Coupling coefficient of two rotated cylindrical dielectric resonators disposed in free space

The coupled-mode theory is an established and important tool in the electromagnetic theory which describes the exchange of energy between modes of a given system. In the framework of this theory, the coupling coefficient is the main parameter that quantifies the intermode interaction strength. In this paper, we introduce practical formulas for calculating the mutual coupling coefficient between two cylindrical dielectric resonators arbitrarily oriented in free space relative to each other. The correctness of the solution is validated against the full-wave numerical simulations performed with the COMSOL Multiphysics electromagnetic solver. In particular, the obtained formulas are suitable to analyze the gain/directivity and transmission/reflection properties of dielectric antennas and metasurfaces consisting of a large but finite number of dielectric resonators.