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Jun 6, 1993 - picoseconds with peak powers of about 10 W can be eas- ..... [I I] C. H. Henry, “Theory of defect-induced pulsations in semiconductor injection ...



High-Power High-Frequency Picosecond Pulse Generation by Passively @Switched 1.55 pm Diode Lasers Peter P. Vasil’ev

Abstract-The theoretical study of high-power high-frequency picosecond pulse generation by passively Q-switched multiple-contact 1.55 p n Fabry-Perot diode lasers is presented. A numerical model is based upon a traveling-wave approach which takes into account gainlloss saturation in each section of the laser, and calculates the spatial distribution of gain, absorption, and recombination time along the length of the laser cavity. The generation of pulses as short as 3-10 ps with 1-5 W peak power at 1-10 GHz repetition rate by a triple contact 1.55 pm laser is predicted. The model is used to show the dependence of optical pulse parameters on laser structure and drive condition.

I. INTRODUCTION EMICONDUCTOR laser diodes which generate ultrashort optical pulses offer the possibility of producing reliable, compact, and cheap sources of stable picosecond and subpicosecond pulse trains at ultrahigh repetition rates. These lasers are ideal candidates for use in ultrahigh-bit-rate data processing systems, in fiber optics telecommunications, and in commercial electrooptic sampling systems. Passive @switching of multiple-contact diode lasers is known as one of the simplest techniques of generating picosecond optical pulses [ 11, [2]. Pulses as short as a few picoseconds with peak powers of about 10 W can be easily obtained from three contact GaAs-AlGaAs DH lasers operating in the 850 nm wavelength range [3]. The repetition rates of output pulses can be varied in the gigahertz range by changing the pumping conditions of the laser. Gain switching of semiconductor lasers is an alternative approach to optical pulse generation, requiring no external optical components. However, gain-switched pulses at gigahertz repetition rates are not so short and have typical peak powers in the 10-100 mW range [4]. Moreover, gain switching at high frequency can only be achieved using semiconductor lasers with large modulation bandwidths. Mode-locked diode lasers can generate pulses shorter than both gain-switched and Q-switched lasers.


Manuscript received October 14, 1992; revised January 19, 1993. This work was supported by the Royal Society and the U.K. Science and Engineering Research Council. The author is with the Optoelectronics Division, P. N. Lebedev Physical Institute, Russian Academy of Sciences, Moscow 117924, Russia, on leave at the School of Physics, University of Bath, Bath BA2 7AY, England. IEEE Log Number 92091 19.

However, a typical peak power of pulses generated by mode-locked lasers without external amplification and compression is less than 50 mW for the 1.5 pm wavelength region and about 1 W for AlGaAs-GaAs laser diodes. In this case, the pulse repetition rate is determined by the optical length of a laser cavity. The mechanism of operation of ultrashort pulse generation in multiple-contact laser diodes arises from instability in the continuous wave operation of a laser with a saturable absorber where the absorption cross section is much higher than the gain cross section. This can occur in a laser diode consisting of two or three sections. As there is a nonlinear dependence of gain and absorption on the carrier density [5], the cross sections of the gain and absorbing regions of a multicontact laser can be readily controlled by using different current input, and hence selfQ-switching can result. Bistable behavior [6], [7] and mode locking [8], [9] have also been observed in multiple-contact diode lasers using this effect. In our previous experiments [3], we used for the first time the laser geometry with an absorber section in the middle between the gain regions. We also applied a reverse bias on the absorber. This has dramatically improved the pulse parameters generated by three-section lasers as compared with previous results for two-section devices [5]-[7], [lo], [ 111. To our knowledge, this is due to the significant decreasing of the absorber recovery time caused by the reverse bias on the absorber. Electron-hole pairs in the absorbing section can be rapidly moved from the active layer by the electric field between the contacts of the lasers. To some extent, the reverse-biased absorber is similar to a built-in small-area photodiode in the laser cavity. One can deduce that if the maximum pulse repetition rate observed experimentally is more than 18 GHz [3], then the recovery of the absorber can occur within 50-60 ps. In the present paper, we assume that the absorber section is reversed biased, and due to this the absorption recovery time, is shorter than the spontaneous recombination time. To date, most studies of passively Q-switched multiple-contact lasers have been made in the 850 nm wavelength range. On the other hand, the 1.55 pm wavelength region is also most attractive, particularly because of potential applications in optical fiber communications. In this paper, therefore, a theoretical analysis of picosecond

