Sameh Y. Elnaggar, Richard Tervo, Saba M. Mattar
A time-coupled mode theory is developed to study the coupling between resonators in the radio frequency (RF), microwave (MW), millimeter and sub-millimeter regions. The theory fulfills the boundary conditions for different structures. For many practical cases, the boundary conditions are satisfied at each point on the enclosing conducting cavity. It is also shown that open structure resonators (Dielectric, Loop-gap, Split-ring, etc.) do not significantly alter the boundary conditions across internal interfaces because they are usually small compared to the resonant wavelength. The formalism is in the form of an eigenvalue problem, in which the eigenvalues represent the square of the frequencies of the coupled system while the eigenvectors represent the coefficients of the electromagnetic field components. The theory can be applied to an arbitrary number of resonators and modes. Although originally developed to design new electron paramagnetic resonance (EPR) probes, it can be used to study complex systems used in different application fields. This includes electron-nuclear double resonance (ENDOR), electron-electron double resonance (ELDOR), magnetic resonance imaging (MRI), wireless power transfer (WPT) and the interaction of meta-material elements. The eigenvalue equation is proven to obey the energy conservation principle and hence is named energy coupled mode theory (ECMT). The theory suggests that coupling depends on two operators: the material operator represented by the polarization matrix and the free space operator represented by the free space matrix.
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http://arxiv.org/abs/1305.6085
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