Step-Pulse Modulation of Gain-Switched Semiconductor Pulsed Laser

Article Step-Pulse Modulation of Gain-Switched Semiconductor Pulsed Laser

Bin Li , Changyan Sun, Yun Ling *, Heng Zhou and Kun Qiu

School of Information and Communication Engineering, University of Electronic Science and Technology of China, Chengdu 611731, China; [email protected] (B.L.); [email protected] (C.S.); [email protected] (H.Z.); [email protected] (K.Q.) * Correspondence: [email protected]

Received: 12 December 2018; Accepted: 8 February 2019; Published: 12 February 2019

Featured Application: The proposed novel approach presented in this paper offers a highly effective modulated method for a gain-switched semiconductor laser. As a result, we can acquire the output pulse with a higher peak power (the limit can be reached) and shorter width and can be incorporated as a practical and cost-effective approach for many ﬁelds which need high extinction ratio short pulse, such as the optical time domain reﬂectometry.

Abstract: To improve the peak power and extinction ratio and produce ultra-short pulses, a novel approach is presented in this paper offers a highly effective modulated method for a gain-switched semiconductor laser by using step-pulse signal modulation. For the purpose of single pulse output, then the effects on the output from the gain-switched semiconductor laser are studied by simulating single mode rate equation when changing the amplitude and width of the modulated signal. The results show that the proposed method can effectively accelerate the accumulation speed of the population inversion and we can acquire the output pulse with higher peak power and shorter width. Compared with the traditional rectangular wave modulation, this method is advantageous to obtain a high gain switching effect by increasing the second modulation current and reduce the pulse width to saturation at the best working point. It can be incorporated as a practical and cost-effective approach for many ﬁelds which need high extinction ratio short pulse, such as the optical time domain reﬂectometry.

Keywords: gain-switched semiconductor laser; rate equation; step modulation; simulation; curve ﬁtting

1. Introduction In recent decades, the short pulsed laser has been widely utilized in the ﬁelds of production, medical, detection and communication, and so on, as the ultra-short pulse laser technology develops rapidly [1,2]. Among various types of lasers, semiconductor lasers are suitable for producing ultra-short optical pulses because of their large gain bandwidth, small volume and high modulation efﬁciency [3–5]. The direct modulation technology of the semiconductor laser is mainly used to generate optical pulses, which has the advantages of simple operation, low cost, and mature technology. However, in order to achieve high-speed modulation in the optical communication system, the driving current is higher than the threshold current. As a result, the output pulse width is similar to that of the driving current, and the pulse power is proportional to the amplitude of the driving current. There is a trade-off between the high extinction ratio and the short pulse width [6–9]. Gain-switched technology is another direct modulation method to generate short optical pulses by using the relaxation oscillation of the semiconductor laser, and it has been widespread use because of

Appl. Sci. 2019, 9, 602; doi:10.3390/app9030602 www.mdpi.com/journal/applsci Appl. Sci. 2019, 9, 602 2 of 8 its compact structure, stable performance, and flexible setting. The relaxation oscillation is a transient phenomenon in lasers, which refers to a series of gradually decaying spike pulse sequence attributing to the self-oscillation before the laser achieves stabilized output. The standard gain-switched arrangement is to drive a laser, biased below the threshold. The idea is to excite the first spike of relaxation oscillation, and terminate the electrical pulse before the onset of the second optical spike, resulting in a short light pulse. Repeat this process to achieve a pulse sequence on the order of picosecond [10,11]. Compared with other pulse generation methods, this idea has an advantage that a simple driving circuit can be used to generate an ultra-short optical pulse, and the output pulse width is much smaller than the modulation current pulse. Theoretical analysis indicates that the photon lifetime of a typical semiconductor laser is 2~3 picosecond, so a ten picosecond laser pulse can be produced theoretically by using a hundred picosecond current pulse in the process of gain switching [12,13]. The characterization of the gain-switched semiconductor laser pulse is also affected by the modulation parameters. In Reference [14], it has been verified that using the rectangular wave modulation can achieve high pulse power and a small tail, compared to the sine and triangle waves with the same magnitude. Besides, the peak power of the output pulse increases with the increase of rectangular modulated signal width, and finally reaches saturation, according to the study on relaxation oscillation [15]. According to the typical study for the gain switching process of the semiconductor laser, the peak power and width of the output pulses are mainly determined by the accumulation speed after the carrier density reaches the threshold. Based on this theory, a step-pulse modulated signal is proposed on more peak power improvements. In this paper, we primarily focus on the effect of step modulated signal’s variation on gain-switched semiconductor lasers, demonstrate the feasibility of the proposed methods and find the best modulation parameter. Moreover, we get a function between the amplitude of the signal and the pulse width by curve fitting technic. The simulation results show that the proposed scheme can further compress the laser pulse width and increase the amplitude value. The final simulation results show that the proposed method can further compress the laser pulse width and increase the amplitude value.

