Passive and hybrid mode locking in multi-section terahertz quantum cascade lasers
P. Tzenov, I. Babushkin, R. Arkhipov, M. Arkhipov, N. Rosanov, U. Morgner, C. Jirauschek
aa r X i v : . [ phy s i c s . op ti c s ] N ov Passive and hybrid mode locking in multi-sectionterahertz quantum cascade lasers
P. Tzenov
Technical University of Munich, 80333 Munich, Germany
I. Babushkin
Institute of Quantum Optics, Leibniz University Hannover, 30167 Hannover, GermanyMax Born Institute, 12489 Berlin, Germany
R. Arkhipov
St. Petersburg State University,199034 St. Petersburg, RussiaITMO University, 197101 St. Petersburg, Russia
M. Arkhipov
St. Petersburg State University,199034 St. Petersburg, Russia
N. Rosanov
ITMO University, 197101 St. Petersburg, RussiaVavilov State Optical Institute, Kadetskaya Liniya v.o. 14/2, St Petersburg 199053, RussiaIoffe Physical Technical Institute, Politekhnicheskaya str. 26, St Petersburg 194021, Russia
U. Morgner
Institute of Quantum Optics, Leibniz University Hannover, 30167 Hannover, Germany
C. Jirauschek
Technical University of Munich, 80333 Munich, GermanyE-mail: [email protected]
Abstract.
It is believed that passive mode locking is virtually impossible in quantum cascadelasers (QCLs) because of too fast carrier relaxation time. Here, we revisit this possibility andtheoretically show that stable mode locking and pulse durations in the few cycle regime atterahertz (THz) frequencies are possible in suitably engineered bound-to-continuum QCLs. Weachieve this by utilizing a multi-section cavity geometry with alternating gain and absorbersections. The critical ingredients are the very strong coupling of the absorber to both field andenvironment as well as a fast absorber carrier recovery dynamics. Under these conditions, evenif the gain relaxation time is several times faster than the cavity round trip time, generationof few-cycle pulses is feasible. We investigate three different approaches for ultrashort pulsegeneration via THz quantum cascade lasers, namely passive, hybrid and colliding pulse modelocking. . Introduction
Quantum cascade lasers (QCLs) are unipolar, electrically pumped semiconductor devices inwhich the optical transition occurs between bound electron states in the conduction band ofa specially designed quantum well heterostructure [1]. Due to the intersubband nature of theradiative transition, QCLs are highly tunable and allow for the generation of coherent radiationin the underdeveloped terahertz (THz) and mid-infrared (MIR) portions of the electromagneticspectrum.Since the first experimental realization of a QCL in 1994 [2], this technology has experiencedremarkable advancement, with some of the most notable milestones being the realization of aroom temperature MIR QCL emitting power at the Watt level [3], the demonstration of a THzQCL operating at the record high temperature of 200 Kelvin [4], as well as the successfulgeneration of broadband coherent frequency combs by free running devices both in the MIR andTHz spectral regions [5, 6].Naturally, it is also of great scientific and practical interest to enable the formation of short,mode locked pulses of light with QCLs. This would be a major advancement for THz and MIRspectroscopy as it will open up the stage for ultrafast optical experiments, such as for exampletime-resolved THz spectroscopy [7], with compact, on-chip, direct sources. Additionally, sincemode locked pulses are frequency combs in the Fourier domain, ultrashort pulse generation viaQCLs will provide an alternative approach to obtain broadband frequency combs.Unfortunately, experience shows that QCLs are notoriously difficult to mode lock [8], with theshortest pulse widths achieved so far being around 2.5 ps in the THz via active modulation of theinjection current [9]. It is believed that, due to the ultrafast processes that govern intersubbandtransitions, active mode locking of QCLs is feasible only close to lasing threshold, whereas passivemode locking (PML), in the traditional sense, is virtually impossible [10]. This is because theintrinsically short carrier relaxation times, typically several times smaller than the cavity roundtrip time, obstruct the formation of short bursts of light since the trailing edges of any propagatingpulse would be amplified by the fast recovering gain [11].We believe that there is no fully conclusive evidence to support these claims, especially in theTHz, as the gain recovery dynamics has not been extensively studied. In fact, to the our bestknowledge, to present date there have been only two publications experimentally investigatingthe gain recovery time in bound-to-continuum (BTC) THz devices, and none in resonant-phononQCLs. Interestingly, both experimental results indicate sub-threshold lifetimes on the orderof several tens of picoseconds [12, 13]. These measurement techniques are based on a pump-probe experimental method where a perturbing resonant