,” Phys. Rev. B 83(24), 245119 (2011).
[Crossref]

Neshev, D. N.

I. Staude, A. E. Miroshnichenko, M. Decker, N. T. Fofang, S. Liu, E. Gonzales, J. Dominguez, T. S. Luk, D. N. Neshev, I. Brener, and Y. Kivshar, “Tailoring Directional Scattering through Magnetic and Electric Resonances in Subwavelength Silicon Nanodisks,” ACS Nano 7(9), 7824–7832 (2013).
[Crossref] [PubMed]

Ng, J.

J. Chen, J. Ng, Z. Lin, and C. T. Chan, “Optical pulling force,” Nat. Photonics 5(9), 531–534 (2011).
[Crossref]

Ni, X.

X. Ni, N. K. Emani, A. V. Kildishev, A. Boltasseva, and V. M. Shalaev, “Broadband Light Bending with Plasmonic Nanoantennas,” Science 335(6067), 427 (2012).
[Crossref] [PubMed]

Nieto-Vesperinas, M.

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

Pertsch, T.

C. Menzel, E. Hebestreit, R. Alaee, M. Albooyeh, S. Mühlig, S. Burger, C. Rockstuhl, C. Simovski, S. Tretyakov, F. Lederer, and T. Pertsch, “Extreme coupling: A route towards local magnetic metamaterials,” Phys. Rev. B 89(15), 155125 (2014).
[Crossref]

C. Rockstuhl, C. Menzel, S. Mühlig, J. Petschulat, C. Helgert, C. Etrich, A. Chipouline, T. Pertsch, and F. Lederer, “Scattering properties of meta-atoms,” Phys. Rev. B 83(24), 245119 (2011).
[Crossref]

Peters, D. W.

J. C. Ginn, I. Brener, D. W. Peters, J. R. Wendt, J. O. Stevens, P. F. Hines, L. I. Basilio, L. K. Warne, J. F. Ihlefeld, P. G. Clem, and M. B. Sinclair, “Realizing Optical Magnetism from Dielectric Metamaterials,” Phys. Rev. Lett. 108(9), 097402 (2012).
[Crossref] [PubMed]

Petschulat, J.

C. Rockstuhl, C. Menzel, S. Mühlig, J. Petschulat, C. Helgert, C. Etrich, A. Chipouline, T. Pertsch, and F. Lederer, “Scattering properties of meta-atoms,” Phys. Rev. B 83(24), 245119 (2011).
[Crossref]

Pfeiffer, C.

C. Pfeiffer and A. Grbic, “Metamaterial Huygens’ Surfaces: Tailoring Wave Fronts with Reflectionless Sheets,” Phys. Rev. Lett. 110(19), 197401 (2013).
[Crossref] [PubMed]

Reinhardt, C.

Rockstuhl, C.

C. Menzel, E. Hebestreit, R. Alaee, M. Albooyeh, S. Mühlig, S. Burger, C. Rockstuhl, C. Simovski, S. Tretyakov, F. Lederer, and T. Pertsch, “Extreme coupling: A route towards local magnetic metamaterials,” Phys. Rev. B 89(15), 155125 (2014).
[Crossref]

S. Mühlig, C. Menzel, C. Rockstuhl, and F. Lederer, “Multipole analysis of meta-atoms,” Metamaterials (Amst.) 5(2-3), 64–73 (2011).
[Crossref]

C. Rockstuhl, C. Menzel, S. Mühlig, J. Petschulat, C. Helgert, C. Etrich, A. Chipouline, T. Pertsch, and F. Lederer, “Scattering properties of meta-atoms,” Phys. Rev. B 83(24), 245119 (2011).
[Crossref]

Sáenz, J. J.

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

Shalaev, V. M.

X. Ni, N. K. Emani, A. V. Kildishev, A. Boltasseva, and V. M. Shalaev, “Broadband Light Bending with Plasmonic Nanoantennas,” Science 335(6067), 427 (2012).
[Crossref] [PubMed]

Shevchenko, A.