2. Step Modulation Principles The relaxation oscillation process can be set up by the rate equations, in which the steady and dynamic characteristics of a semiconductor laser can be described efﬁciently and accurately with the following single mode rate equations [16–18]:

dN J g (N − N )S N = − 0 t − , (1) dt eV 1 + εS τN

dS Γg (N − N )S S N = 0 t − + Γβ , (2) dt 1 + εS τP τN The output power is given in terms of the photon density [19]:

η0Vhν Pout = S. (3) 2ΓτP where N and S are the carrier density and photon density, J is the injected current, other parameters and their typical values are shown in Table1. Figure1 shows the evolution in the carrier and photon densities during a gain switch cycle, assuming that the bias current is 0 and that the initial photon density in the laser can be ignored. A rectangular wave modulation process is given in Figure1a: At time t0, a current pulse is applied to a laser with the amplitude of I0 and pulse width of T0. The initial rate of increase in photon density is very low, due to its low initial value. Without being signiﬁcantly consumed by stimulated emission, injected electrons rapidly build the carrier density up to threshold Ntr at time t1. After that, the population inversion can be achieved, and the laser begins to emit the light pulse. When the Appl. Sci. 2019, 9 3

τ -9 N Total spontaneous emission carrier lifetime 3×10 s τ -12 Appl.P Sci. 2019, 9, 602Average photon lifetime inside the cavity 10 s 3 of 8 Γ Mode confinement factor 0.44 - ε Gain compression factor 3.4×10-23 m-3 stimulated emission begins to consume the carrier signiﬁcantly, the population inversion reaches the β Fraction of the spontaneous emission 4×10-4 - maximum value Nmax. With the generation of laser pulses, the carrier density drops to the threshold at e Electronic charge 1.6×10-19 C time t2, at which point the output pulse power reaches its peak value. At this time, the current should V Active region volume 9×10-17 m3 be terminated quickly to restrain the secondary oscillation. Therefore, to form a single pulse output η Differential quantum efficiency 1 - with0 high peak power, the rectangular current pulse must be terminated for the ﬁrst time when the h Plank’s constant 6.6×10-34 J·s carrier density drops to the steady-state threshold [20]. ν Frequency 193.9×10-12 Hz

