Investigations On The Nonlinear Dynamic Characteristics Of Quantum Dot Laser Under External Perturbation

Semiconductor lasers composed of low-dimensional materials can be divided into quantum well lasers,quantum wire lasers and quantum dot lasers(QDL)according to their structure of the active region.QDL is a new type of self-assembled nanometer-sized laser whose active layer is composed of some discrete quantum dots.Electrons and holes are three-dimensionally confined into several tens of nanometer-scale semiconductor crystals.Owing to the three-dimensional quantum confinement of carriers,the QDL has some promising advantages such as low threshold current density,low phase noise,low chirp,weak optical feedback sensitivity,high temperature stability and high beam quality.The QDL is expected to take place of the traditional quantum well laser in the fields of next-generation photonic integrated circuits,optical interconnection,optical information processing,and photonic neurons.Now,high-density,high-optical quality quantum dot have been realized through improved molecular beam epitaxy growths and QDL with better temperature characteristics are in the stage of mass-production for a data-com market.Because of the discrete energy level structure and finite intraband relaxation time,the QDL has different lasing modes.A QDL can exhibit ground-state(GS)transition in addition to excited-state(ES)transition,these two emission states can occur exclusively or simultaneously.Accordingly,a QDL can emit two wavelengths that differs several tens of nanometers,thus being possible for terahertz application.For simplify the descriptions in the following discussion,the free-running QDL emitting exclusively in the GS and ES are named as GS-QDL and ES-QDL,and the QDL emitting simultaneously from GS and ES is called two-state QDL.The previous research shows that,under suitable external perturbation,the QDL with different emission modes can exhibit rich nonlinear dynamic behaviors such as periodic pulse,low-frequency antiphase fluctuation,bistability and chaos.The research on these dynamic characteristics not only opens up a new way for the application of the QDL in the fields of photonic microwave signal generation,chaotic secure communication,all-optical switching,chaotic radar and all-optical information conversion.But also has a very important practical significance for understanding the physical mechanism of nonlinear dynamics generation in these systems and improving the system performance of such laser devices.Based on this consideration,we systematically study the nonlinear dynamic characteristics of the QDL with different emission modes under external optical injection and optical feedback in addition to its application in photonic microwave signal generation,aiming to deeply analyze the various dynamic characteristics and internal physical mechanism of the QDL system under external perturbation,and explore the nonlinear dynamic control method.The research contents and results are as follows:1.Based on the exciton model of the QDL,the nonlinear dynamics of a two-state QDL subject to optical injection is numerically studied.The simulation results show that,for a two-state QD laser operating at the GS and ES emitting simultaneously,through adjusting the injection parameters,the two emission states can exhibit the stable,injection locking,suppression,period-one,period-two,multi-period and chaotic pulse states when the frequency of the injection light is close to the GS emission frequency.Further mapping of these dynamic states in the parameter space of injection strength and frequency detuning,it is found that the complex dynamic behaviors are mainly distributed in the negative frequency detuning region.In addition,the complexity of the chaotic signal is qualified by the permutation entropy(PE)calculating,and the high complexity signal with PE value over 0.95 is obtained.Moreover,within a certain frequency detuning range,the ES emission can be completely suppressed by increasing the injection strength.The results can provide a theoretical support for the application of the two-state QDL in related fields.2.Based on the electron-hole asymmetry model of the QDL,the power-induced lasing state switching and bistability in a two-state QDL under optical injection is investigated theoretically.The studied results show that,when a free-running two-state QDL emit from the GS under relativity low bias current,a power-induced lasing state switching between the GS and the ES is obtained by employing optical injection with a frequency close to the ES emission frequency.In addition,for the different scanning routes of the injection power,the critical injection power required for the state switching is different,which results in state bistability.For forward scanning injection power,as the frequency detuning increases,the injection power required for the state switching decreases gradually and exhibits slight fluctuations.However,for backward scanning injection power,with the increase of frequency detuning,the injection power required for the state switching exhibits obvious fluctuations.The width of the hysteresis loop fluctuates with frequency detuning,and the fluctuation amplitude is raised with the increase of the bias current.Moreover,it is shown that the inhomogeneous broadening factor and