Q-factor of optical delay-line based cavities and oscillators

In this paper a theoretical derivation of unloaded and loaded Q-factor of delay-line cavities, such as optical fiber delay-lines, and delay-line based oscillators, such as optoelectronic oscillators (OEOs), is presented based on three approaches: (I) second-order resonator approximation, (II) linear time-invariant phase-space model and (III) energy approach. Theoretical expressions for unloaded and loaded Q-factor of delay-line based cavities and oscillators are derived. We show that the Q-factor of a delay-line based cavity is a function of its round-trip time that is not equal to the energy decay-time of usual microwave or optical resonators. Hence, the behavior of the Q-factor of a delay-line based cavity will not be the same as that of the usual resonators. We show that the loaded Q-factor of a delay-line cavity is greater than its unloaded Q-factor!, besides we show that the Q-factor of a lossy delay-line cavity is the same as that of the lossless one! (in contrast to the behavior of the usual resonators). We also show that the Q-factor of a delay-line based oscillator is proportional to the half of the round-trip time of its delay line while the Q-factor of an oscillator based on a usual resonator is proportional to the energy decay time of its resonator.