Dispersive Instabilities In Passively Mode-Locked Integrated External-Cavity Surface-Emitting Lasers

In spite of its early discovery in 1965 [1], the passive mode locking of lasers is still a subject of intense research. A type of nonlinear cavity has appeared over the past decade, the so-called mode-locked integrated external-cavity surface-emitting laser (MIXSEL) [2], in which both the gain and the saturable absorber share the same microcavity. In this contribution, we show that due to third-order dispersion from the Gires-Tournois-interferometer-like microcavity, pulses can have a series of decaying satellites on the leading edge [5]. The schematic setup of a MIXSEL system is depicted in Fig. 1 (a). We consider the case of a resonant cavity and we denote the microcavity field over an antinode by E and the field in the external cavity impinging on the top distributed Bragg reflector by Y. After normalization, one obtains the rate equations for the field E, the gain N
1
, and the absorber N
2
population inversions as follows [3],[4]:\begin{align*} & \dot E = \left[ {\left( {1 - i{\alpha _1}} \right){N_1} + \left( {1 - i{\alpha _2}} \right){N_2} - 1} \right]E + hY\tag{1} \\ & {\dot N_1} = {\gamma _1}\left( {{J_1} - {N_1}} \right) - |E{|^2}{N_1},\quad {\dot N_2} = {\gamma _2}\left( {{J_2} - {N_2}} \right) - s|E{|^2}{N_2}\tag{2} \\ & Y = \eta O(t - \tau ) = \eta [E(t - \tau ) - Y(t - \tau )].\tag{3}\end{align*}