Close link between Fabry–Pérot resonance and natural-resonance frequencies

Abstract

Mathematical and numerical analyses have been performed to examine the close link between Fabry–Pérot resonance and natural-resonance frequencies. For the mathematical analysis, the conditions resulting in minimum magnitudes of reflection coefficients in frequency-domain are derived for air-backed and metal-backed low-loss non-dispersive (or weakly dispersive) dielectric samples with relative complex permittivity and thickness L for free-space wave propagation at normal incidence. The close relation between Fabry–Pérot resonance and natural-resonance frequencies is demonstrated for three different sample scenarios as (i) no-dispersion and lossless case ( and L = 50 mm), (ii) no-dispersion and low-loss case ( and L = 50 mm), and (iii) weak-dispersion and low-loss case ( and L = 50 mm where σ is the conductivity of the sample and ω is the angular frequency). It is noted that operating frequency should be increased to observe late-time natural-resonance frequencies for a sample with smaller length or vice versa.