Interaction of magnetic resonators studied by the magnetic field enhancement

Abstract

It is the first time that the magnetic field enhancement (MFE) is used to study the interaction of magnetic resonators (MRs), which is more sensitive than previous parameters–shift and damping of resonance frequency. To avoid the coherence of lattice and the effect of Bloch wave, the interaction is simulated between two MRs with same primary phase when the distance is changed in the range of several resonance wavelengths, which is also compared with periodic structure. The calculated MFE oscillating and decaying with distance with the period equal to resonance wavelength directly shows the retardation effect. Simulation also shows that the interaction at normal incidence is sensitive to the phase correlation which is related with retardation effect and is ultra-long-distance interaction when the two MRs are strongly localized. When the distance is very short, the amplitude of magnetic resonance is oppressed by the strong interaction and thus the MFE can be much lower than that of single MR. This study provides the design rules of metamaterials for engineering resonant properties of MRs.

Coherence of magnetic resonators in a metamaterial

“…The effect of retarded interaction of MRs at normal incidence was studied in the previous work. 5 Under oblique incidence, there are relative phase differences between the MRs in addition to the retardation effect. The relative phase difference can be changed by varying the incident angle, which is equal to 2π d · sin θ /λ R , where d is the spacing between adjacent MRs and λ R is the resonant wavelength.…”

“…1,2 Magnetic dipoles of MRs corresponding to a circulating electric current are fundamental electromagnetic excitations that are different from those associated with the familiar classical or quantum mechanical dipoles. 3,4 While quantum-mechanical spin is an intrinsic moment, the magnetic-dipole moment of MRs is an extrinsic moment and sensitive to the variation of interaction between MRs. 5 The retardation effect plays a key role in MR interactions when there is no primary phase difference between MRs, [3][4][5] and thus it is important to understand how the retarded interaction affects the diffraction of MRs in a metamaterial. X-ray diffraction is commonly utilized to determine the atomic and molecular structure of a crystal, and Bragg's law gives the angles for coherent scattering from a crystal lattice.…”