Active frequency combs in fast and slow gain media

Integrated frequency combs based on active cavities are of interest for sensing, but they are typically described very differently depending on the gain dynamics. I will discuss our recent demonstration of an operator-based mean-field theory that non-adiabatically describes the dynamics of bidirectional active cavities, both fast and slow. It is based on first principles and semi-exactly replaces the Maxwell-Bloch equations, but is flexible enough to accomodate non-trivial lineshapes and population dynamics. Our results are general and apply to any bidirectional or unidirectional active cavity, and as a result, generalize to essentially any chip-scale laser.