pump pulse is injected into the gainmedium followed by a temporally detuned probe pulse interacting with the saturated gain. Inthe publication in Ref. [12], the photocurrent induced by stimulated emission between the upperand the lower laser level was recorded as a function of the delay between both pulses, and aGaussian fit was used to infer the speed of the recovery of population in the upper laser state.The measured lifetimes were ≈ ps which, as we will show, are long enough to enable modelocking. In fact one might argue that BTC QCLs are amongst the most optimal devices for modelocking, since the energy exchange between the propagating pulse and the saturable gain is mostefficient when the carrier dynamics is faster than the round trip time.Our idea is based on well established techniques for quantum dot and conventionalsemiconductor lasers [14, 15, 16, 17, 18, 19], where PML is routinely achieved based on a saturableabsorber (SA) and a gain medium as separate components of a multi-section wave guide. Hereabsorption is implemented by reverse biasing the gain medium. Carrying this concept to QCLswas first suggested by Franz Kärtner [20], whereas Talukder and Menyuk were the first to pointout that rather than reverse biasing the gain, carefully chosen positive biases should be used forQCLs [21]. In this work the authors simulated passive mode locking for MIR devices, where theintensity dependent saturation was implemented via a (slow) quantum coherent absorber. Alongthese lines simulations for PML in THz QCLs have also been presented [22, 23]. Here, we expandupon the previous work by i) using an extended theoretical model, ii) showing that guided byclassical principles one can achieve passive mode locking by simply using a fast saturable absorbernstead [24], and iii) in addition to the conventional PML approach, we also discuss the possibilityof hybrid and colliding pulse mode locking.The way in which the fast saturable absorber (FSA) enables mode locking is two-fold [25, 26].First, the FSA provides more gain for shorter pulses, strong enough to bleach the material, whileat the same time it also suppresses weak background fluctuations. Secondly, it also acts as acompensator for the dispersion introduced by the gain medium, as both gain and loss interactresonantly with the intracavity intensity, albeit with different signs in the polarization term. Asa result, if the gain and absorber sections are packed into a compact structure, with the smallround trip time only several times longer than the relaxation time in the gain section, very stablemode locking with one or two pulses per round trip arises.This paper is organized as follows: in Sec. 2 we present the theoretical model and in Sec. 3we investigate several different approaches which might lead to the generation of picosecondTHz pulses via QCLs, namely conventional passive mode locking, Sec. 3.1, colliding pulse modelocking, Sec. 3.2, and hybrid mode locking, Sec. 3.3.
2. Theoretical model (a) E ( e V ) - ULL/ LLL/
Optical transition Drift transportMinibandsQCL period (c)
Substrate (b)
Substrate GG A
Figure 1.
An example of multi-section Fabry-Perot (FP) cavity geometry, consisting of spatiallyseparated gain (G) and absorber (A) regions for (a) conventional passive mode locking and (b)colliding pulse mode locking. (c) Conduction band diagram and wave functions of a typicalbound to continuum (BTC) GaAs/Al . GaAs . THz quantum cascade laser (the structure isanalogous to that in Ref. [27]). The upper and lower laser levels, ULL and LLL, are outlined withthick lines. The electron transport in the device is characterized by drift transport (scattering)inside the miniband and optical transition between minibands.The multi-section cavity design envisaged by us is illustrated in Fig. 1 for a Fabry-Perot(FP) geometry and two different configurations, the A-G and G-A-G alignments, favouringconventional and colliding pulse mode locking, respectively. The general geometry consists oftwo or more sections with different biases and effective dipole moments. This can be realizedeither via wafer-bonding of separately designed and grown structures, or by designing a singleheterostructure operating either as a gain or absorber medium, depending on the driving current[28]. Despite the more challenging fabrication as compared to having epitaxially stacked gainand absorption layers, or external cavity multi-section QCLs [29], we insist on monolithic waveguides as they offer two obvious advantages: i) these structures provide short round trip lengths,i.e. relatively small round trip times, and also ii) arranging the gain and absorber in series, asdepicted in the figure, allows for independent control of the injection current in all sections.Before we write down the equations of motion, a careful consideration of the transportprocesses in a BTC quantum cascade laser is in order. An exemplary such