FigureTable 1 shows 1. Descriptions the evolution of parameters in the carrier in Equations and photon (1)–(3) densities and their during values a used gain in switch our numeral cycle, assuming simulation.that the bias A dashcurrent (-) in is the 0 and “Units” that column the initial means photon that the density valueis in dimensionless. the laser can be ignored. A rectangularParameter wave modulation Symbol process is given Description in Figure 1(a): At time t0 , a current Value pulse is applied Units −12 3 −1 to a laser with theg0 amplitude of I0 and Gainpulse slope width constant of T0 . The initial rate 3of× increase10 in photonm s 24 −3 density is very low,Nt due to its low initialCarrier value. density Without at transparency being significantly consumed1.2 × 10 by stimulatedm −9 τN Total spontaneous emission carrier lifetime 3 × 10 s emission, injected electrons rapidly build the carrier density up to threshold Ntr − 12at time t1 . After τP Average photon lifetime inside the cavity 10 s that, the populationΓ inversion can be achieved,Mode conﬁnement and the laser factor begins to emit the light 0.44 pulse. When the - stimulated emissionε begins to consume theGain carrier compression significantly, factor the population3.4 inversion× 10−23 reachesm the−3 β Fraction of the spontaneous emission × −4 - maximum value N . With the generation of laser pulses, the carrier density drops4 10 to the threshold e max Electronic charge 1.6 × 10−19 C −17 3 at time t2 , at whichV point the output pulseActive power region reache volumes its peak value. At9 this× 10 time, the currentm should be terminatedη0 quickly to restrainDifferential the secondary quantum oscillation. efﬁciency Therefore, to form 1 a single pulse - h Plank’s constant 6.6 × 10−34 J·s output with high peak power, the rectangular current pulse must be terminated for the first time ν Frequency 193.9 × 10−12 Hz when the carrier density drops to the steady-state threshold [20].

(,)IT22 (,)IT current pulse current pulse 00 (,)IT11 N Nmax max

Ntr Ntr photon density photon density carrier density carrier density

′ ′ ′ t0 t1 t2 Time t0 t1 t2 Time (a) (b) Figure 1. Evolutions in the carrier and photon densities during a gain switch cycle: (a) Modulated by Figure 1. Evolutions in the carrier and photon densities during a gain switch cycle: (a) Modulated by rectangular waves; (b) modulated by step rectangular wave. rectangular waves; (b) modulated by step rectangular wave.

The aboveThe above analysis analysis shows shows that, before that, before the carrier the carrier density density reaches reaches the threshold, the threshold, the photons the photons are are mainlymainly generated generated by the by spontaneous the spontaneous emission emission of the of laser. the laser.Afterward, Afterward, the carriers the carriers injected injected into the into the laser beginlaser begin to be converted to be converted into stimulated into stimulated emission emission photons. photons. The peak The reversal peak reversal rate of rate carrier of carrier density density R = NN/ givengiven in the in Reference the Reference [21] [21is ] is R =maxNmaxtr/,N andtr, and with with increasing increasing R,R the, the peak peak power power of of the outputoutput pulse pulseincreased increased whilewhile thethe fullfull width at half maxima (FWHM) (FWHM) decreased. decreased. Therefore, Therefore, if if we we can can increase increase the the modulationmodulation current current suddenly suddenly at at the the moment moment when when the the carrier carrier density density reaches reaches the threshold, the peak peak reversalreversal rate can be increased, increased, and and the the opti opticalcal pulse pulse with with higher higher power power and and shorter shorter width width will will be be obtained.obtained. To Todo dothis this a step-pul a step-pulsese modulated modulated signal signal is designed, is designed, as shown as shown in Figure in Figure 1(b), in1b, which in which the amplitudethe amplitude of the of first the modulation ﬁrst modulation current current is I1 , istheI1 ,pulse the pulse width width is T1 , is theT1 ,second the second modulation modulation currentcurrent amplitude amplitude is I is, andI2, and the the pulse pulse width width is is TT2. .Figure Figure 11(b)b shows shows the the step-pulse step-pulse modulation modulation process: 2 0 2 When the current is injected at time t0,′ the carrier density increases gradually and achieves the process: When the current0 is injected at time t0 , the carrier density increases gradually and achieves threshold at time t1; then the increase rate of carrier density is obviously improved and the peak power of output pulse increases as the modulation current becomes larger; ﬁnally the peak power reaches a 0 maximum when the carrier density drops to the threshold at time t2. Appl. Sci. 2019, 9 4