0018-9197/93$03.00 0 1993 IEEE


pulse generation by a passively Q-switched Fabry-Perot three-contact 1.55 pm laser is presented. To the best of the author's knowledge, all previous theories on passively Q-switched diode lasers have described the temporal dynamics of two-section AlGaAs-GaAs DH lasers with a forward-biased absorber located at the end of the laser cavity [l], [2], [5]-[7], [lo], [ l l ] . In that case, a set of coupled nonlinear (ordinary differential) rate equations for photon density in the laser cavity and two carrier densities in each of two parts of the diode was adopted for modeling the two-section devices. This model did not include the spatial distributions along the cavity axis of all variables. This assumption is valid for cases where generated pulses are substantially longer then the cavity round-trip time. However, for pulses shorter than 10 ps, this is not the case, and hence such models have not been found to agree with recent experimental results of Q-switched lasers generating pulses shorter than 10 ps [3], [12]. Here, therefore, we describe a numerical travelingwave time domain approach to modeling of passively Qswitched semiconductor lasers. This model is similar to that which is used for the description of active mode locking of laser diodes with external cavities [ 131. The model has been tested for AlGaAs-GaAs DH Q-switched lasers, and has shown good agreement with experimental results obtained in [3]. It also allows the simulation of novel cavity geometries and operating conditions, and can also be applied to both gain-switched and mode-locked laser diodes. The theoretical model of the laser is described in detail in Section 11. The results of the computer simulation and the dependence of the pulse generation on laser cavity configuration and the pumping conditions are discussed in Section 111. 11. THEORETICAL MODEL The schematic diagram of the passively Q-switched three-contact diode laser is shown in Fig. 1. The laser is divided into three sections, with different pumping currents Ig and I, into the end regions and center region, respectively. The central segment of the laser is set to act as a saturable absorber, and the other two segments are driven to provide gain, i.e., Ig >> I,. We assume that the gain/loss in the laser is the nonlinear function on the carrier density. The gaidabsorption versus carrier density is schematically shown in Fig. 2 [5]. The feature of the curve is the decreasing slope with increasing carrier density, so that the absorption cross section au/an is larger than the gain cross section ag/an. We assume also that variations of photon and carrier densities in the transverse dimensions are not significant, i.e., the laser diode operates in a single transverse mode. We use the time-domain approach, the z axis representing the longitudinal direction along the laser, and do not take into account the spectral behavior of the laser. The basic traveling-wave rate equations are partial differential equations, and describe the interaction between the forward and backward traveling photon densities S+(z, t) and



Light output

Gain regions

Absorbing region

Fig. 1. Schematic diagram of a passively Q-switched laser diode

canier concentration




Fig. 2. Schematic illustration of gain-loss dependence on carrier density which is assumed to be appropriate in a diode laser. n, is the transparency density.

S-(z, t) and the carrier density n(z, t). The traveling-wave rate equations can be written as [ 131, [ 141

as + v g as at +


az +



s+,s - ) ( n

- vpjs-



+ p -n 7,


(n - n , ) ( S +

+ S-)


where vg is the group velocity, r is the optical confinement factor, ai is the internal loss, p is the spontaneous emission factor, r, is the spontaneous lifetime, g(z, S + , S -) is the differential gain/loss coefficient, n, is the carrier transparency density, j(z, t ) is the current density, e is the electronic charge, and d is the active layer thickness. For simplicity, we approximate the gain and loss to linear functions of carrier density, each function having a different slope (see Fig. 2).' 'We have also used the model with a nonlinear dependence of gain/loss on the carrier density, and have found the results of the computer simulation to be approximately the same.


Due to the strong effect of the gain saturation mechanisms on the dynamics of long-wavelength GaInAsP semiconductor lasers [ 151, [ 161, we should include nonlinear gain effects into the model, and the differential gain coefficient can be written as

where E is the gain saturation coefficient. In the model, we use a parameter U as follows: U = -

aa/an ag / an



TABLE I Variable


Wavelength Laser cavity length Absorber length Waveguide width Active layer thickness Gain coefficient Confinement factor Transparency density Group refractive index Internal loss Spontaneous emission factor Spontaneous recombination parameters

x L W

d go


n, tl ff,




Gain saturation coefficient Mirror reflectivities



1.5 100-400



which indicates the ratio of the differential loss to the differential gain, so that in terms of the inputs to the model,

> n, for n < n,.


e RI > Rz

IO-I00 3.5 0.18 2.4 . 0.35 1.2 . 1Ol8 3.1 40 10-~ 2 . IO8 1 ' 10-10 3 . 1 . 5 . io-''


for n

g(z) =


The carrier lifetime is dependent on the carrier density because of nonlinear recombination mechanisms, and is also different for the gain and absorbing regions, so that for the gain sections, we have 1


7s(z,n )

- (A

+ Bn + Cn2)

and for the absorber,



i1 0.5






Time @s)

Fig. _I.The pulse generation in time domain by a self-Q-switched triplecontact laser. Model parameters: 1 , = 0.2L. U = 8 , T~~ = 50 ps, I , = 0 .