active region isillustrated in Fig. 1(c). Typically, electron transport through the heterostructure can be describedby three different lifetimes, the superlattice relaxation time, i.e. τ SL , defined as the transit timef a carrier from the top of the miniband to the upper laser level, τ defined as the lifetime ofthe upper laser level and lastly τ denoting the same for the lower laser level [30].A usual modelling approach in literature is to eliminate the population of the lower laser level, ρ , from the system of equations by assuming that ρ ≈ at all times [21, 31, 32]. This choicecan be justified by the relatively fast out-scattering from this level to lower energetic states inthe miniband, compared to the other non-radiative lifetimes in the system, i.e. τ ≪ τ , τ SL .Such an approximation is valid for determining the steady state solutions of the rate equations inthe absence of an optical field, however it breaks down when one additionally considers photonassisted scattering, since it dramatically reduces the upper laser level lifetime [30]. Concretely,when /τ < /τ + 1 /τ st ( | E | ) , where τ st ( | E | ) is the stimulated emission/absorption lifetimeand E is the electric field, the dynamics of the lower laser level can no longer be excluded, sincethe QCL essentially operates as a three level system [30]. A value of τ ≈ ps was reported forthe first THz BTC-QCL [33], indicating that typical values for the lower laser level lifetime areof that order.Keeping this in mind, we employ a density matrix model to describe the electron transportthrough the triplet ρ SL , ρ and ρ for the population density of the electrons in the miniband,the upper laser level and the lower laser level, respectively. Where necessary, we denote thevarious system parameters with sub-/superscript index g to indicate that those quantities arerelated to the gain section alone. A similar system was used in the work of Choi et al. to provideevidence for quantum coherent dynamics in MIR QCLs, where an excellent agreement betweensimulation and experimental data was achieved [34].Expanding on the usual two level Bloch equations approach, we write down the Maxwell-Bloch(MB) equations for the three level system, in the rotating wave and slowly varying amplitudeapproximations, taking into account counter-propagating waves and spatial hole burning. Thefull system of equations for the gain medium is given by ∂E g ± ∂x ± n c ∂E g ± ∂t = − i Γ g µ g ω ε cn N g η ± − a E g ± , (1a) dρ SL dt = ρ τ − ρ SL τ SL , (1b) dρ dt = ρ SL τ SL − ρ τ + i µ g ~ (cid:2) ( E g + ) ∗ η + + ( E g − ) ∗ η − − c.c. (cid:3) , (1c) dρ dt = ρ τ − ρ τ − i µ g ~ (cid:2) ( E g + ) ∗ η + + ( E g − ) ∗ η − − c.c. (cid:3) , (1d) dρ + SL dt = ρ +11 τ − ρ + SL τ SL , (1e) dρ +22 dt = ρ + SL τ SL − ρ +22 τ + i µ g ~ (cid:2) ( E g − ) ∗ η + − ( E g + ) η ∗− (cid:3) , (1f) dρ +11 dt = ρ +22 τ − ρ +11 τ − i µ g ~ (cid:2) ( E g − ) ∗ η + − ( E g + ) η ∗− (cid:3) , (1g) dη ± dt = − i ( ω g − ω ) η ± + i µ g ~ (cid:2) E g ± ( ρ − ρ ) + E g ∓ ( ρ ± − ρ ± ) (cid:3) − η ± T g . (1h)The symbols E g ± denote the forward and backward propagating field envelopes and η ± thecorresponding slowly varying coherence terms between levels 1 and 2. The interference patternof the counter-propagating waves leads to the formation of standing waves inside the cavity,which results in a population grating and consequently in spatial hole burning. According to thestandard approach [31, 35, 36], we take the following ansatz for the population of the j th state ρ jj = ρ jj + ρ + jj e ik x + ( ρ + jj ) ∗ e − ik x , (2)where ρ jj is the average population, ρ + jj denotes the (complex) amplitude of the grating, k = ω n /c is the carrier wave number expressed in terms of the carrier angular frequency and the background refractive index is n ≈ . . Furthermore, c denotes the velocity of lightin vacuum, ε the permittivity of free space and ~ the Plank constant. The rest of the simulationparameters for both absorber and gain are specified in Table 1.In order to impose a minimal set of assumptions about the absorber, we model it as a twolevel density matrix system in the rotating wave and slowly varying amplitude approximationwith average inversion ∆ , inversion grating amplitude ∆ + and a coherence term π ± . Again, weuse sub-/superscript a to specify where a particular parameter or variable relates solely to thesaturable absorber. The usual MB equations read ∂E a ± ∂x ± n c ∂E a ± ∂t = − i Γ a µ a ω ε cn N a π ± − a E a ± , (3a) d ∆ dt = i µ a ~ (cid:2) ( E a + ) ∗ π + + ( E a − ) ∗ π − − c.c. (cid:3) − ∆ − ∆ eq T a , (3b) d ∆ + dt = i µ a ~ (cid:2) ( E a − ) ∗ π + − ( E a + ) π ∗− (cid:3) − ∆ + T a , (3c) dπ ± dt = − i ( ω a − ω ) π ± + i µ a ~ (cid:2) E a ± ∆ + E a ∓ ∆ ± (cid:3) − π ± T a . (3d)By far the most well established method for the numerical analysis of mode locking insemiconductor lasers is the travelling wave model [26, 37, 25], which treats the optical field in asimilar manner as in Eq. (1a) and Eq. (3a), however restricts the modelling of the gain/absorberdynamics to classical rate equations. This essentially "flat gain" approximation necessitatesthe inclusion of additional numerical techniques to impose the bandwidth limit of the gainmedium [26]. By contrast, the Maxwell-Bloch equations intrinsically capture the spectraldependence of the gain, namely via the inclusion of the polarization equations, i.e. Eq. (1h)and Eq. (3d), and thus constitute a more complete model. Table 1.
