Investigations On The Nonlinear Dynamic Characteristics Of Multi-transverse Mode Vertical-cavity Surface-emitting Laser Subject To External Perturbation

Semiconductor lasers can be divided in two main categories depending on the structure and light emitting characteristics of the active area:edge-emitting lasers?EEL?and vertical-cavity surface-emitting lasers?VCSELs?.The configuration of the VCSEL includes multilayered high reflectivity Bragg reflectors?DBR?of the top and the bottom,conductive confinement region,active region,and substrate.The light is emitted from the perpendicular surface of the semiconductor substrate.Compared with conventional EEL,the configuration and manufacturing process of VCSEL are different,and VCSEL possess some unique advantages,such as single-longitudinal mode operation,low threshold current,circular output-beam profile,high coupling efficiency,high-speed modulation,easy fabrication in two-dimensional arrays,and low manufacturing cost,and so on.Therefore,VCSEL has attracted more attention and become one of the hot topics of research.In recent years,much research has shown that,VCSEL subject to external perturbations,such as optical injection,optical feedback,current modulation,photoelectric feedback,can exhibit period one,period doubling,injection locking,quasi-period,and chaos state with the appropriate parameters.Meanwhile,due to the cylindrically symmetric structure and weak anisotropy,VCSEL with the influence of external perturbation easily induces the particular polarization switching and polarization bistable.These nonlinear dynamics have potential applications in chaos secure optical communications,photonic microwave generation,optical switches,optical memories,all-optical information conversion,high-speed pulse ranging,laser lidar,optical information processing,and fast physical random number generation.At present,a lot of research on single-transverse-mode VCSEL has been conducted,which has made people deeply understand the performance of VCSEL.It is expected to replace EEL in the fields of optical communication and optical interconnection and so on.With the gradual improvement of the manufacturing process,the stability of VCSEL has been continuously improved.However,due to its relatively large radial size,when the bias current of VCSEL is high,the high-order transverse mode can be lased for the spatial-hole burning effect?SHB?and the VCSEL is operated in a multi-transverse mode state.Compared with single-transverse mode,the research on multi-transverse mode is still scarce,because multi-transverse mode is prone to produce inter-mode crosstalk,which is not conducive to signal transmission in practical applications.Therefore,the previous researches are focused mostly on the case of suppressing high-order transverse mode,and making VCSEL operated in single-transverse mode.However,with the development of technology,multi-transverse mode has some new applications,such as short-reach links optical communication,high-performance computing,parallel optical interconnects,multi-channel chaotic secure communication,inter-chip interconnect,multi-channel physical random number generation,and mode-division multiplexing.Further explore the nonlinear dynamic characteristics of multi-transverse mode VCSEL with external perturbation,and analyze its intrinsic physical mechanism,which has important guiding significance for new application fields of multi-transverse mode VCSEL.The main work and results of our studies are summarized as follows:1.Based on the Lang-Kobayashi model,a multi-channel wideband chaotic signal generated by a multi-transverse mode VCSEL with chaotic optical injection is analyzed.In the model,a multi-transverse mode VCSEL?master laser,ML?under optical feedback can be driven into the chaotic states,and then these chaotic signals are unidirectionally injected into another multi-transverse mode VCSEL?slave laser,SL?.In the simulation,taking two low-order transverse modes of LP₀₁ and LP₁₁ as an example and taking into account the spatial effects and carrier diffusion,and analyzing two cases of total chaotic optical injection and selected chaotic optical injection.The results show that under suitable optical feedback,both the LP₀₁ and LP₁₁ modes of the ML can be driven into the chaotic states with relatively narrow bandwidths about 8 GHz.Under the global chaotic optical injection,for a given frequency detuning,by increasing the injection strength,the chaotic bandwidths of the LP₀₁ and LP₁₁ modes of the SL increase first,and then decrease after reaching a maximal value.When the injection strength is large enough,both the chaotic bandwidths of the LP₀₁ and LP₁₁ modes from the SL are close to those of the corresponding injection chaotic signal.Meanwhile the physical mechanism has been analyzed.Next,the chaotic bandwidths of the LP₀₁ and LP₁₁ modes from the SL in the parameter space of the injection strength and frequency detuning have been described and determined the parameter regions of two-channel wideband chaotic signals.Finally,under the mode-selective chaotic optical