Optical Parametric Oscillator Longitudinal Modes Suppression Based on Smith Predictor Control Scheme

Fiber optical parametric oscillators (FOPOs) contain multiple longitudinal modes arising from the hundreds of meters to a kilometer scale length of their cavity. To obtain better understanding of the longitudinal modes and to find out how to suppress them, a model for the operation of FOPOs is introduced. This model utilizes the sinusoidal-input describing function (SIDF) as a quasi-linear approximation of the nonlinear dynamics of parametric amplification. Applying this model, the SIDF of the FOPO is derived, which predicts that the origin of the longitudinal modes is the presence of the cavity round-trip delay term in the characteristic equation (the denominator) of the transfer function. To eliminate the effect of the delay term, a modified Smith predictor control scheme has been applied to the FOPO cavity, and a control algorithm is developed. This algorithm has been numerically analyzed and experimentally implemented, where the results indicate drastic suppression of the longitudinal modes.