The parameters for the absorber (A) and gain (G) section of the two-section ringQCL from Fig. 1(a). In the tables below e ≈ . × − C denotes the elementary charge.Parameter Unit Value (G) Value (A)Dipole matrix el. ( µ j ) nm · e 2 6Resonant angular freq. ( ω j ) ps − . × π . × π Gain superlattice transport time ( τ SL ) ps 40 × Gain upper laser level lifetime ( τ ) ps 40 × Gain lower laser level lifetime ( τ ) ps 2 × Absorber lifetime ( T a ) ps × T a/g ) fs 200 160Length ( L j ) mm 1 0.125Doping density ( N j ) cm − × × Overlap factor ( Γ j ) dimensionless 1.0 1.0Linear power loss ( a ) cm −
10 10
3. Modelocking of QCLs
In the following sections we investigate various schemes which might enable the generationof ultrashort pulses with THz QCLs. Besides conventional passive mode locking, we alsotreat colliding pulse and hybrid mode locking as alternative approaches to improve the pulsecharacteristics. Importantly, for our envisaged design to work, a slowly saturable gain, withinversion recovery time only several times faster than the round trip time, must be coupled witha fast saturable absorber [26]. To model this scenario we assume a parameter set as presented inTable 1, with values we believe realistic for THz QCLs. Specifically, for the BTC-QCL lifetimesssumed in Table 1, simulations similar to Ref. [38] yield a gain inversion lifetime of T g ≈ ps, while for the 1.125 mm FP cavity the round trip time is about 28 ps. In all of the followingsections, we present results from simulations of free-running, self-starting devices. To solveEq. (1) and Eq. (3), we use the numerical method outlined in [39] and start all simulationsfrom random noise. Due to the nature of the employed approximations, our results are limitedto pulses with durations not significantly shorter than ∼ ps. For sub-picosecond dynamics,memory effects become also relevant, and can be taken into account by using a non-Markovianapproach, however at the cost of considerably increased numerical complexity [40, 41]. One of the main results from the classical theory of passive mode locking is the condition thatthe absorber should saturate faster than the gain [24]. The non-linear saturation parameter isgiven by ǫ j = µ j T j T j / ~ and denotes the inverse of the saturation value of the electric fieldsquared | E | in each active region ( j = { a, g } ). When the condition r = ǫ a /ǫ g > is met, thepropagating pulse will bleach the absorber more strongly than the amplifier and thus will opena net round trip gain window. In fact, simulations for quantum dot lasers have shown [26] thatthe pulse duration decreases approximately exponentially with increasing value of r . Conversely,classical theory and also our simulations (results not shown here) predict that no mode lockingis possible when r < [26, 24]. Time (ps)-4 -2 0 2 4 N o r m . i n t en s i t y (a) P u l s e F W H M ( p s ) N o r m . i n t en s i t y (b)(c) Irregular pulsationsPML(a)
Figure 2. (a) Normalized pulse intensity vs time for values of the absorber lifetimes of 2 ps,3 ps and 5 ps. (b) The intensity FWHM duration as T a is varied between 2-9 ps, where for T a = 7 ps and 9 ps, the FWHM values of the main and also the satellite pulses are presented.(c) The normalized optical intensity for T a = T a lifetime for modelocking. Upon entering the absorber, the pulse front will saturate the active medium, whichon the other hand, will be quick enough to recover prior to arrival of the pulse tail. This typeof dynamics would naturally shorten the pulse as the duration of the net gain window willdecrease with decreasing T a . Following this logic, one might expect to obtain shorter pulseswith decreasing absorber lifetimes, which is indeed confirmed by our simulations. Importantly,absorbers with fast carrier recovery ought to be easy to realize based on resonant phonon QCLdesigns, taking advantage of strong longitudinal optical phonon scattering.Similarly to their zero-dimensional counterparts (quantum dot lasers), we argue that QCLscould be passively mode locked provided systems with suitably chosen parameters are designed.o illustrate this possibility we simulated Eq. (1) and Eq. (3) with a parameter set characteristicfor QCLs (see Table 1).To investigate the importance of absorber lifetime for PML of QCLs, we varied the recoverytime of the absorber between 2 and 9 ps and