′ the threshold at time t1 ; then the increase rate of carrier density is obviously improved and the peak Appl.power Sci. of2019 output, 9, 602 pulse increases as the modulation current becomes larger; finally the peak power4 of 8 ′ reaches a maximum when the carrier density drops to the threshold at time t2 . According toto thethe process process of of step-pulse step-pulse modulation modulation process, process, the the primary primary function function of the of first-stagethe first- stagemodulation modulation current current (FSMC) (FSMC) is to accumulate is to accumulate the carrier, the whilecarrier, the while output the pulse output characteristic pulse characteristic is mainly is mainly affected by the second-stage modulation current (SSMC). So when0 0 Ttt<−′′, the carrier affected by the second-stage modulation current (SSMC). So when T1 < t1 − t0, the110 carrier density in densitythe laser in does the notlaser reach does the not threshold reach the after threshold the end after of thethe FSMC,end of untilthe FSMC, the SSMC until has the been SSMC injected has been for injecteda period. for Thus, a period. the SSMC Thus, isthe not SSMC fully is utilized not fully for util notized the for entire not the injected entire carrierinjected is carrier converted is converted into the 0 0 ′′−<<−0 0 ′′ intostimulated the stimulated photon. Whenphoton.t1 −Whent0 < TttTtt101 < t2 − 120t0, the laser, the has laser entered has entered the stimulated the stimulated emission emission state at statethe end at the of theend FSMC, of the andFSMC, the and SSMC the willSSMC not will entirely not entirely increase increase the carrier the carrier injection injection rate. As rate. a result, As a 0 0 combined with the studies of Reference [22], a simple design of the FSMC is T1 = t − t=−, that′′ is to say, result, combined with the studies of Reference [22], a simple design of the FSMC is1 Ttt1100 , that is the semiconductor laser works stably at the threshold level before the SSMC begins. to say, the semiconductor laser works stably at the threshold level before the SSMC begins. 3. Step Modulation Simulation and Discussion 3. Step Modulation Simulation and Discussion In order to analyze the effect of the parameter setting of the second stage modulated signal on the outputIn lightorder pulse, to analyze we establish the effect the of simulation the parameter models setting of single of the mode second rate stage equations modulated (Equations signal on (1) theand output (2)) by light SIMULINK, pulse, we which establish is a visualthe simulation simulation models of MATLAB. of singleTo mode simulate rate equations the variation (Equation of the (1)output and (2)) pulse, by weSIMULINK, excite the which semiconductor is a visual lasersimulation with aof single MATLAB. current To pulse.simulate The the amplitude variation of the output pulse, we excite the semiconductor laser with a single current pulse. The amplitude of the first-stage modulation current is set to I1 = 34 mA, and the width is T1 = 0.971 ns, which is equal to I = 34 T = 0.971 first-stagethe time of modulation carrier density current reaching is set the to threshold1 mA, for and the firstthe width time. Theis bias1 current ns, is which set to 0is mAequal in toorder the totime get of a highcarrier extinction density reaching ratio [23]. the The threshold block diagram for the of first step time. modulation The bias simulation current is set is shown to 0 mA in inFigure order2. to get a high extinction ratio [23]. The block diagram of step modulation simulation is shown in Figure 2.

Figure 2. BlockBlock diagram diagram of the step modulation for simulation in the semiconductor laser.