P. Grahn, A. Shevchenko, and M. Kaivola, “Electromagnetic multipole theory for optical nanomaterials,” New J. Phys. 14(9), 093033 (2012).
[Crossref]

Shore, R.

R. Shore and A. D. Yaghjian, “Complex waves on periodic arrays of lossy and lossless permeable spheres. Part 1: Theory,” Radio Sci. 47, RS2014 (2012).

Silveirinha, M. G.

M. G. Silveirinha, “Generalized Lorentz-Lorenz formulas for microstructured materials,” Phys. Rev. B 76(24), 245117 (2007).
[Crossref]

Simovski, C.

C. Menzel, E. Hebestreit, R. Alaee, M. Albooyeh, S. Mühlig, S. Burger, C. Rockstuhl, C. Simovski, S. Tretyakov, F. Lederer, and T. Pertsch, “Extreme coupling: A route towards local magnetic metamaterials,” Phys. Rev. B 89(15), 155125 (2014).
[Crossref]

Simovski, C. R.

C. R. Simovski, “Material parameters of metamaterials (a Review),” Opt. Spectrosc. 107(5), 726–753 (2009).
[Crossref]

Sinclair, M. B.

S. Liu, M. B. Sinclair, T. S. Mahony, Y. C. Jun, S. Campione, J. Ginn, D. A. Bender, J. R. Wendt, J. F. Ihlefeld, P. G. Clem, J. B. Wright, and I. Brener, “Optical magnetic mirrors without metals,” Optica 1(4), 250–256 (2014).
[Crossref]

L. K. Warne, L. I. Basilio, W. L. Langston, W. A. Johnson, and M. B. Sinclair, “Perturbation Theory in the Design of Degenerate Spherical Dielectric Resonators,” IEEE Trans. Antenn. Propag. 61(4), 2130–2141 (2013).
[Crossref]

S. Campione, M. B. Sinclair, and F. Capolino, “Effective medium representation and complex modes in 3D periodic metamaterials made of cubic resonators with large permittivity at mid-infrared frequencies,” Phot. Nano. Fund. Appl. 11(4), 423–435 (2013).
[Crossref]

L. K. Warne, L. I. Basilio, W. L. Langston, W. A. Johnson, and M. B. Sinclair, “Perturbation theory in the design of degenerate rectangular dielectric resonators,” Prog. Electromagn. Res. B 44, 1–29 (2012).
[Crossref]

J. C. Ginn, I. Brener, D. W. Peters, J. R. Wendt, J. O. Stevens, P. F. Hines, L. I. Basilio, L. K. Warne, J. F. Ihlefeld, P. G. Clem, and M. B. Sinclair, “Realizing Optical Magnetism from Dielectric Metamaterials,” Phys. Rev. Lett. 108(9), 097402 (2012).
[Crossref] [PubMed]

L. I. Basilio, L. K. Warne, W. L. Langston, W. A. Johnson, and M. B. Sinclair, “A Quick and Easy Simulation Procedure to Aid in Metamaterial Unit-Cell Design,” IEEE Antennas Wirel. Propag. Lett. 10, 1567–1570 (2011).
[Crossref]

Staude, I.

I. Staude, A. E. Miroshnichenko, M. Decker, N. T. Fofang, S. Liu, E. Gonzales, J. Dominguez, T. S. Luk, D. N. Neshev, I. Brener, and Y. Kivshar, “Tailoring Directional Scattering through Magnetic and Electric Resonances in Subwavelength Silicon Nanodisks,” ACS Nano 7(9), 7824–7832 (2013).
[Crossref] [PubMed]

Stevens, J. O.

J. C. Ginn, I. Brener, D. W. Peters, J. R. Wendt, J. O. Stevens, P. F. Hines, L. I. Basilio, L. K. Warne, J. F. Ihlefeld, P. G. Clem, and M. B. Sinclair, “Realizing Optical Magnetism from Dielectric Metamaterials,” Phys. Rev. Lett. 108(9), 097402 (2012).
[Crossref] [PubMed]

Tetienne, J.-P.

