Vertical external-cavity surface-emitting lasers: mode-locked dynamics and master equation

Abstract

Passively Mode-locked (PML) lasers can generate ultra-stable picosecond pulse trains with high repetition rates and are fundamental components of many modern technologies. Vertical External-Cavity Surface-Emitting Lasers (VECSELs) based on III-V semiconductor nanotechnology and operated in the PML regime are a particularly versatile design that consists in coupling a low finesse gain cavity, the “half VCSEL”, to a resonant saturable absorber mirror (RSAM) micro-cavity. The interplay between these two detuned micro-cavities leads to a variety of regimes, among them ultra-low (MHz) repetition rate Mode-Locking in the so-called long cavity regime where the gain recovery is much shorter than the cavity round-trip. Our work is the first theoretical study to show the crucial influence of the relative detuning between the two coupled micro-cavities and to explain how the cavity-induced chromatic dispersion influences the dynamics of the pulses. Our analysis use a first principle model based upon Delay Algebraic Equations that elegantly model the multiple reflections in the external cavity, and that contains naturally the chromatic dispersion induced by the detuned micro-cavities. We identify the cavity detuning as an experimentally crucial design parameter that can defines the range of existence of stable emission and we show that the latter induces a regime in which the pulses develop an apparent wiggling motion, which is rarely observed in time invariant, autonomous dynamical systems. Lastly, we present for the first time a rigorous derivation of the equivalent Haus Master Equation for a VCSEL-RSAM system that contains the effect of the gain micro-cavity filtering as well as the second and third order dispersion stemming from the mode pulling-pushing between the coupled detuned cavities. We identify as well as an effective saturation parameter, dressed by the micro-cavity effect.