Localized magnetic plasmons in all-dielectric $\ensuremath{\mu}&lt;0$ metastructures

Localized magnetic plasmons in all-dielectric $μ < 0$ metastructures

R. Paniagua-Domínguez, L. S. Froufe-Pérez, J. J. Sáenz, and J. A. Sánchez-Gil

Phys. Rev. B 91, 235120 – Published 11 June 2015

Abstract

Metamaterials are known to exhibit a variety of electromagnetic properties nonexisting in nature. We show that an all-dielectric (nonmagnetic) system consisting of deep-subwavelength, high-permittivity resonant spheres possesses effective negative magnetic permeability (dielectric permittivity being positive and small). Due to the symmetry of the electromagnetic wave equations in classical electrodynamics, localized “magnetic” plasmon resonances can be excited in a metasphere made of such metamaterial. This is theoretically demonstrated by the coupled-dipole approximation and numerically for real spheres, in full agreement with the exact analytical solution for the scattering process by the same metasphere with effective material properties predicted by effective medium theory. The emergence of this phenomenon as a function of structural order within the metastructures is also studied. Universal conditions enabling effective negative magnetic permeability relate subwavelength sphere permittivity and size with critical filling fraction. Our proposal paves the way towards (all-dielectric) magnetic plasmonics, with a wealth of fascinating applications.

Received 10 December 2014
Revised 27 May 2015

DOI:https://doi.org/10.1103/PhysRevB.91.235120

Authors & Affiliations

R. Paniagua-Domínguez^1,*, L. S. Froufe-Pérez^1,†, J. J. Sáenz², and J. A. Sánchez-Gil^1,‡

¹Instituto de Estructura de la Materia, Consejo Superior de Investigaciones Científicas, Serrano 121, 28006 Madrid, Spain
²Condensed Matter Physics Department and Centro de Investigación en Física de la Materia Condensada (IFIMAC), Universidad Autónoma de Madrid, Francisco Tomás y Valiente 7, 28049 Madrid, Spain

^*Present address: Data Storage Institute, Agency for Science, Technology and Research, 117608 Singapore.
^†Present address: Physics Department, University of Fribourg, CH-1700 Fribourg, Switzerland.
^‡Corresponding author: j.sanchez@csic.es

Article Text (Subscription Required)

Click to Expand

References (Subscription Required)

Click to Expand

Issue

Vol. 91, Iss. 23 — 15 June 2015

Reuse & Permissions

Access Options

Author publication services for translation and copyediting assistance advertisement

Images

Figure 1
Optical properties under plane wave illumination of a sphere with $R = 1$ mm, $ɛ = 1000$ , and $μ = 1$ . (a) Scattering efficiency (black), together with the dipolar electric (red) and dipolar magnetic (green) contributions. (b) Real (black) and imaginary (red) parts of the electric polarizability. (c) Real (black) and imaginary (red) parts of the magnetic polarizability. The inset shows a detail for frequencies around the resonance.
Reuse & Permissions
Figure 2
Effective material properties of a medium made of the spherical particles of Fig. 1 with a filling fraction $f = 0.263$ . (a) Real (black) and imaginary (red) parts of the effective electric permittivity. (b) Real (black) and imaginary (red) parts of the effective magnetic permeability.
Reuse & Permissions
Figure 3
(a) Mie theory scattering efficiency (black solid curve) of a sphere with radius $R_{eff} = 6$ mm and material properties $ɛ = ɛ_{eff}$ and $μ = μ_{eff}$ taken from Fig. 2, including separately the contributions from the electric ( $a_{1}$ , red solid curve) and magnetic ( $b_{1}$ , blue solid curve) dipole, and the magnetic ( $b_{2}$ , cyan dashed curve) quadrupole terms; together with the scattering cross section (green dashed curve with diamonds), numerically computed using the CEMD method, of $N = 57$ distributed electric-and-magnetic dipoles with polarizabilities taken from Figs. 1 and 1. Full numerical calculation considering the HRI spheres is shown as a black dashed curve with hollow squares (filling fraction $f = 0.263$ ), including separately (see text) the Cartesian electric $P$ (red dashed curve), magnetic $M$ (blue dotted curve with circles), and toroidal $T$ (orange dashed curve) dipole contributions, along with the spherical electric dipole contribution $P_{sph} = P + i k T$ (red dotted curve with circles). The insets show the CEMD computed scattering pattern (right) and the FEM computed magnetic field (lines and amplitude at the surface of the spheres) at the maximum of the magnetic resonance (left). (b) CEMD computed SCS for $N_{r e a} = 10^{5}$ realizations of random arrangements of dipoles with several exclusion radii, $R_{excl}$ .
Reuse & Permissions
Figure 4
Schematic depicting the region of negative permeability ( $μ_{eff} ≪ - 1$ ) in the parameter space $(x, n)$ , shown as a rotated ellipsoid. The oblique back line identifies the asymptotic (Mie) magnetic-dipole resonance ( $n x = π$ , valid for $n > 2.5$ ), predominating over any other resonance, in between the Rayleigh region $x ≪ 1, n x ≪ 1$ (where the dipolar electric term is dominant) and the region $x ≫ 1, n x ≫ 1$ , wherein higher-order resonances are larger. Two lower limits of validity are established for two filling fractions $f = 0.265, 0.5$ , below which the magnetic permeability becomes $μ_{eff} > - 1$ at half resonance according to the Clausius-Mosotti formula. Squares denote realistic configurations throughout the EM spectrum (see text), the diamond indicating the particular one studied above.
Reuse & Permissions

Physical Review B

covering condensed matter and materials physics

Localized magnetic plasmons in all-dielectric $μ < 0$ metastructures

R. Paniagua-Domínguez, L. S. Froufe-Pérez, J. J. Sáenz, and J. A. Sánchez-Gil

Phys. Rev. B 91, 235120 – Published 11 June 2015

Abstract

Authors & Affiliations

Article Text (Subscription Required)

References (Subscription Required)

Issue

Access Options

Physical Review B

covering condensed matter and materials physics

Localized magnetic plasmons in all-dielectric μ<0 metastructures

R. Paniagua-Domínguez, L. S. Froufe-Pérez, J. J. Sáenz, and J. A. Sánchez-Gil

Phys. Rev. B 91, 235120 – Published 11 June 2015

Abstract

Authors & Affiliations

Article Text (Subscription Required)

References (Subscription Required)

Issue

Access Options

Authorization Required

Other Options

Download & Share

Images

Figure 1

Figure 2

Figure 3

Figure 4

Log In

Search

Article Lookup

Paste a citation or DOI

Enter a citation

Localized magnetic plasmons in all-dielectric $μ < 0$ metastructures