Geometrical scaling and modal decay rates in periodic arrays of deeply subwavelength Terahertz resonators

It is well known that due to the high conductivity of noble metals at terahertz frequencies and scalability of macroscopic Maxwell equations, a geometrical downscaling of a terahertz resonator results in the linear upscaling of its resonance frequency. However, the scaling laws of modal decay rates, important for the resonator excitation efficiency, are much less known. Here, we investigate the extent to which the scale-invariance of decay rates is violated due to the finite conductivity of the metal. We find that the resonance quality factor or the excitation efficiency may be substantially affected by scaling and show that this happens as a result of the scale-dependence of the metal absorption rate, while the radiative decay and the dielectric cavity absorption rates are approximately scale-invariant. In particular, we find that by downscaling overcoupled resonators, their excitation efficiency increases, while the opposite happens with undercoupled resonators.