Figure3 shows the simulation results of output pulses at different I when the T = 64 ps. Figure 3 shows the simulation results of output pulses at different I2 when the T2 = 64 ps. From Figure3a, in which the dotted line corresponds to the end time of the modulation2 current,2 it is From Figure 3(a), in which the dotted line corresponds to the end time of the modulation current, it directly seen that with the increase of I2, the rising edge of the output pulse becomes steep, the peak istime directly is short, seen and that the with peak the power increase is of high. I2 , However,the rising edge the pulse of the width output decreases pulse becomes at ﬁrst steep, and then the peakincreases, time asis shownshort, and in Figure the peak3b. IfpowerI2 = 34is high.mA, the Ho stepwever, modulated the pulse signal width can decreases change into at first a rectangular and then modulated wave, it is clearly seen that usingI = the34 step modulation can cause pulse energy increase and increases, as shown in Figure 3(b). If 2 mA, the step modulated signal can change into a pulserectangular duration modulated decrease. wave,When itI is2 =clearly64 mA seen, the that output using power the step reaches modulation the maximum can cause value pulse at the energy time corresponding to the dotted line, also, the FWHM= pulse width is smallest. When I2 < 64 mA, the peak increase and pulse duration decrease. When I2 64 mA, the output power reaches the maximum pulse power lags behind the end time of current and the output pulse rise time is short, that is because value at the time corresponding to the dotted line, also, the FWHM pulse width is smallest. When the carrier density has not fallen to the threshold before the end of the current, even if terminating the I < 64 mA, the peak pulse power lags behind the end time of current and the output pulse rise time injection2 current there will be excess carriers converted into photons. Therefore, as the accumulation rate of carriers increases proportionally to the I2, the output pulse becomes narrow, and the peak power becomes large. When I2 = 64 mA, the output pulse has reached the peak before the current Appl. Sci. 2019, 9 5 is short, that is because the carrier density has not fallen to the threshold before the end of the current, even if terminating the injection current there will be excess carriers converted into photons. Therefore, as the accumulation rate of carriers increases proportionally to the I , the output pulse Appl. Sci. 2019, 9, 602 2 5 of 8 = becomes narrow, and the peak power becomes large. When I2 64 mA, the output pulse has reached the peak before the current is terminated, and the pulse tail will appear with the injection of is terminated, and the pulse tail will appear with the injection of excess carriers. The bigger is the I2, excess carriers. The bigger is the I2 , and the more serious is the tailing. Thus, the conclusion one is: and the more serious is the tailing. Thus, the conclusion one is: When T2 is certain, I2 should be set to T I Whenmeet the 2 condition–the is certain, 2 output shouldpower be set to reaches meet the the condition–the maximum time output is equal power to the reaches current the termination maximum timetime, is in equal order to to the minimize current thetermination width of thetime, output in order pulse. to minimize the width of the output pulse.

100 I2=34 mA 120 36

I2=44 mA 80 I2=54 mA

I2=64 mA 90 60 32 I2=74 mA

I2=94 mA 60 40 I2=124 mA FWHM (ps)

Power (mW) 28 Peak power (mW) power Peak 20 30

0 24 0.990 1.025 1.060 1.095 34 44 54 64 74 94 124 Time (ns) I2 (mA) (a) (b)

Figure 3. SimulationSimulation results results of of output output pulses pulses at at different II ,, when whenI I == 3434 mA,mA, TT =0.9710.971 ns,ns, 22 1 1 11 T2 = 6464 ps:ps: (a)) TimeTime domaindomain graph;graph; ((bb)) thethe peakpeak powerpower andand fullfull widthwidth atat halfhalf maximum.maximum. 2

