Spectral modeling of laser systems with diffractive cavities

We present a comprehensive modeling framework for predicting the spectral output of pulsed, narrow-linewidth lasers based on dispersive optical resonators. Our approach integrates polarization-dependent losses, mode steering, and dispersive effects within a unified round-trip matrix formalism, enabling the calculation of a wavelength-dependent resonator feedback function. By combining this feedback function with transient gain dynamics, the model provides estimates of the energy distribution among longitudinal modes and resulting laser linewidths for lasers in transient regime. The linewidths predictable by our model spans from a few hundreds MHz, limited by spectral phase noise, and up to tens of GHz, limited by temporal resolution of the gain dynamics simulation. We compare the simulation results with experimental measurements of Ti:Sapphire laser configurations with intra-cavity etalons, birefringent filters, and diffraction gratings. The agreement with experimental results demonstrates that this framework offers a practical tool for resonator design and optimization, bridging the gap between traditional element-wise analysis and holistic spectral prediction. Our method supports the development of tunable, narrow-linewidth lasers for applications such as resonance-ionization and high-resolution spectroscopy.