Abstract
We characterize the modes with real and complex wavenumbers for both longitudinal and transverse polarization states (with respect to the mode traveling direction) in three dimensional (3D) periodic arrays of titanium dioxide (TiO2) microspheres in the frequency range between 250 GHz and 350 GHz. Modal results are computed by using a single magnetic dipole approximation (SDA) and an SDA model with correction (SDA-WC) that assumes the array to be embedded in a host with an effective permittivity computed through Maxwell Garnett formulas. Moreover, for the transverse polarization case, modal wavenumbers are computed also by fitting the full-wave simulation magnetic field (one point per unit cell) in a finite thickness structure, and their agreement and disagreement are discussed. The longitudinal polarization is not affected by the artificial correction introduced in the SDA-WC; in the transverse polarization case, instead, the correction is needed to obtain results in better agreement with the full-wave data fit. In the observed frequency range, there are one longitudinal mode and two transverse modes, one forward and one backward, where the forward one is “dominant” (i.e., it contributes mostly to the field in the array). Therefore, in the case of transverse polarization, we describe the composite material in terms of homogenized refractive index and relative permeability, comparing results from (i) modal analysis (with and without correction), (ii) Maxwell Garnett formulas, and (iii) Nicolson–Ross–Weir retrieval method from scattering parameters of finite thickness structures. The agreement among the different methods justifies the performed homogenization procedure in the case of transverse polarization. We show that artificial magnetism is generated from a nonmagnetic composite material.
Highlights
The lack of strong magnetism in natural materials has motivated in recent years the use of metamaterials to generate artificial magnetism from nonmagnetic constitutive materials, especially at high frequencies where natural magnetism disappears.Several metamaterial configurations have been proposed to overcome this natural limitation throughout the frequency spectrum
We extend and provide the analytical formulation based on Green’s function (GF) for magnetic dipoles
The effective relative permeability from the single magnetic dipole approximation (SDA) method can be computed as μeff neff 2 ; in the SDA with correction (SDA-WC) case, p eff eff instead, μ n ∕ εeff, where εeff is as defined in the subsection
Summary
The lack of strong magnetism in natural materials has motivated in recent years the use of metamaterials to generate artificial magnetism (i.e., the relative permeability tensor is different from the unity tensor) from nonmagnetic constitutive materials, especially at high frequencies where natural magnetism disappears.Several metamaterial configurations have been proposed to overcome this natural limitation throughout the frequency spectrum. Artificial magnetism has been generated through the split ring resonator (SRR) structure [1], initially introduced at microwave frequencies, and extended to infrared frequencies by scaling the dimensions of the SRR [2,3] [further miniaturization would not be effective because of the growth of the kinetic (internal) inductance [3]]. Another way to generate artificial magnetism is through pair-based metamaterials, whose working principle is based on the excitation of an antisymmetric resonance associated to an equivalent current loop, such as staples [4], strips [5,6], dogbones [7,8,9,10], and metallic nanospheres/nanoshells [10,11,12], based on the original design with double bars in [13]. The packing of plasmonic nanoparticles in an engineered fashion to create nanoclusters [31,32,33]
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