N. Yu, P. Genevet, M. A. Kats, F. Aieta, J.-P. Tetienne, F. Capasso, and Z. Gaburro, “Light Propagation with Phase Discontinuities: Generalized Laws of Reflection and Refraction,” Science 334(6054), 333–337 (2011).
[Crossref] [PubMed]

Tretyakov, S.

C. Menzel, E. Hebestreit, R. Alaee, M. Albooyeh, S. Mühlig, S. Burger, C. Rockstuhl, C. Simovski, S. Tretyakov, F. Lederer, and T. Pertsch, “Extreme coupling: A route towards local magnetic metamaterials,” Phys. Rev. B 89(15), 155125 (2014).
[Crossref]

Vaillon, R.

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

Wang, D. S.

Warne, L. K.

L. K. Warne, L. I. Basilio, W. L. Langston, W. A. Johnson, and M. B. Sinclair, “Perturbation Theory in the Design of Degenerate Spherical Dielectric Resonators,” IEEE Trans. Antenn. Propag. 61(4), 2130–2141 (2013).
[Crossref]

L. K. Warne, L. I. Basilio, W. L. Langston, W. A. Johnson, and M. B. Sinclair, “Perturbation theory in the design of degenerate rectangular dielectric resonators,” Prog. Electromagn. Res. B 44, 1–29 (2012).
[Crossref]

J. C. Ginn, I. Brener, D. W. Peters, J. R. Wendt, J. O. Stevens, P. F. Hines, L. I. Basilio, L. K. Warne, J. F. Ihlefeld, P. G. Clem, and M. B. Sinclair, “Realizing Optical Magnetism from Dielectric Metamaterials,” Phys. Rev. Lett. 108(9), 097402 (2012).
[Crossref] [PubMed]

L. I. Basilio, L. K. Warne, W. L. Langston, W. A. Johnson, and M. B. Sinclair, “A Quick and Easy Simulation Procedure to Aid in Metamaterial Unit-Cell Design,” IEEE Antennas Wirel. Propag. Lett. 10, 1567–1570 (2011).
[Crossref]

Wendt, J. R.

S. Liu, M. B. Sinclair, T. S. Mahony, Y. C. Jun, S. Campione, J. Ginn, D. A. Bender, J. R. Wendt, J. F. Ihlefeld, P. G. Clem, J. B. Wright, and I. Brener, “Optical magnetic mirrors without metals,” Optica 1(4), 250–256 (2014).
[Crossref]

J. C. Ginn, I. Brener, D. W. Peters, J. R. Wendt, J. O. Stevens, P. F. Hines, L. I. Basilio, L. K. Warne, J. F. Ihlefeld, P. G. Clem, and M. B. Sinclair, “Realizing Optical Magnetism from Dielectric Metamaterials,” Phys. Rev. Lett. 108(9), 097402 (2012).
[Crossref] [PubMed]

Wright, J. B.

Yaghjian, A. D.

R. Shore and A. D. Yaghjian, “Complex waves on periodic arrays of lossy and lossless permeable spheres. Part 1: Theory,” Radio Sci. 47, RS2014 (2012).

Yu, N.

N. Yu, P. Genevet, M. A. Kats, F. Aieta, J.-P. Tetienne, F. Capasso, and Z. Gaburro, “Light Propagation with Phase Discontinuities: Generalized Laws of Reflection and Refraction,” Science 334(6054), 333–337 (2011).
[Crossref] [PubMed]

Yu, Y. F.