The simulation results of the output pulses at different T2 are shown in Figure4, in which the The simulation results of the output pulses at different T2 are shown in Figure 4, in which the I2 = 64 mA. From Figure4a, it is directly seen that the output pulses have the similar front-end when I = 64 mA. From Figure 4(a), it is directly seen that the output pulses have the similar front-end fixing2 I2 , and the peak power increases with T2 until it reaches saturation. Similarly, with the increase of T , the changingI rule of FWHM is first reduced andT then increased, before reaching a steady value, when2 fixing 2 , and the peak power increases with 2 until it reaches saturation. Similarly, with the as shown in Figure4b. When T2 = 64 ps, the peak power of output pulse reaches the maximum for increase ofT2 , the changing rule of FWHM is first reduced and then increased, before reaching a the first time, which means the carrier density= drops to the threshold at the moment of cutting the steady value, as shown in Figure 4(b). When T2 64 ps, the peak power of output pulse reaches the driving current completely. When T2 < 64 ps, the photon density is still on the rise, so the extended maximummodulation for time the canfirst increasetime, which the cumulativemeans the carrier number density of carriers drops and to the thus threshold enhance at the the peak moment power. of cutting the driving current completely. WhenT < 64 ps, the photon density is still on the rise, so the In such a situation, if T2 is small, the gain coefficient2 changes greatly with T2 and the accumulation extendedrate of the modulation photon is fast, time which can incr leadsease to the FWHMcumulative becomes number small; of carriers else, the and front-end thus enhance of output the pulses peak change slowly, and the FWHM becomesT big. When T > 64 ps, the peak power does not changeT with power. In such a situation, if 2 is small, the gain2 coefficient changes greatly with 2 and the accumulationthe increase of rateT2 because of the photon of the is photon fast, which density leads saturation to the FWHM phenomenon. becomes However, small; else, the the extension front-end of the modulation time causes the post-stage oscillation to appear, and the pulse> tail becomes worse. of output pulses change slowly, and the FWHM becomes big. When T2 64 ps, the peak power The fall time are 28.9 ps (64 mA), 32.7 ps (74 mA), 49.2 ps (94 mA) and 83.1 ps (124 mA) respectively. does not change with the increase of T because of the photon density saturation phenomenon. As stated in the introduction, the semiconductor 2 laser would generate a series of gradually decaying However,spike pulse the sequence extension before of the the modulation laser achieves time stabilized causes outputthe post-stage attributing oscilla to thetion relaxation to appear, oscillation. and the pulse tail becomes worse. The fall time are 28.9 ps (64 mA), 32.7 ps (74 mA), 49.2 ps (94 mA) and 83.1 Therefore, when T2 = 124 ps, another peak appears on the falling edge of the pulse, which means psthe (124 terminal mA) timerespectively. of the electrical As stated pulse in the is toointr lateoduction, to suppress the semiconductor the onset of the laser second would optical generate spike. a series of gradually decaying spike pulse sequence before the laser achieves stabilized output To make it clear, the simulation output of T2 = 500 ps is used as a reference, indicated in Figure4a by = attributingdotted lines. to Thus,the relaxation the conclusion oscillation. two is:Therefore, When I2 whenis certain, T2 the124 optimal ps, anotherT2 should peak appears be equal on to the fallingminimum edge time of the required pulse, to which saturate means the the peak terminal power oftime the of optical the electrical pulse, that pulse is, regulatingis too late toT2 suppressuntil the = theoutput onset peak of the power second reaches optical saturation. spike. To make it clear, the simulation output of T2 500 ps is used Figure5a is the relation between I2 and T2, in which the green curve2 is the result based on as a reference, indicated in Figure 4(a) by dotted lines. Thus, the conclusion two is: When I2 is conclusion one, and the blue curve1 is the result based on conclusion two. It can be seen clearly that T certain,curves1 the and optimal 2 are basically 2 should coincident. be equal To to fitthe the minimum curve1 and time curve2 required separately, to saturate we the design peak an power inverse of thefunction optical expression pulse, that as is, follows: regulating T2 until the output peak power reaches saturation. a T2 = + c (4) I2 + b Appl. Sci. 2019, 9 6

60 T =34 ps 40 2 60 T2=44 ps 45 T =54 ps 2 36 T2=64 ps 50

T2=74 ps 30 T =94 ps 32 2 40 T2=124 ps Appl. Sci. 2019, 9, 602 6 of (ps) FWHM 8 Power (mW) Power Peak power (mW) 15 30 28

