A Reliable Master Equation For Passively Mode-Locked Lasers

A rigorous and comprehensive theoretical framework for describing passively mode-locked lasers is a long-sought goal in laser physics since the seminal contributions of Hermann Haus five decades ago. When passive mode-locking (PML) is achieved using a saturable absorber, Haus proposed two separate theoretical frameworks for describing the fast and slow [1] saturable absorber cases. As for the gain dynamics, Haus master equation (ME) approach in general requires that the gain evolution is much slower than the cavity roundtrip time, which makes it unsuitable for many semiconductor lasers. An alternative PML description in semiconductor lasers has been pursued using delay differential equations resulting in the Vladimirov-Turaev (VT) model [2] which, unlike Haus approach, aims at capturing large changes of the light field per cavity roundtrip. More recently, MEs for PML have been derived from the VT model [3], [4], and the predictions from both approaches have compared successfully. Both these approaches, however, result in mathematical problems or physical limitations: 1) The lack of periodic boundary conditions for the gain and absorption variables [3] requires special care to avoid numerical artifacts since coherent structures drift, causing the pulses to exit/enter from one side of the temporal simulation window. 2) The methodology in [3] requires the assumption of gain recovery times exceedingly slower than the cavity roundtrip time and the saturable absorber, representing a problem to external-cavity semiconductor lasers.