Magnetoinductive waves in one, two, and three dimensions

Abstract

The propagation of waves supported by capacitively loaded loops is investigated using a circuit model in which each loop is coupled magnetically to a number of other loops. Since the coupling is due to induced voltages the waves are referred to as magnetoinductive (MI) waves. The mathematical formulations are mostly analytical thanks to long standing previous work on the magnetic and electric fields generated by currents flowing in loops. Retardation is neglected, i.e., dimensions of the structure are assumed to be small relative to the free space wavelength. The dispersion relations, derived in the most general case for a tetragonal three-dimensional structure, exhibit both forward and backward waves within a pass band. It is shown that for reproducing the salient features of the waves it is sufficient to take nearest neighbor coupling into account but coupling between loops further away must also be considered if higher accuracy is required. The investigations include that of resonances, conditions for the existence of traveling waves, tolerances, and streamlines of the Poynting vector. Waveguide components, like bends, power dividers and couplers are considered due to the potential applications of the MI waves as magnetic guides. Generality of the results, their possible implications for transverse electromagnetic wave propagation, previous work on similar waves, including the possibility of phase conjugation, are discussed in a separate section.

Spectral Collapse in Ensembles of Metamolecules

“…We attribute the observed size-dependent resonant response of the coherent metamaterial to the existence of strong interactions between the meta-molecules mediated by magneto-inductive surface waves [7]. It follows from symmetry arguments that magnetic dipoles coherently oscillating perpendicular to the plane of an infinite (or very large) regular array can re-radiate only in its plane, which ensures very low scattering losses and therefore a high Q-factor of the system.…”

Hybridization effect in coupled metamaterials

“…Indeed, MP resonance has been already applied to a one-dimensional sub-wavelength waveguide in the microwave range [55][56][57]. Shamonina et al proposed a propagation of waves supported by capacitively loaded loops using a circuit model in which each loop is coupled magnetically to a number of other loops [55].…”

“…Shamonina et al proposed a propagation of waves supported by capacitively loaded loops using a circuit model in which each loop is coupled magnetically to a number of other loops [55]. Since the coupling is due to induced voltages, the waves are referred to as magneto-inductive waves (MI).…”

Realistic metamaterial lenses: Limitations imposed by discrete structure

“…11͒: while with the realistic losses the shifted sources can be well resolved, the patterns at low loss are not comprehensive and could not be improved even by frequency variation. This is a consequence of numerous magnetoinductive excitations ͑spatial resonances͒ across the lens structure 25,26 which are favored by low dissipation and relatively small size of the entire lens. This leads to various standing wave patterns which depend on frequency and coil parameters.…”