Combined feedback stabilization and iterative pulse shaping for regenerative optical amplifiers

Regenerative amplifiers (RAs) are a common tool to generate high-intensity laser pulses by circulating them through an optical gain medium inside a cavity until the stored energy is depleted. This paper presents a control strategy that simultaneously suppresses dynamical instabilities while generating output pulses with a desired pulse shape. To enable model-based design, we derive a reduced nonlinear discrete-time model of the amplifier by combining spectral small-gain approximation with spatially averaged population dynamics in the gain medium. The resulting model captures both the dynamical and spectral behavior of the amplifier. Stabilization of a desired operating point is achieved through a linear–quadratic regulator (LQR) combined with an Extended Kalman Filter (EKF) for state estimation based on output energy measurements. This subordinate feedback scheme suppresses bifurcations and mitigates excitations induced by changes in the spectral pulse shape. On top of this control loop, we apply model-based iterative learning control (ILC) to asymptotically track desired output spectra. Projected ILC laws are used to adapt both the input filter and the provided pump-light intensity. The proposed method is validated in simulation on a distributed-parameter model calibrated to measurements of a Ho:YAG-based RA. Results demonstrate robust convergence to desired pulse shapes and highlights its feasibility for real-time implementation.