Due to the reverse bias on the absorber, we assume that 7, is less than the spontaneous recombination time. The current density j ( z , r ) also varies along the cavity length, and is introduced into the model either as pulsed or dc form. Boundary conditions at the laser facets are needed to solve the traveling-wave equations. We use the simplest boundary conditions, which are Sf(O, r) = R I S - ( O , r )

S-(L, r)


R2S+(L,r )

where R I and R, are the power facet reflectivities and L is the cavity length. Typical values used in the numerical model are shown in Table I. A numerical technique employing the method of lines and Gear's method is used for solving the nonlinear partial differential equations (1)-(3). It is normally necessary to determine values for U and 7, as these are not well known. To check the validity of the theoretical model, results of the computer simulations of passively Q-switched AlGaAs-GaAs laser diodes have been obtained. These results show that the model describes the experiments well when we use the values of 8-10 for U and when the absorber carrier lifetime 7, is in the range of 50-100 ps.

111. RESULTSAND DISCUSSION Fig. 3 shows a typical calculated temporal dependence of output optical power and carrier densities in the gain and loss sections in a continuously driven triple-contact laser. The main optical pulse parameters (pulsewidth, peak power, and repetition rate) depend strongly on the "quality" of the saturable absorber, i.e., on the values of U , 7,, and on how small the carrier density in the absorber is just before a pulse is emitted. The peak pulse power is determined by the peak carrier concentration in the gain regions just before the beginning of the absorber bleaching. The presence of the saturable absorber implies higher losses in the cavity than those under uniform current injection (gain-switched lasers). consequently, higher pumping currents and higher carrier density levels are needed to generate optical pulses. As a result, the peak power of Q-switched pulses is much higher than of gainswitched and mode-locked pulses. Another feature of Q-switched pulses, shown in Fig. 3 , is their clean shape without any tail structure or subpulses. This is due to strong depletion of carriers caused by an optical pulse. A typical range of camer concentration variation during the process in the gain region is (1.5-4.5) n,. So, strong dynamic gain saturation, low level of the



















RepRate 10

a C




z 1.5 g a


-H 6


G 4












carrier density just after the emission of the pulse, and additional loss due to the absorber are the main reasons for the clean shape of output pulses. The pulse shape is asymmetrical, with a falling edge of two-three times longer than the leading edge, which is due to the dynamic self-induced gain saturation. The pulse repetition rate depends on the gain and loss recovery rates. The gain recovery occurs due to the current injection, and obviously increases as the current density increases. The absorber parameters U , 7, also strongly affect the pulse repetition rate (see Figs. 5 and 8). The pulsewidth, the pulse peak power, and the repetition rate are shown in Fig. 4 as a function of the applied current in the gain sections. The laser threshold current under uniform current injection is about 40 mA. Fig. 4 illustrates the strong effect of current amplitude on repetition rate and the very weak effect on pulsewidth and peak power. This is very similar to that observed experimentally in GaAs-AlGaAs Q-switched laser diodes [3] when the pulse repetition rate changes through variation of the current amplitude, whereas individual pulses in the train have constant width and amplitude. Repetition rates above 10 GHz can be achieved by applying currents seven-ten times greater than the threshold current under the uniform current injection. In this case, calculations indicate pulsewidths of a few picoseconds, and typical values of the peak power are above 1 W . For small negative absorber currents I, < 0, pulsewidths and peak powers of pulses remain approximately the same as for I, = 0 (Fig. 4), whereas the pulse repetition rate decreases with an increase of the absolute value of I,. It is well known that the absorber recovery rate is one of the most important parameters in ultrashort pulse generation using saturable absorbers [17]. Fig. 5 shows the calculated pulsewidths, peak powers, and repetition rates as a function of recombination time in the absorber. The pulse parameters are strongly dependent on r, within the range of 100-1000 ps, but for 7, less than 50 ps, this dependence vanishes. According to the model, an ultrashort recovery time of the absorption is not necessary, and a value of 7, of about 100 ps is enough to generate pulses of width 3-4 ps. As we mentioned in Section I, it is the reverse bias applied to the absorber that seemingly results







Absorber recombinationtime @s)

Current mA

Fig. 4. Current dependence of pulse parameters for a 100 pm long laser. I" = 0.





z g

a a


3 a'



Fig. 5. Calculated pulse parameters versus absorber recovery time. Laser length 100 j "I , = 140 mA, U = 8.

