A theoretical study of injection tuning of optical parametric oscillators

The time dynamics of injection tuning of optical parametric oscillators (OPO\´s) are studied. A mathematical model is used which can account for all modes which are under the gain profile of the oscillator. The model also accounts for pump depletion, cavity- factors, nonlinear coupling constants, and the (external) pump-laser field strength (distinct from the pump-mode amplitude internal to the oscillator cavity). The multimode model shows that the injected mode and the fastest growing mode are the main participants in the time dynamics of (pulsed) injection tuning of OPO\´s. A set of prescriptive criteria is developed for successful injection tuning. These are given in terms of the parameters over which the designer has some control, such as pump strength, (OPO) cavity , and the parametric gain profile. A set of approximate analytical expressions is given for the dynamic time intervals of the injection tuning, including the time interval of injection-tuned output, the duration of which is used to define "successful" injection tuning. The criteria, by focusing on the coupling constant of the injected mode, relative to that of the fastest growing mode, are interpretable directly into the frequency range of tuning for a given pump-power level. It is also observed that a sharply rising pump pulse may improve the spectral range of injection tuning.