Verified comprehensive approach for the design of optically pumped Sub-Picosecond passively Mode-Locked VECSEL

This paper presents a design method for the passively mode-locked Vertical External Cavity Surface Emitting Laser (VECSEL) combining the Haus master equation (HME) with the traveling wave model (TWM). In the traditional method for solving the HME using the split-step Fourier transform, the gain chip is considered as an operator in the frequency domain. However, this approach does not adequately address how variations in the pump power affect the laser output and carrier density. On the other hand, the TWM provides a detailed modeling of laser outputs and carrier density rates based on the parameters of the gain and absorber chips. However, this approach is not suitable for long-cavity configurations due to the exceptionally large processing volume required. The method introduced in this paper resolves this problem by coupling the HME with the TWM equations, thereby accurately determining how laser output and carrier density depend on parameters such as pump power and chip structure. In this regard, we designed a Z-type cavity configuration using this model to achieve a stable pulse train with a duration of 795 fs and an average output power of 900 mW, operating at a pulse repetition rate of 892.5 MHz corresponding to 1.13 kW peak power. This model can analyze the dynamics of the carrier density and output pulse of laser, as well as identify regions of pulse instability. To the best of our knowledge, this is the first demonstration of coupling the HME with TWM to achieve kilowatt peak power pulses in passively mode-locked VECSELs, while also investigating the effect of optical pump power on the formation of the output pulse and the rate of change of carrier density within the active medium and the SESAM.