simulated the coupled system for around 400 roundtrips. Since the change of T a also changes the value of r , for each simulation we re-adjusted theabsorber dipole moment in order to maintain constant r . This was necessary since we wantedto have controlled numerical experiments where only T a and not r was varied. Finally, thegain carrier density was also adjusted from its value in Table 1, in order to ensure that in allsubsequent simulations the active medium was biased at 1.2 times above threshold.The results from these simulations are presented in Fig. 2(a) and Fig. 2(b) and displaybehaviour in agreement with our expectation. When the absorber lifetime is sufficiently short,Fig. 2(a), as T a increases so does also the pulse duration. In fact, for the PML regime of lasingin Fig. 2(b) we observe a clear linear relationship between T a and the intensity full width at halfmaximum (FWHM) pulse duration. On the other hand, for slower absorbers, the complicatedinterplay between the optical field and the active region dynamics produces irregular pulsations(IP) with no well defined temporal profile. From Fig. 2(c) we see that the onset of this regimeoccurs already for absorber lifetimes T a ≥ ps and is characterized by multiple pulses withvarying intensity. Additionally, for those cases one can also observe modulation of the pulseamplitude with a period spanning several tens of round trips, a phenomenon baring resemblanceto Q-switched mode locking [42]. These results unequivocally validate the important role ofthe absorber lifetime for the pulsation dynamics and confirm that for successful mode lockingof QCLs, besides slowly saturable gain media, also absorbers with short T a lifetime and large r = ǫ a /ǫ g ratio are essential. Length (mm)0 0.2 0.4 0.6 0.8 1 N o r m . i n t en s i t y P op . i n v e r s i on -101Gain Abs. Gain (a)Freq. (THz)-1 -0.5 0 0.5 1 N o r m . i n t en s i t y B ea t no t e ( d B ) -100-80-60-40-200(b) (c) Figure 3. (a) A snapshot of the optical intensity (left y-axis) and population inversion (righty-axis) inside the cavity. (b) Optical spectrum of the field emitted from the right facet of thecavity. (c) A log plot of the beatnote signal versus frequency (normalized to the cavity roundtrip frequency f rt ) produced by the device.A special type of passive mode locking, useful for shortening even further the pulse duration,but probably more importantly to achieve high repetition rates, is the so called colliding pulsemode locking, where two gain sections of equal length are symmetrically placed around theabsorber [43, 25]. When such a geometric arrangement is achieved, two identical pulses perround trip can be emitted from the device, resulting in doubled repetition rate equal to theecond harmonic of the round trip frequency. In fact, we expect that CPML will be easier toachieve via BTC quantum cascade lasers as the short gain recovery time will naturally favoursuch multi-pulse regime of operation [22].To understand why CPML occurs, consider the schematic in Fig. 1(b), illustrating a multi-section cavity design in the G-A-G (gain-absorber-gain) configuration. Let us assume that asingle pulse with amplitude E propagates inside a gain medium with some group velocity v g .Close to the resonator mirrors, during its forward pass the pulse will saturate the gain and therewill be not enough time for the latter to recover in order to re-amplify the reflected signal. Thisleads to a reduction of the effective length of the gain medium by ∆ L = v g τ gr / , which is halfthe distance travelled by the pulse in time τ gr , where τ gr = T g denotes the time it takes for thegain to recover to its threshold value. It can be shown that τ gr is a monotonously increasingfunction of | E | , and as such ∆ L will be shorter if the pulse would split into two identical copieswith half the total intensity each, since then τ gr will also decrease. The most stable two-pulseconfiguration in a G-A-G Fabry-Perot cavity are indeed pulses, colliding in the cavity centre, asthose will saturate the absorber more deeply and further reduce the round trip losses.To confirm these expectations, we simulated Eq. (1) and Eq. (3) in the G-A-G arrangement forthe parameter set in Table 1. Figure 3 illustrates the results. After about 50 round trips the laseremission transforms into two identical counter-propagating pulses which collide inside the centreof the cavity, Fig. 3(a). The spectrum in Fig. 3(b) consists of more than 15 modes separated bytwice the round trip frequency, f rt , whereas beatnote calculations, Fig. 3(c), indicate a strongcomponent at the second harmonic of f rt . This second harmonic regime is stable over hundredsof round trips, with the beatnote linewidth in Fig. 3(c) being limited by the Fourier transformresolution of our simulations. Such a device essentially represents a very stable local oscillatorwith a repetition frequency of around ≈
