Polarized Frequency Combs in a Mode-Locked VECSEL

We present a detailed and rigorous derivation of the delay differential equations of the spin-flip model for vertical external cavity lasers with a semiconductor saturable absorption mirror. This model describes mode-locked semiconductor lasers in the ring-resonator geometry with unidirectional lasing. This contribution completes a previous communication [Vladimirov et al.
Opt. Lett.
, 45, 252 (2020)]. Furthermore, we present a comprehensive analytical derivation that considers phase and amplitude anisotropies, as well as the different delay times for orthogonal linear polarizations. Our findings demonstrate the coexistence of two linearly polarized frequency combs generation with slightly different repetition rates, which can be attributed to the birefringence-induced time-of-flight difference.