injection,the chaotic bandwidths of the LP₀₁ and LP₁₁ modes from the SL have been analyzed,respectively.It is concluded that only the injected mode can be driven into broadband chaotic signals.2.The nonlinear dynamic characteristics of multi-transverse mode 1550 nm VCSEL under parallel optcal injection have been experimentally investigated.In the experiment,a free running multi-transverse mode 1550 nm VCSEL can emit the Y polarization component of the fundamental transverse mode(Y-LP₀₁)and the first-order transverse mode(Y-LP₁₁).The polarization of injection light is along the Y polarization component,which is defined as the parallel optical injection.The results show that,as the frequency of the injection light is closer to the frequency of Y-LP₀₁,whose frequency difference?named as frequency detuning?is fixed,during the process of continuously increasing injection power,the Y-LP₀₁ mode can exhibit four-wave mixing,injection locking,period one,period doubling,multi-period,chaos.But less dynamical states are observed for the Y-LP₁₁ mode.With the increase of the injection power,the output power of the Y-LP₁₁ mode is decreased gradually and suppressed.Therefore,multi-transverse mode 1550 nm VCSEL operates at single transverse mode,i.e.the mode selection for the fundamental mode achieves.With the increase of the frequency detuning,the minimal injection power required for achieving the fundamental transverse mode selection decreases firstly,and then increases.For a given frequency detuning,the minimum injection power becomes greater with the increase of the bias current.In addition,the case that the frequency of the injection light is closer to the frequency of the Y-LP₁₁ mode is studied.Within the suitable injection parameters,The Y-LP₁₁ mode and Y-LP₀₁ mode can show steady state,period one,multi-period,and chaos.The gain of Y-LP₀₁ mode is relatively large,and it is not easy to be suppressed.Under the experimental conditions,the Y-LP₀₁ mode has not been suppressed.3.The nonlinear dynamic characteristics of two multi-transverse mode 1550 nm VCSELs under mutually coupled are experimentally investigated.Under the suitable bias current,two multi-transverse mode 1550 nm VCSELs can also emit the Y polarization component of fundamental transverse mode(Y-LP₀₁)and the first-order transverse mode(Y-LP₁₁).The frequency detuning is defined as the difference of the frequency of Y-LP₀₁ from the two free running lasers.The results show that the frequency detuning and the injection parameter are the key parameters that affect the dynamic state of the output of two VCSELs.For a given frequency detuning,when the injection parameter is different,the Y-LP₀₁ and Y-LP₁₁ modes of the two VCSELs can exhibit rich nonlinear dynamics,such as steady state,period one,period doubling,multi-period,and chaos.When the injection parameter is enough large,the Y-LP₁₁mode of both lasers can be suppressed,and the mode selection phenomenon of the Y-LP₀₁ mode is obtained.Meanwhile,when the two mutually coupled VCSELs operate in the periodic states,a localized synchronization is observed.In addition,the X-LP₀₁ and Y-LP₀₁ modes of VCSEL2 can coexist in the proper range of the frequency detuning and injection parameter.Additionally,the distribution of nonlinear dynamic states of two mutually coupled multi-transverse mode 1550 nm VCSELs in the parameter space of frequency detuning and injection parameter is described.4.A wide bandwidth optical frequency combs?OFCs?generated by optical injection gain-switched multi-transverse mode 1550 nm VCSEL is experimentally studied.The bias current of multi-transverse mode 1550 nm VCSEL is modulated by external signals from a microwave frequency synthesizer?MFS?.Firstly,when the bias current is low,the multi-transverse mode 1550 nm VCSEL only emits the fundamental transverse mode(LP₀₁).The results show that,under the appropriate modulation parameters,the multi-transverse mode 1550 nm VCSEL with optiacal injection can be driven into OFCs.With the increase of the wavelength of the injection light,the bandwidth of OFCs increases first,after reaching a maximal value,and then decreases,and which the intrinsic physical mechanism is analyzed.When two orthogonal polarization components of LP₀₁ mode coexist,the bandwidth of the OFCs reaches a maximum value that is about 95 GHz.Next,the bias current is increased,and the multi-transverse mode 1550 nm VCSEL can simultaneously emit the fundamental transverse mode(LP₀₁)and the first-order transverse mode(LP₁₁).Under the different modulation power,the OFCs generated by the multi-transverse mode 1550 nm VCSEL with double optical injection is analyzed.The results show that,under the appropriate injection parameters,when the modulation intensity is low,the multi-transverse mode1550 nm VCSEL can output two-channel flat OFCs.While the modulation power is strong,the OFCs generated by LP₀₁ mode and LP₁₁ mode of multi-transverse mode1550 nm VCSEL can be combined and obtain a flat OFCs with the bandwidth over 150GHz.The research opens a new field for the application of multi-transverse mode VCSELs.