Presentazioni e Articoli Tecnici

The pursuit of artificial magnetism within metamaterials research has long been a focal point. Traditional methods rely on analyzing complex configurations such as arrays of subwavelength particles or split-rings, but unfortunately they fail at subwavelength scales. Revisiting Mie theory we have already demonstrated that a high-index dielectric sphere accurately replicates the external near-field characteristics of a negative-permeability sphere at its lowest Mie resonance frequency [1]. Furthermore, for subwavelength spheres with permittivity within the range of 10³ to 10⁵, the resulting magnetic sphere exhibits an effective permeability close to -2 [2]. Here we focus on near-field operations, showing that a high-index hollow sphere at Mie resonance can accurately sustain an external near-field pattern resembling that of a arbitrary negative-permeability hollow sphere of equivalent dimensions. In order to carry out our analysis we used a finite-element-based commercial software package: COMSOL Multiphysics [3] (RF module, setting the default frequency-domain study). The electromagnetic field is excited using a non-resonant loop coil, modeled as an Integral-type Boundary Probe, with axis along the z axis and placed at a distance d = 7 mm from the sphere (R₁=30 mm). We exploited the setup’s z-axis rotational invariance in order to perform 2D full-wave simulations in cylindrical coordinates (r, z). The exciting loop-coil has zero thickness along the z-axis (internal and external radii set as 8 mm and 11.5 mm, respectively) and a constant surface current density only along the azimuthal component. With the geometry illustrated in Fig. 1a, we can identify three domains: (i) the one outside the sphere and (ii) inside the cavity have been modeled as vacuum-zones, while (iii) the remaining one as a high-index metamaterial. The computational domain is delimited by scattering boundary conditions (spherical-waves type). Finally, we adopted the user-controlled mesh calibrated for General Physics of the predefined extra-fine free triangular type, corresponding to a minimum discretization step of 1.35 * 10^-5 m. Operatively, at the lowest Mie resonance frequency, found performing a frequency domain study (for the considered setup f_res ranges from 157 to 231 MHz), we investigated the scattering from the equivalent magnetic hollow sphere by performing a parametric sweep of the negative magnetic permeability μ _eff, in order to find the value of μ _eff that accurately reproduces the field distribution outside the sphere. In Fig. 1b, we plot μ _eff as a function of the normalized cavity radius R₂/R₁. As expected, the effective permeability is μ _eff ≈ -2 when R₂ = 0, whereas, by increasing the cavity radius R₂ (up to 25 mm), μ _eff spans values up to -9. In addition, in Fig. 1 (c-e), we report, for both the spheres, the absolute value of the magnetic field along the z-axis for R₂ = 0, 20, 25 mm, respectively. These results provide numerical evidence that the dielectric hollow sphere accurately reproduces the scattered magnetic field of the electromagnetic configuration with negative permeability outside the sphere (i.e., for z > R₁). The research was supported by the PRIN-2022 PNRR initiative (GAMING project, CUP E53D23014870001) and the University of L’Aquila (PAT-BOOSTER-GAMING, CUP C18H23000780002).