Y. H. Fu, A. I. Kuznetsov, A. E. Miroshnichenko, Y. F. Yu, and B. Luk’yanchuk, “Directional visible light scattering by silicon nanoparticles,” Nat Commun 4, 1527 (2013).
[Crossref] [PubMed]

ACS Nano (1)

I. Staude, A. E. Miroshnichenko, M. Decker, N. T. Fofang, S. Liu, E. Gonzales, J. Dominguez, T. S. Luk, D. N. Neshev, I. Brener, and Y. Kivshar, “Tailoring Directional Scattering through Magnetic and Electric Resonances in Subwavelength Silicon Nanodisks,” ACS Nano 7(9), 7824–7832 (2013).
[Crossref] [PubMed]

IEEE Antennas Wirel. Propag. Lett. (1)

L. I. Basilio, L. K. Warne, W. L. Langston, W. A. Johnson, and M. B. Sinclair, “A Quick and Easy Simulation Procedure to Aid in Metamaterial Unit-Cell Design,” IEEE Antennas Wirel. Propag. Lett. 10, 1567–1570 (2011).
[Crossref]

IEEE Trans. Antenn. Propag. (1)

L. K. Warne, L. I. Basilio, W. L. Langston, W. A. Johnson, and M. B. Sinclair, “Perturbation Theory in the Design of Degenerate Spherical Dielectric Resonators,” IEEE Trans. Antenn. Propag. 61(4), 2130–2141 (2013).
[Crossref]

J. Appl. Phys. (1)

A. Alu and N. Engheta, “Polarizabilities and effective parameters for collections of spherical nanoparticles formed by pairs of concentric double-negative, single-negative, and/or double-positive metamaterial layers,” J. Appl. Phys. 97(9), 094310 (2005).
[Crossref]

J. Opt. Soc. Am. (1)

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

Metamaterials (Amst.) (1)

S. Mühlig, C. Menzel, C. Rockstuhl, and F. Lederer, “Multipole analysis of meta-atoms,” Metamaterials (Amst.) 5(2-3), 64–73 (2011).
[Crossref]

Nat Commun (2)

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

Y. H. Fu, A. I. Kuznetsov, A. E. Miroshnichenko, Y. F. Yu, and B. Luk’yanchuk, “Directional visible light scattering by silicon nanoparticles,” Nat Commun 4, 1527 (2013).
[Crossref] [PubMed]

Nat. Photonics (1)

J. Chen, J. Ng, Z. Lin, and C. T. Chan, “Optical pulling force,” Nat. Photonics 5(9), 531–534 (2011).
[Crossref]

New J. Phys. (1)

P. Grahn, A. Shevchenko, and M. Kaivola, “Electromagnetic multipole theory for optical nanomaterials,” New J. Phys. 14(9), 093033 (2012).
[Crossref]

Opt. Express (1)

Opt. Spectrosc. (1)

C. R. Simovski, “Material parameters of metamaterials (a Review),” Opt. Spectrosc. 107(5), 726–753 (2009).
[Crossref]

Optica (1)

Phot. Nano. Fund. Appl. (1)

S. Campione, M. B. Sinclair, and F. Capolino, “Effective medium representation and complex modes in 3D periodic metamaterials made of cubic resonators with large permittivity at mid-infrared frequencies,” Phot. Nano. Fund. Appl. 11(4), 423–435 (2013).
[Crossref]

Phys. Rev. B (5)

C. Menzel, E. Hebestreit, R. Alaee, M. Albooyeh, S. Mühlig, S. Burger, C. Rockstuhl, C. Simovski, S. Tretyakov, F. Lederer, and T. Pertsch, “Extreme coupling: A route towards local magnetic metamaterials,” Phys. Rev. B 89(15), 155125 (2014).
[Crossref]

A. Alù, “Restoring the physical meaning of metamaterial constitutive parameters,” Phys. Rev. B 83(8), 081102 (2011).
[Crossref]

M. G. Silveirinha, “Generalized Lorentz-Lorenz formulas for microstructured materials,” Phys. Rev. B 76(24), 245117 (2007).
[Crossref]

