 We assume a two-mirror Fabry-Pérot resonator of geometrical length formula_14, homogeneously filled with an active laser medium of refractive index formula_15.We define the reference situation, namely the passive resonator mode, for a resonator whose active medium is transparent, i.e., it does not introduce gain or absorption.The round-trip time formula_16 of light travelling in the resonator with speed formula_17, where formula_18 is the speed of light in vacuum, and the free spectral range formula_19 are given by
Light in the longitudinal resonator mode of interest oscillates at the q-th resonance frequency
The exponential outcoupling decay time formula_22 and the corresponding decay-rate constant formula_23 are related to the intensity reflectances formula_24 of the two resonator mirrors formula_25 by
The exponential intrinsic loss time formula_27 and the corresponding decay-rate constant formula_28 are related to the intrinsic round-trip loss formula_29 by
The exponential photon-decay time formula_31 and the corresponding decay-rate constant formula_32 of the passive resonator are then given by
All three exponential decay times average over the round-trip time formula_34 In the following, we assume that formula_14, formula_15, formula_37, formula_38, and formula_29, hence also formula_22, formula_27, and formula_12 do not vary significantly over the frequency range of interest.