where the units of I2 and T2 are mA and ps. In the experimental data disposal, the coefficient of determination0 is often used as a criterion of fitting goodness.20 In the case of I1 = 34 mA and T1 =240.971 1.04 1.12 1.20 1.28 34 44 54 64 74 94 124 ns, calculations showed that the coefficient of determination of the fitting curve to curve1 is 0.99139, Time (ns) T2 (ps) and the coefficient of determination(a) for curve2 is 0.99242, when a = 4328.3 (b) mA·ps, b = 24.6 mA, Appl.c = 18.3Sci. 2019 ps., 9 Therefore, Equation (4) can be used to characterize the relationship between I2 and T2. 6 Figure 4. Simulation results of output pulses at different T , when I = 34 mA, T = 0.971 ns, 2 1 1 I = 64 mA: (a) Time domain graph; (b) the peak power and full width at half maximum. 60 2 T =34 ps 40 2 60 T2=44 ps Figure 5(a) is the relation between I2 and T2 , in which the green curve2 is the result based on 45 T2=54 ps conclusion one, and the blue curve1 is the result based on conclusion two. It can be seen clearly36 that T2=64 ps 50

curves1 and 2 are basically coincident. T To2=74 fit ps the curve1 and curve2 separately, we design an inverse function30 expression as follows: T =94 ps 32 2 40 T2=124 ps a (ps) FWHM Power (mW) Power =+ Tc2 + Peak power (mW) (4) 15 Ib2 30 28 I T where the units of 2 and 2 are mA and ps. In the experimental data disposal, the coefficient 0 20 = 24 of determination1.04 is often 1.12 used 1.20as a criterion 1.28 of fitting 34goodness. 44 54 64In the 74 case 94of I1 34 124 mA and Time (ns) T (ps) T = 0.971 2 1 ns, calculations(a) showed that the coefficient of determination of (b) the fitting curve to curve1 = is 0.99139, and the coefficient of determination for curve2 is 0.99242, when a 4328.3 mA·ps, = FigureFigure 4. SimulationSimulation= results results of of output pulses at different TT,, when whenII =3434 mA, TT ==0.9710.971ns,ns, b 24.6 mA, c 18.3 ps. Therefore, Equation (4) can be22 used to1 1characterize 1 1 the relationship = I22 6464 mA:mA: (aa)) TimeTime domaindomain graph;graph; ((bb)) thethe peakpeak powerpower andand fullfull widthwidth atat halfhalf maximum.maximum. betweenI2 and T2 . 600 50 100Figure 5(a) is the relation between digital I 2 curve1 and T2 , in which the green curve2 is the result based on digital curve2 conclusion one, and the blue curve1 fitting is the curveresult based on conclusion two. It can be seen clearly that 450 40 curves175 and 2 are basically coincident. To fit the curve1 and curve2 separately, we design an inverse function expression as follows: 300 30

(ps) a 2 50 Tc=+ T 2 + (4) Ib2 FWHM (ps)

25 I T (mW) power Peak 150 20 where the units of 2 and 2 are mA and ps. In the experimental data disposal, the coefficient = of determination is often used as a criterion of fitting goodness. In the case of I1 34 mA and = 0 0 10 T1 0.9710 ns, 250 calculations 500 showed 750 that 1000 the coefficient 1250 of determination200 400 of the 600 fitting 800 curve 1000 to curve1 I (mA) I (mA) 2 2 = is 0.99139, and the coefficient(a) of determination for curve2 is 0.99242, (b)when a 4328.3 mA·ps, = = b 24.6 mA, c 18.3 ps. Therefore, Equation (4) can be used to characterize the relationship Figure 5. ((aa)) SimulationSimulation resultsresults of of the the relation relation between betweenI andI andT based T based on conclusion on conclusion one (green one (green trace) betweenI2 andT2 . 2 2 2 2 andtrace) conclusion and conclusion two (blue two trace),(blue trace), when whenI1 = 34 I mA,= 34T1mA,= 0.971 T =ns;0.971 (b) Thens; ( peakb) The power peak power and full and width full 1 600 1 50 at half maximum of the output pulse digital when curve1I2 and T2 and satisfy the fitting curve in (a). 100width at half maximum of the output pulse whenI2 andT2 satisfy the fitting curve in (a). digital curve2 fitting curve Figure5b shows the variation of the peak power and450 the FWHM of the output pulse when I402 and Figure 5(b) shows the variation of the peak power and the FWHM of the output pulse when I T2 satisfy75 the relationship of Equation (4). According to the fitting curve in Figure5a, it is directly seen2 that:and T To2 getsatisfy a short the pulserelationship with high of Equation peak power, (4). firstly, According we can to increase the fittingI2, andcurve then in reduceFigure T52 (a),, so thatit is 300 30 the (ps) output pulse is more and sharper at the same peak power, until I2 and T2 satisfy the analogous directly2 50 seen that: To get a short pulse with high peak power, firstly, we can increaseI2 , and then T