C. Rockstuhl, C. Menzel, S. Mühlig, J. Petschulat, C. Helgert, C. Etrich, A. Chipouline, T. Pertsch, and F. Lederer, “Scattering properties of meta-atoms,” Phys. Rev. B 83(24), 245119 (2011).
[Crossref]

A. Ahmadi and H. Mosallaei, “Physical configuration and performance modeling of all-dielectric metamaterials,” Phys. Rev. B 77(4), 045104 (2008).
[Crossref]

Phys. Rev. Lett. (3)

C. Pfeiffer and A. Grbic, “Metamaterial Huygens’ Surfaces: Tailoring Wave Fronts with Reflectionless Sheets,” Phys. Rev. Lett. 110(19), 197401 (2013).
[Crossref] [PubMed]

F. Monticone, N. M. Estakhri, and A. Alù, “Full Control of Nanoscale Optical Transmission with a Composite Metascreen,” Phys. Rev. Lett. 110(20), 203903 (2013).
[Crossref] [PubMed]

J. C. Ginn, I. Brener, D. W. Peters, J. R. Wendt, J. O. Stevens, P. F. Hines, L. I. Basilio, L. K. Warne, J. F. Ihlefeld, P. G. Clem, and M. B. Sinclair, “Realizing Optical Magnetism from Dielectric Metamaterials,” Phys. Rev. Lett. 108(9), 097402 (2012).
[Crossref] [PubMed]

Prog. Electromagn. Res. B (1)

L. K. Warne, L. I. Basilio, W. L. Langston, W. A. Johnson, and M. B. Sinclair, “Perturbation theory in the design of degenerate rectangular dielectric resonators,” Prog. Electromagn. Res. B 44, 1–29 (2012).
[Crossref]

Radio Sci. (1)

R. Shore and A. D. Yaghjian, “Complex waves on periodic arrays of lossy and lossless permeable spheres. Part 1: Theory,” Radio Sci. 47, RS2014 (2012).

Science (2)

N. Yu, P. Genevet, M. A. Kats, F. Aieta, J.-P. Tetienne, F. Capasso, and Z. Gaburro, “Light Propagation with Phase Discontinuities: Generalized Laws of Reflection and Refraction,” Science 334(6054), 333–337 (2011).
[Crossref] [PubMed]

X. Ni, N. K. Emani, A. V. Kildishev, A. Boltasseva, and V. M. Shalaev, “Broadband Light Bending with Plasmonic Nanoantennas,” Science 335(6067), 427 (2012).
[Crossref] [PubMed]

Other (5)

M. Decker, I. Staude, M. Falkner, J. Dominguez, D. N. Neshev, I. Brener, T. Pertsch, and Y. S. Kivshar, “High-efficiency light-wave control with all-dielectric optical Huygens’ metasurfaces,” arXiv:1405.5038 (2014).

R. E. Collin, Field Theory of Guided Waves (McGraw Hill, 1960).

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (John Wiley & Sons, Inc., 1983).

J. D. Jackson, Classical Electrodynamics (Wiley, 1999).

C. H. Papas, Theory of Electromagnetic Wave Propagation (Dover Publications, Inc., 1995).

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Figures (11)

Fig. 1
Fig. 1

A subwavelength resonator under plane wave illumination scatters a far field that can be decomposed in terms of multipolar field components, i.e. dipole, quadrupole, and higher order terms.

Fig. 2
Fig. 2

Sketch of (a) E- and (b) H-field drive conditions. The phases of the counter propagating plane waves are chosen to cancel either the magnetic field (for E-field drive) or the electric field (for H-field drive) at the center of the resonator.

Fig. 3
Fig. 3

(a) Radiated far-field amplitudes and (b) power associated with the multipoles m MD y , p ED x , and Q MQ z y of a cubic dielectric resonator. Sampling positions are located on the θ = 90 ° plane at φ = 90 ° for E-field drive (black squares) and at φ = 0 ° for H-field drive (red triangles). The inset shows a schematic of the geometry including the sampling points depicted by black and red crosses.