2.5 2 1.5


z g

0. 1


a ....... ..... 0


0.4 0.6 0.8 1 1.2 Gain saturation Coen EPS ,'10"(-17) cub. an


0.5 0 1.6

Fig. 6. Pulsewidth, peak power, and repetition rate versus gain saturation coefficient.

in a decrease of the absorber recovery time in Q-switched AlGaAs-GaAs lasers. The assumption of 7, to be about 50-100 ps in the present model results in very good agreement of the model with experimental data obtained for GaAlAs-GaAs triple-contact lasers. Recent investigations on gain saturation mechanisms have been shown to have a strong effect on laser diode dynamics [13], [15], [16], [18]. Gain saturation due to effects such as dynamic carrier heating and spectral hole burning have been included in the theoretical model using the gain expression shown in (4). Fig. 6 shows the effect of the gain saturation on the calculated pulse parameters. The pulsewidth linearly increases with increasing gain saturation coefficient, while the peak power decreases. However, the gain saturation does not greatly influence the repetition rate of output pulses. The numerical model has also shown a similar dependence of pulse parameters on the gain saturation coefficient to that observed in gainswitched and mode-locked lasers. The differential gain coefficient go is another important laser parameter which significantly affects the pulsewidth and peak power of ultrashort pulses generated by modelocked and gain-switched laser diodes [13], [19]. Fig. 7 illustrates the dependence of Q-switched pulse parameters on go. As the gain coefficient increases, the pulsewidth decreases and the repetition rate increases, the peak power being approximately constant. As a result, in order to generate better pulses, a large differential gain is required, and hence Q-switched multiple quantum well (MQW) lasers are potentially more promising than bulk devices,


1 2.5


.... J ......... ....’ .... ............. LL.’’ ,,.*/ ---_- - - - _ _ _

8 ~


p 2



, -



- - _-..


6 0”







pulsewiak..-= 2






wavelength range has been predicted. The pulse repetition rate linearly increases with driving current, and values above 10 GHz can be achieved at moderate current levels. A strong dependence (similar to that in gain-switched and & mode-locked laser diodes) of pulsewidth on the gain satn B uration coefficient is found. One of the potential ways of Y I generating shorter pulses is to increase the differential gain coefficient by the use of quantum well lasers. In contrast to external cavity mode-locked diode lasers, passively Q-switched lasers exhibit no multiple-pulse behavior due to very strong carrier density depletion induced by the first pulse, the gain not being high enough to allow the generation of a secondary pulse. This also prevents the generation of pulses with a tail structure, as often found in gain-switched laser diodes [4], [20].

l2 z

c w t t







ACKNOWLEDGMENT The author is indebted to I. H. White for his great assistance during the preparation of this work and helpful discussions. 2







Crcw-sectionabsorber/amplifier ratio

Fig. 8. Calculated pulsewidth, peak power, and repetition rate as function of loss/gain cross-section ratio U.

provided nonlinear gain saturation effects are kept low. This approach has already been successfully used in gain switching where the pulsewidth has been shortened from typical values of 15-20 ps to about 4 ps by using MQW lasers [ 191. Fig. 8 illustrates the dependence of pulse parameters on the losdgain cross-section ratio. It shows the increase in peak power and decrease in pulsewidth with increasing U. The pulse repetition rate decreases due to the improved effectiveness of the saturable absorber and the enhancement of loss for larger 0.Consequently, it takes a longer time to achieve a sufficient carrier density in the amplifier to bleach the absorber. However, the pulse repetition rate can be increased in this case by applying larger current levels to the gain sections. IV. CONCLUSIONS A numerical model of a passively Q-switched threecontact 1.55 pm laser diode based on the traveling-wave approach is described. The model includes the effects of spatial distribution along the laser cavity length, gain/loss saturation, and different recovery rates for the gain and absorbing parts of the active region. It is assumed that the absorption recovery time is less than the spontaneous recombination time because of the reverse bias on the absorber section. The validity of the model has been assessed by comparison with results of previous experiments using AlGaAs-GaAs Q-switched lasers. The generation of high-repetition-rate picosecond pulses with peak power of a few watts in the 1.55 pm

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Peter P. Vasil’ev was born in Moscow, Russia, in 1958. He received the Diploma in physics from Moscow State University in 1981, and the Ph.D. degree in physics from P. N. Lebedev Physical Institute in 1986. In 1981 he joined the P. N . Lebedev Physical Institute, Russian Academy of Sciences, Moscow. He is presently on leave, working as a member of the Research Staff at the University of Bath, England. His interests are focused on picosecond laser diodes, ultrafast phenomena in semiconductors, and picosecond optoelectronics. Dr. Vasil’ev received the Electronics Letters Premium from the IEE, England, in 1991 and the Royal Society Fellowship in 1992.

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