71 GHz [44].
SubstrateGainAbs. (b)
Time (ps)0 50 100 150 N o r m . i n t en s i t y Absorber lifetime (ps)2 4 6 8 P u l s e F W H M ( p s ) (a) IPHML
Figure 4. (a) Schematic diagram of hybrid mode locking with RF modulation of the absorberbias. (b) Intensity profile for T a = m sin(2 πf rt t ) in the right hand side ofEq. (3b), modelling the RF source [36], where the modulation amplitude was set to 25 % ofthe DC current, i.e. m = 0 . × ∆ eqa /T a . Again, we repeated the simulations from Fig. 2 toevaluate how effective this active+passive mode locking will be as compared to the simple PMLcase. The results are plotted in Fig. 4(b).rom Fig. 4(b), within the fast absorber regime (i.e. T a = 2 − ps), we see that applied RFmodulation does not seem to have any significant impact on the pulse widths, as the calculatedFWHM-values are of almost the same magnitude as in Fig. 2(b). This is not so surprising asthe laser already operates in a mode locking regime and so additional RF-injection would havelittle to no effect on the dynamics. However, substantial improvement in the pulse structure andduration is observed for slower absorbers as the satellite pulsations are strongly suppressed infavour of more regular pulses. In particular, comparing the time-domain profile of the intensityin Fig. 2(c) and Fig. 4(b), we see that as a result of this additional active modulation, the pulse at T a = 7 ps has completely recovered its integrity whereas the pulse substructures for T a = 9 psare drastically reduced. Again, drawing insights from the quantum dot laser community [46, 47],one might expect that with this HML technique an improvement in the overall stability of thepulse train and mode locking parameter range can be achieved, as compared to when utilizingthe passive mechanism alone.
4. Conclusion
We have suggested feasible approaches for ultrashort pulse generation in self-starting bound-to-continuum terahertz quantum cascade lasers. Our scheme is based on the realization of aparadigmatic model for passive mode locking via a fast saturable absorber, implementable viamulti-section monolithic Fabry-Perot cavities. We predict the formation of short picosecondpulses with FWHM limited by the gain bandwidth of the device. Our investigations show thatbesides a suitably engineered gain medium with slowly recovering population inversion, a fastsaturable absorber with very strong coupling to the optical field is essential. Carefully conductedsimulation experiments indicate that the multi-section configuration is prone to entering into aregime of irregular pulsations if the absorber recovery time is very large, which should be animportant point to consider in future designs. Furthermore, besides passive mode locking, wehave also discussed alternative approaches to ultrashort pulse generation in QCLs, i.e. hybridand colliding pulse mode locking. By utilizing active modulation of the injection current in theabsorber, the former method recovers the regular pulsations from a regime of irregular such. Onthe other hand, CPML might be easier to achieve with THz QCLs as multi-pulse lasing is thenaturally preferred mode of operation in fast gain recovery active media.
Funding Information
This work was supported by the German Research Foundation (DFG) within the Heisenbergprogram (JI 115/4-1) and under DFG Grant No. JI 115/9-1 and the Technical University ofMunich (TUM) in the framework of the Open Access Publishing Program.
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