Investigation On Polarization State Bistability Characteristics In A Vertical-cavity Surface-emitting Laser Subject To Parallel Optical Injection

Semiconductor lasers?SLs?have the advantages of small size,lower cost,and high reliability,which are widely utilized in the increasing number of application fields.SLs can be driven into various nonlinear dynamical states after introducing optical injection,such as period one,period two,quasi-period,and chaos,as well as polarization switching and injection locking which have potential applications in the generation of photonic microwaves,fast physical random number,secure optical communication,chaotic lidar,etc.As a type of SL currently under development,vertical-cavity surface-emitting lasers?VCSEL?have received more attention because of their unique features,such as low threshold current,easy fabrication into two-dimensional arrays,high coupling efficiency to optical fibers,two orthogonal polarization modes and low manufacturing cost,and then bistability is typically used in popular communication fields such as optical communications,optical storage,and optical interconnects.Research shows that when system parameter of a VCSEL under parallel optical injection?POI?is continuously varied along different routes,polarization state bistability?SB?occurs:VCSEL appear pure-mode state which is injection locking?IL?or different dynamic behaviors by one route,however VCSEL occurs polarization switching?PS?and appear mixed-mode state by another route.Very recently,such SB is experimentally and theoretically reported,but there is no attention to the dependence of hysteresis loop width on the adjustable parameters.In this paper,we have theoretically and experimentally investigated the characteristics of such a SB and focus on the dependence of hysteresis loop width on frequency detuning and injection power for a VCSEL biased at different currents subject to POI.Based on the established SFM theoretical model,the SB characteristics of VCSEL under different operating currents are theoretically explored.The polarization directions of the free running VCSEL at two different currents are orthogonal,and the injected light is always along the lasing polarization direction in the solitary VCSEL.The theoretical simulation results show that:in the case that the injected light frequency is less than the frequency of lasing polarization mode,the VCSEL exhibits the SB phenomenon when the injection power(P_inj)is varied along different paths,ie,type I SB.Under POI,in the case of fixing frequency detuning???defined as the frequency difference between injected light and the free-running VCSEL lasing polarization mode?,the suppressed polarization mode of solitary VCSEL may be switch on or off for a given P_inj depending on the varying route of P_inj.Further,the dependence of SB on negative??are displayed.With the increase in|??|>5,there is no large fluctuation for the width of the hysteresis loop located at the smaller P_inj,while the width of that located at the larger P_inj tends to increase quickly.In addition,the minimum P_inj required for the suppressed mode of free running VCSEL to be switched on and off during the process of increasing P_inj is given,named as the PS point.Similarly,the values of PS points also increase with increasing|??|>5 and that occurs at the larger P_inj increase quickly.On the other hand,the type II SB is further studied,that is,the SB phenomenon occur by varying??along different paths in VCSEL under parallel optical injection for a given P_inj.There also exist two hysteresis loops in which the laser may operate at a pure-or mixed-mode state and both are also observed in the condition of??<0.With the increase of P_inj,the hysteresis loop width located at lower|??|increases sharply and then decreases after reaching a maximum.However,for the hysteresis loop located at higher|??|,the loop width gradually increases with the increase of P_inj.Based on this,SB phenomenon under POI is experimentally investigated.The experimental results show that the results of the type I SB are very good agree with the theoretical results,excluding the fraction of power which the parallel injection light is reflected on the surface reflection of the laser in the experiment.