Artificial magnetism at terahertz frequencies from three-dimensional lattices of TiO_2 microspheres accounting for spatial dispersion and magnetoelectric coupling

Abstract

We employ the generalized Lorentz-Lorenz method to investigate how both magnetoelectric coupling and spatial dispersion influence the artificial magnetic capabilities at terahertz frequencies of the representative case of a metamaterial consisting of a three-dimensional (3D) lattice of TiO 2 microspheres. The complex wavenumber dispersion relations pertaining to modes supported by the array, traveling along one of the principal axes of the array with electric or magnetic field polarized transversely and longitudinally (with respect to the mode traveling direction), are studied and thoroughly characterized. One mode with transverse polarization is dominant at any given frequency for the analyzed dimensions, proving that the 3D lattice can be treated as a homogeneous medium with defined electromagnetic material parameters. We show, however, that bianisotropy is a direct consequence of magnetoelectric coupling, and the dyadic expressions of both effective and equivalent material parameters are derived. In particular, we analyze the effect of spatial dispersion on the effective parameters relative to a composite material made by a 3D lattice of TiO 2 microspheres with filling fraction around 30% and near the first Mie magnetic dipolar resonance. Finally, we homogenize the metamaterial in terms of equivalent index and impedance, and by comparison with full-wave simulations, we explain the presence of the unphysical antiresonance permittivity behavior observed in previous work.

Negative index and mode coupling in all-dielectric metamaterials at terahertz frequencies

“…In the following, we report on the mode coupling effect which plays a dominant role in the electromagnetic properties of metamaterials [33][34][35][36], notably, in the achievement of negative effective index. Magnetic and electric mode coupling effects in ADMs have been separately studied from each other in the microwave by Zhang et al [34].…”

Magnetic Nanoantennas Made of Plasmonic Nanoclusters for Photoinduced Magnetic Field Enhancement

“…Moreover, in [23][24][25][26], it is shown that by tuning the dimensions of SRR and by implementing a precise fabrication, the magnetic resonance at near infrared and visible frequencies, is achievable. In [27][28][29][30] using effective medium theory, a three-dimensional collection of polaritonic, nonmagnetic spheres have been shown to produce negative permeability at terahertz and infrared frequencies. Furthermore, other structures such as the spherical constellations [31][32][33][34][35], composite medium made of arrays of dielectric spheres [36], a periodic lattice of clusters comprising four silver plasmonic dimers [37] have been used to make metamaterial constituents which provide magnetic polarization in the visible and infrared spectrum.…”

Photoinduced Magnetic Nanoprobe Excited by an Azimuthally Polarized Vector Beam

“…On the other hand, even though natural optical magnetism vanishes, metamaterials with equivalent magnetic dipolar responses have been widely studied in the past decade. For example, arrays of magnetic meta atoms are employed in engineering bulk effective permeability [2]- [7]. Several studies have been devoted to generating artificial magnetism (i.e., effective relative permeability different from unity) for such structures leading to effective permeability engineering.…”