There is recent interest in the inter/intra-element interactions of metamaterial unit cells. To calculate the effects of these interactions which can be substantial, an "ab-initio" general coupled mode equation, in the form of an eigenvalue problem, is derived. The solution of the master equation gives the coupled frequencies and fields in terms of the uncoupled modes. By doing so, the problem size is limited to the number of modes rather than the, usually large, discretized spatial and temporal domains obtained by full-wave solvers. Therefore, the method can be considered as a numerical recipe which determines the behavior of a complex system once its simpler ingredients are known. Besides quantitative analysis, the coupled mode equation proposes a pictorial view of the split rings' hybridization. It can be regarded as the electromagnetic analog of molecular orbital theory. The solution of the eigenvalue problem for different configurations gives valued information and insight about the coupling of metamaterials unit cells. For instance, it is shown that the behavior of split rings as a function of the relative position and orientation can be systematically explained. This is done by singling out the effect of each relevant parameter such as the coupling coefficient and coupled induced frequency shift coefficients.
Similar to the hybridization of three atoms, three coupled resonators interact to form bonding, anti-bonding and non-bonding modes. The non-bonding mode enables an electromagnetic induced transparency like transfer of energy. Here the non-bonding mode, resulting from the strong electric coupling of two dielectric resonators and an enclosure, is exploited to show that it is feasible to transfer power over a distance comparable to the operating wavelength. In this scheme, the enclosure acts as a mediator. The strong coupling permits the excitation of the non-bonding mode with high purity. This approach is different from resonant inductive coupling which works in the sub-wavelength regime. Optimal loads and the corresponding maximum efficiency are determined using two independent methods: Coupled Mode Theory and Circuit modelling. It is shown that, unlike resonant inductive coupling, the figure of merit depends on the enclosure quality and not on the load, which emphasizes the role of the enclosure as a mediator. Briefly after the input excitation is turned on, the energy in the receiver builds up via all coupled and spurious modes. As time elapses, all modes except the non-bonding cease to sustain. Due to the strong coupling between the dielectrics and the enclosure, such systems have unique properties such as high and uniform efficiency over large distances; and minimal fringing fields. These properties suggest that electromagnetic induced transparency like schemes which rely on the use of dielectric resonators can be used to power autonomous systems inside an enclosure or find applications when exposure to the fields needs to be minimal. Finite Element computations are used to verify the theoretical predictions by determining the transfer efficiency, fields profile and coupling coefficients for two different systems. It is shown that the three resonators must be present for efficient power transfer; if one or more are removed, the transfer efficiency reduces significantly.
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