Fig. 4
Fig. 4

Far-field patterns versus θ and ϕ for a cubic dielectric resonator at the magnetic dipole resonance, electric dipole resonance, and magnetic quadrupole resonance, computed via (a-c) full-wave simulations and reproduced via (d-f) multipolar expansion.

Fig. 5
Fig. 5

Angular distribution in the y-z and x-z planes of the far-field scattered by a cubic dielectric resonator at the magnetic dipole resonance (black solid), electric dipole resonance (red dashed), and magnetic quadrupole resonance (blue dotted).

Fig. 6
Fig. 6

Radiated far-field amplitudes of single-split cubes with gap of (a) 100 nm and (b) 200 nm. Sampling positions are located on the θ = 90 ° plane at ϕ = 90 ° for E-field drive (black squares) and at ϕ = 0 ° for H-field drive (red triangles). The insets show schematics of the two geometries.

Fig. 7
Fig. 7

The relative location of electric (black squares) and magnetic (red triangles) polarizabilities of subwavelength resonators is controllable through geometry. Solid: Real part; dashed: imaginary part. (a) Full-cube. (b) Single-split cube with gap s = 100 nm. (c) Single-split cube with gap s = 200 nm and d = 1.53 µm. The monochromatic time harmonic convention, exp ( i ω t ) , is assumed.

Fig. 8
Fig. 8

(a) Polarizability result shown in Fig. 6(b). The frequencies that satisfy the first Kerker condition are indicated by the dashed-dotted vertical lines. (b) Scattered radiation pattern of an isolated single-split dielectric cube resonator excited through plane wave incidence for three excitation frequencies: forward scattering is evident (i.e. only one lobe at θ = 180 degrees) when the first Kerker condition is satisfied. Only data between 0 and 180 degrees is reported; the scattering is specular between 180 and 360 degrees.

Fig. 9
Fig. 9

(a) Reflectance and (b) transmittance of a two-dimensional array of dielectric resonators [full cubes as in Fig. 6(a) and single-split cubes as in Fig. 6(c)] arrayed on a square lattice with a period of 2.6 µm. Phase of the (c) reflection coefficient and of the (d) transmission coefficient for the cases in (a)-(b).

Fig. 10
Fig. 10

Radiated far-field amplitudes of a four-split cube as in the inset. Sampling positions are located on the θ = 90 ° plane at ϕ = 90 ° for E-field drive (black squares) and at ϕ = 0 ° for H-field drive (red triangles).

Fig. 11
Fig. 11

(a) Radiated far-field amplitudes ( | E ϕ | ) of the three resonator designs analyzed in this paper. Sampling positions are located on the θ = 90 ° plane at ϕ = 90 ° for E-field drive. (b) Quadrupolar resonance shift in Eq. (10) versus the three resonator designs analyzed in this paper.

Tables (3)

Tables Icon

Table 1 Power associated with each multipole for a subwavelength dielectric cube. The powers radiated by multipolar components not reported here are smaller by more than two orders of magnitude.

Tables Icon

Table 2 Powers radiated by the dominant multipoles for a subwavelength single-split dielectric cube (s = 200 nm and d = 1.53 µm). The powers radiated by multipolar components not reported here are smaller by more than two orders of magnitude.

Tables Icon

Table 3 Powers radiated by the dominant multipoles for a subwavelength four-split dielectric cube (s = 50 nm and d = 1.53 µm). The powers radiated by multipolar components not reported here are smaller by more than two orders of magnitude.

