This research investigated the critical slowing down in polarization switching (PS) of vertical-cavity surface-emitting lasers (VCSELs). The experiments were performed by step-function current injection in two types: step-up and stepdown. In the case of step-up and step-down, the relationship between relaxation time and final current in this experiment resembles critical slowing down (CSD). The critical currents of two step-function current experiment are compared. The PS in this experiment is a static case. We also find that the divergence of relaxation time follow a power law. These results contribute to the understanding of the mechanism of CSD in VCSEL's PS (VPS).
The phase transition in the polarization switching (PS) of vertical-cavity surface-emitting lasers (VCSELs) was recently reported to be a second-order phase transition (SOPT). However, some features of this phase transition indicate that the VCSEL’s PS (VPS) is different from the traditional SOPTs. Most of the phase transition investigations of the laser employ the laser’s intensity as the order parameter. In Landau’s paradigm, that parameter evolutes from zero to non-zero values, or vice versa, during SOPTs, corresponding to a transition between a disordered phase and an ordered phase. Nevertheless, in the VPS, the laser’s intensity remains constant before and after the PS, revealing an order-to-order transition. Furthermore, the laser’s transverse modes cannot transfer to each other through continuous deformations in geometry. That feature attributes a topological characteristic to the laser’s transverse modes. The spatial coherence of the laser also implements a globally geometric characteristic to the laser’s output. Accordingly, there are two similarities between the VPS and quantum phase transitions (QPTs) with topological order. First, both of them belong to the orderto- order phase transitions. Second, in both transitions, two ground states are orthogonal, and are degenerate at the critical point. This paper investigated the analogy between the QPT with topological order and the VPS, exploring that the VPS has a potential to simulate the QPTs of other physical systems.
An Ising simulation is used to interpret the phase transition in the polarization switching (PS) of vertical-cavity surfaceemitting lasers (VCESLs) in this paper. From a point of view of spatial coherence, a simulation with Gaussiandistribution interaction shows a weak first-order phase transition for disorder-to-order transition due to the inhomogeneous interaction in space. For the order-to-order transition in the VCESL’s polarization switching (VPS), the Ising simulation with an external field could give an appropriate description to understand the interaction in VPS and suggest VPS is a first order phase transition (FOPT). Furthermore, via comparing with the Ising model with an external field, the interaction in VPS system should be strong enough to make whole system be in a spontaneous order state. Moreover, there is an injected signal related to injected current in VPS system and playing a role as external field in Ising model. This injected signal could cause the two degenerate states separate into a metastable state and a stable state. The last results which is modulating iteration times of Ising simulation with an external field indicates that the variation of the PS currents regarding the modulation frequency is a dynamical result. This investigation would give numerous contributions for understanding the phase transition and the interaction in VPS’s system.