Axial magnetic resonances of rotationally symmetric high-permittivity dielectric particles of arbitrary shape

Abstract

We develop a simple semi-analytical approach for calculating the magnetic response of rotationally symmetric high-permittivity dielectric particles to an axially applied magnetic field. By using this approach, magnetic resonances of dielectric rings of arbitrary width and thickness and of dielectric cones with arbitrary height-to-diameter aspect ratio are studied. The approach is validated by a comparison with the results of rigorous numerical simulations using the Maxwell equations.

Resonant phenomena in an all-dielectric rectangular circuit induced by a plane microwave

“…The characteristic frequency ω 0 arising in equation ( 7) depends upon the circuit's geometric parameters and its dielectric permittivity ε, the attenuation decrement γ depends on the specific conductivity Ï. Similar resonant frequency formulas were obtained earlier for the ring and for the elliptic circuit [6,9]. Note, that equations ( 5)-( 7) are valid for orientation B (figure 1) due to the replacement a 1 ↔ b 1 , F a → F b , therefore, the resonant frequency f 0 , determined in equation ( 7), remains unchanged, since the capacity and self-inductance do not depend on the circuit rotation.…”

“…This topic is also related to the antieikonal limit, as presented in [7]. The resonant frequencies have been calculated for isotropic spheres [8] and rotationally symmetric particles [9]. Elliptically shaped plane circuits, providing angular anisotropy of the magnetic mode, were examined in [10].…”

Applicability of point-dipoles approximation to all-dielectric metamaterials

“…Silicon nanodimers, exhibiting both electric and magnetic dipole responses, have recently been experimentally demonstrated to enhance electric and magnetic fields in the optical range [17]. High permittivity dielectric rings are of particular interest, because they possess a strong broadband magnetic response [18][19][20]. In addition, they have more degrees of freedom for tuning the resonance frequency by geometrical parameters than, for example, spheres, cubes or cylinders.…”

“…In addition, they have more degrees of freedom for tuning the resonance frequency by geometrical parameters than, for example, spheres, cubes or cylinders. Furthermore, they exhibit resonances on the THz frequencies [19][20][21][22], a very promising range for emerging applications. Appearing most frequently as periodical structures composed of subwavelength elements (the metamaterial lattice constant is on the order of λ/20 − λ/4), three-dimensional metamaterials are often treated as continuous media (the procedure referred to as homogenization) described by some effective parameters, e.g., permittivity ε, permeability μ, refractive index n, and impedance z, which simplifies their description.…”

Applicability of point dipoles approximation to all-dielectric metamaterials

“…In addition, they have more degrees of freedom for tuning the resonance frequency by geometrical parameters than, for example, spheres, cubes or cylinders. Furthermore, they exhibit resonances on the THz frequencies [19][20][21][22], a very promising range for emerging applications.…”