It is convenient to denote cavity frequencies with a complex number ω ω ~ ~ = ω ω − − i γ γ / 2 , where ω ω = R e ( ω ω ~ ~ ) is the angular resonant frequency and γ γ = 2 I m ( ω ω ~ ~ ) is the inverse of the mode lifetime. Cavity perturbation theory has been initially proposed by Bethe-Schwinger in optics , and Waldron in the radio frequency domain. These initial approaches rely on formulae that consider stored energy