Equations (26)

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E s = n = 1 m = n n ( a m n N e m n + b m n M o m n ) .
E tot = E ED + E MD + E EQ + E MQ + E EO + E MO + higher order terms,
E ED = Z 0 c k 2 4 π e i k r r r ^ × p × r ^ , E MD = Z 0 k 2 4 π e i k r r r ^ × m ,
E EQ = Z 0 i c k 3 24 π e i k r r r ^ × Q EQ × r ^ , E MQ = Z 0 i k 3 24 π e i k r r r ^ × Q MQ ,
E EO = Z 0 c k 4 120 π e i k r r r ^ × O EO × r ^ , E MO = Z 0 k 4 120 π e i k r r r ^ × O MO ,
E MP = W MP C MP A MP ( θ , ϕ )
W MP C MP = 0 2 π 0 π [ E tot A MP ( θ , ϕ ) ] sin θ d θ d ϕ .
P MP = | W M P | 2 | C M P | 2 2 Z 0 .
p = α ¯ ee E loc , m = α ¯ mm H loc
Quadrupolar resonance shift ( % ) = f Q f D f D × 100
E ED = Z 0 2 c k 2 3 e i k r r p ED x { sin ϕ φ ^ + cos θ cos ϕ θ ^ 8 π / 3 }
E ED = Z 0 2 c k 2 3 e i k r r p ED y { cos ϕ φ ^ + cos θ sin ϕ θ ^ 8 π / 3 }
E ED = Z 0 2 c k 2 3 e i k r r p ED z { sin θ θ ^ 8 π / 3 }
E MD = Z 0 2 k 2 3 e i k r r m MD x [ cos θ cos ϕ φ ^ + sin ϕ θ ^ 8 π / 3 ]
E MD = Z 0 2 k 2 3 e i k r r m MD y [ cos θ sin ϕ φ ^ cos ϕ θ ^ 8 π / 3 ]
E MD = Z 0 2 k 2 3 e i k r r m MD z [ sin θ φ ^ 8 π / 3 ]
E EQ = Z 0 i c k 3 15 e i k r r Q EQ x x [ sin θ sin ϕ cos ϕ φ ^ + sin θ cos θ ( 1 + cos 2 ϕ ) θ ^ 8 π / 5 ]
E EQ = Z 0 i c k 3 15 e i k r r Q EQ y x [ sin θ ( 2 cos 2 ϕ 1 ) φ ^ + 2 sin θ cos θ sin ϕ cos ϕ θ ^ 8 π / 5 ]
E EQ = Z 0 i c k 3 15 e i k r r Q EQ z x [ sin ϕ cos θ φ ^ + ( 2 cos 2 θ 1 ) cos ϕ θ ^ 8 π / 5 ]
E EQ = Z 0 i c k 3 15 e i k r r Q EQ y y [ sin θ sin ϕ cos ϕ φ ^ + sin θ cos θ ( 1 + sin 2 ϕ ) θ ^ 8 π / 5 ]
E EQ = Z 0 i c k 3 15 e i k r r Q EQ z y [ cos θ cos ϕ φ ^ + ( 2 cos 2 θ 1 ) sin ϕ θ ^ 8 π / 5 ]
E MQ = Z 0 i k 3 15 e i k r r Q MQ x x [ sin θ cos θ ( 1 + cos 2 ϕ ) φ ^ + sin θ sin ϕ cos ϕ θ ^ 8 π / 5 ]
E MQ = Z 0 i k 3 15 e i k r r Q MQ y x [ 2 sin θ cos θ sin ϕ cos ϕ φ ^ + sin θ ( 1 2 cos 2 ϕ ) θ ^ 8 π / 5 ]
E MQ = Z 0 i k 3 15 e i k r r Q MQ z x [ cos ϕ ( 2 cos 2 θ 1 ) φ ^ + cos θ sin ϕ θ ^ 8 π / 5 ]
E MQ = Z 0 i k 3 15 e i k r r Q MQ y y [ sin θ cos θ ( 1 + sin 2 ϕ ) φ ^ sin θ sin ϕ cos ϕ θ ^ 8 π / 5 ]
E MQ = Z 0 i k 3 15 e i k r r Q MQ z y [ sin ϕ ( 2 cos 2 θ 1 ) φ ^ cos θ cos ϕ θ ^ 8 π / 5 ]

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