electron escape rate have significant impacts on the bistability.3.Based on the exciton model of the QDL,the nonlinear dynamics of the GS-QDL under external optical injection is numerically studied.The results show that the GS-QDL can generate period-one,period-two,multi-period,chaotic pulse and injection locking states under suitable injection parameters.By analyzing the distribution of these dynamic states in the injection parameter space,it is found that the area of the complex dynamic states is small.Moreover,the complexity of the chaotic signals generated by the GS-QDL is quantified by the PE calculation.It is shown that the complexity of chaotic signals is less than 0.90,which indicates that the GS-QDL is low sensitivity to external optical injection.In addition,the characteristics of the photonic microwave signals generated by a GS-QDL simultaneously subject to optical injection and optical feedback are numerically investigated.First,the performances of the microwave signal generated by an optical injected GS-QDL operating at the period-one state are analyzed.The mappings of the frequency and intensity of the generated microwave in the parameter space of the frequency detuning and injection strength are given,which are roughly similar with those reported experimentally.Next,an optical feedback loop is further introduced to the optically injected GS-QDL for compressing the linewidth of the microwave signal,and the results demonstrate that the linewidth of the generated microwave can be reduced by at least one order of magnitude under suitable feedback parameters,indicating that the introduction of external optical feedback can improve the quality of microwave signals.Finally,the effect of the linewidth enhancement factor(LEF)on the generated microwave signal is analyzed,and found that a smaller linewidth enhancement factor helps to generate a narrower linewidth microwave signal.4.Based on the exciton model of the QDL,the nonlinear dynamic characteristic of an ES-QDL under optical injection is investigated theoretically.The results show that,under proper injection parameters,the ES-QDL can exhibit rich nonlinear dynamical behaviors such us the injection locking,period-one,period-two,multi-period and chaotic pulsation.Through mapping of these dynamic states in the parameter space of frequency detuning and injection coefficient,it is found that the injection locking occupies a wide region and the dynamic evolution routes exhibit multiple forms.The complexity of the chaotic pulsation state is quantified by the PE calculation,and the parameter range for obtaining the high-complexity chaotic signals is determined.Moreover,the effect of the LEF on the dynamical distribution of the ES-QDL is discussed.As the value of LEF increases,the chaotic area expands(shrinks)in the positive(negative)frequency detuning region,and the injection locking region gradually shifts towards the negative frequency detuning.In addition,the enhanced photonic microwave signal generation by using an ES-QDL under both optical injection and optical feedback is numerically studied.Within the range of period-one dynamics caused by the optical injection,the variations of microwave frequency and microwave intensity with the values of frequency detuning and injection strength are exhibited.It is found that the microwave frequency can be continuously tuned by adjusting the injection parameters,and the microwave intensity can be enhanced by changing the injection strength.Moreover,considering that the generated microwave has a wide linewidth,an optical feedback loop is further employed to compress the linewidth,and the effect of feedback parameters on the linewidth is investigated.It is found that with the increase of feedback strength or delay time,the linewidth is evidently decreased due to the locking effect.However,for the relatively large feedback strength or delay time,the linewidth compression effect becomes worse due to the gradually destroyed period-one dynamics.Besides,through optimizing the feedback parameters,the linewidth can be reduced by up to more than one order of magnitude for different microwave frequencies.Compared with the photonic microwave signal generated by GS-QDL,the frequency of the microwave signal generated by ES-QDL is more sensitive to the fluctuation of the injection intensity,and the linewidth is larger,which is due to the smaller relaxation damping ratio of the ES-QDL.Therefore,the performance of microwave signals generated by GS-QDL is better than ES-QDL.Finally,the emission state switching of the ES-QDL with external optical feedback is studied experimentally.The results show that,after introducing external cavity optical feedback,the GS emission can be excited at an appropriate feedback ratio and the ES emission can be completely suppressed when the feedback ratio is large enough,the emission state switching is appeared.At relatively low bias current,owing to mode competition,the antiphase fluctuation of ES and GS emissions occurs during the process of state switching,but this phenomenon is not observed at the relativity high bias current.In addition,it is found that the critical feedback ratio for switching increases with the increase of bias current.The research in this section provides theoretical and experimental support for the application of ES-QDL in related fields.