A high-Q resonator useful at millimeter wave frequencies is the Fabry-Perot resonator, which consists of two parallel metal plates (see figure below). A plane wave traveling at normal incidence between the two plates will exhibit resonance when the plate separation is equal to a multiple of λ/2.
(a) Derive an expression for the resonant frequency of a Fabry-Perot resonator having a plate separation d and mode number
(b) If the plates have conductivity σ, derive an expression for the unloaded Q of the resonator.
(c) Use these results to find the resonant frequency and unloaded Q of a Fabry-Perot resonator having d = 4.0 cm, with copper plates, and with a mode number l = 25
