Practical formulas are derived for calculating the far-field radiation pattern and coupling coefficient of a rectangular dielectric resonator (cuboid) with free space as well as mutual coupling coefficients between two cuboids for their different orientations relative to each other. An approach is developed using the coupled mode theory and the perturbation theory for the Maxwell equations. The correctness of obtained formulas is checked against the full-wave numerical simulations performed by the COMSOL Multiphysics electromagnetic solver. In particular, the obtained formulas can be used for revealing optical features of realistic (i.e., consisting of a finite number of resonators) all-dielectric metasurfaces with arbitrary curved shapes.
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