We focus our attention on the selection processes and turn-on delay for the switch-on of different transverse modes in VCSELs. We consider different excitation conditions and active-region diameters, addressing the experimental situations in which the transient response of gain-guided VCSELs to a current pulse is taken into account (1 ns duration, 100 ps rise-time). We consider two thermal effects, namely, a temperature dependent detuning between the band-gap and the cavity resonance and the thermal lensing (TL) effect.
We study theoretically the non linear polarization dynamics of Vertical-Cavity Surface-Emitting Lasers in the presence of an external cavity providing delayed optical feedback and cross polarization re-injection. We show that far from the laser threshold, the dynamics remains confined close to the equatorial plane of a Stokes sphere of a given radius and we reduce the dynamics to a dynamical system composed of two phases: the orientation phase of the quasi-linear polarization and the optical phase of the field. We explore the complex modal structure given by the double feedback configuration and recovers as particular cases the Lang-Kobayashi modes and the modes founds by Giudici et al. [1]. We also re-interpret the square waves switching dynamics as phase kinks.
We prove that groups acting geometrically on delta-quasiconvex spaces contain no essential Baumslag-Solitar quotients as subgroups. This implies that they are translation discrete, meaning that the translation numbers of their nontorsion elements are bounded away from zero.