expression of Equation (4); when I2 increases indeﬁnitely, T2 changes slowly and tends to be stable.FWHM (ps)

At this time, although the peak power is still increasing, (mW) power Peak the output pulse width changes very little and 25 150 20 tends to stabilize too.

4. Conclusions0 0 10 0 250 500 750 1000 1250 200 400 600 800 1000 I (mA) I (mA) The output characteristics2 of the gain-switched semiconductor laser are2 affected by the modulation (a) (b) signal and the intrinsic parameters of the laser. However, it is impossible to improve the performance of

Figure 5. (a) Simulation results of the relation between I2 and T2 based on conclusion one (green trace) and conclusion two (blue trace), when I = 34 mA, T = 0.971 ns; (b) The peak power and full 1 1 width at half maximum of the output pulse whenI2 andT2 satisfy the fitting curve in (a).

Figure 5(b) shows the variation of the peak power and the FWHM of the output pulse when I2 and T2 satisfy the relationship of Equation (4). According to the fitting curve in Figure 5 (a), it is directly seen that: To get a short pulse with high peak power, firstly, we can increaseI2 , and then Appl. Sci. 2019, 9, 602 7 of 8 the output pulse by controlling the internal factors under the condition that the laser has been fabricated. According to the fact that the accumulation speed mainly determines the peak power and width of the output pulse after the carrier density reaches the threshold, we describe a method for generating ultra-short pulses with high extinction ratio based on step rectangular wave modulation. Then, through numerical simulation, the influence of amplitude I2 and width T2 of the second modulation current on the output pulse is discussed. It is concluded that when I2 is constant, T2 should be adjusted until the maximum time of output pulse power is equal to the injection current termination time. The moment is precisely the same as the injection current termination time; when T2 is fixed, I2 should be adjusted so that the output peak power just reaches saturation. At last, when the laser output pulse is optimal, the inverse proportional relationship between I2 and T2 is obtained by curve fitting. Compared with the rectangular wave modulation, it is shown that the step-pulse can increase the output pulse peak power by increasing the second modulation current and reduce the pulse width to saturation at the best working point. It should be noted that we did not consider the effect of temperature during modulation because of the mature of temperature control, which the precision could reach 0.01 degrees centigrade. Although our simulation is based on the parameters in Table1, the results are applicable to other semiconductors with different parameters because the gain-switched process is always the same. The gain-switched pulse lasers with rectangular wave modulation have been studied for a long time and can be found in commercial products. Our method is an improvement to them, and it is not difficult to be achieved. In the real experiment, we can use the differential circuit in the falling edge of a square wave to generate spike as a scheme of generating step-pulse. Our method has excellent guidance for further improving the performance of the gain-switched semiconductor lasers and solving the application requirements for a high extinction ratio of short pulse signals, such as the optical time domain reflectometry.

Author Contributions: Y.L. proposed the idea. B.L. and C.S. conceived and designed the simulations, analyzed the data, and wrote the paper. Y.L., H.Z. and K.Q. reviewed the paper and simulation results. Funding: This research was supported by the funds described in the Acknowledgements Section. Acknowledgments: This work is currently supported by the National Science Foundation of China (NSFC) (No. 61705033), and the Fundamental Research Funds for the Central Universities (No. ZYGX2016J014). Conﬂicts of Interest: The authors declare no conﬂicts of interest.

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