Stable mode-locked pulses from mid-infrared semiconductor lasers

We report the unequivocal demonstration of mid-infrared mode-locked pulses from a semiconductor laser. The train of short pulses was generated by actively modulating the current and hence the optical gain in a small section of an edge-emitting quantum cascade laser (QCL). Pulses with pulse duration at full-width-at-half-maximum of about 3 ps and energy of 0.5 pJ were characterized using a second-order interferometric autocorrelation technique based on a nonlinear quantum well infrared photodetector. The mode-locking dynamics in the QCLs was modelled and simulated based on Maxwell-Bloch equations in an open two-level system. We anticipate our results to be a significant step toward a compact, electrically-pumped source generating ultrashort light pulses in the mid-infrared and terahertz spectral ranges.

The train of short pulses was generated by actively modulating the current and hence the optical gain in a small section of an edge-emitting quantum cascade laser (QCL).Pulses with pulse duration at full-width-at-half-maximum of about 3 ps and energy of 0.5 pJ were characterized using a second-order interferometric autocorrelation technique based on a nonlinear quantum well infrared photodetector.The mode-locking dynamics in the QCLs was modelled and simulated based on Maxwell-Bloch equations in an open two-level system.We anticipate our results to be a significant step toward a compact, electricallypumped source generating ultrashort light pulses in the mid-infrared and terahertz spectral ranges.
Quantum cascade lasers (QCLs) [13], since their invention in 1994, have become the most prominent coherent light sources in the mid-infrared.One of the most striking differences between these unipolar devices and diode lasers is that their emission wavelength, gain spectrum [14], carrier transport characteristics, and optical dispersion can be engineered.This remarkable design freedom makes QCLs a unique candidate to serve as a semiconductor source of ultra-short pulses in the mid-infrared.
There is, however, an obstacle of fundamental origin that has so far prevented achieving ultrashort pulse generation in QCLs [15,16].In intersubband transitions, the carrier relaxation is extremely fast because of optical phonon scattering.As a result, the gain recovery time in QCLs is typically on the order of a few picoseconds [17,18] which is an order of magnitude smaller than the cavity roundtrip time of 40-60 ps for a typical 2-3mm-long laser cavity.According to conventional mode-locking theory, this situation prevents the occurrence of stable passive mode-locking and impedes the formation of high-intensity pulses through active mode-locking [19].
In this work, we achieve stable mode-locking by designing a QCL structure with longer gain recovery time than conventional QCL designs and actively modulating the pumping current of a small section at one end of the laser cavity to provide net gain to the pulse.To our knowledge, this is also the first stable mode-locking of a laser with fast gain recovery time.Our QCL structure, shown in Figure 1a, is based on a "diagonal transition" in real space [20], i.e. the laser transition takes place between levels confined in two adjacent wells separated by a thick barrier.The reduced wavefunction overlap between the upper and lower laser states results in a phonon-limited upper state lifetime of up to 50 ps below threshold.As we will see later, we are able to identify a parameter range close to the laser threshold where we can form stable mode-locked pulses by modulating the gain in the small section of a device.High above threshold, pulses are broadened by the increased gain saturation in the un-modulated long section, and finally become unstable due to the increased spatial hole-burning and accelerated gain recovery.
There were several reports of mode-locking in QCLs [21][22][23], whose evidence were based on broadband optical spectra with a large number of longitudinal modes and a narrow microwave beat note in the power spectrum at the laser roundtrip frequency, which indicated that the electric field waveform circulating in the laser cavity and thus the phase relationship between the longitudinal modes was stable over a large number of round-trips.However, due to the lack of a suitable apparatus for second-order autocorrelation measurements, no direct evidence was given to demonstrate that the circulating waveform was indeed a periodic sequence of isolated pulses, which would result from all modes having equal and stable phases.Subsequent pulse characterization using autocorrelation techniques showed that under the previous conditions, the output of free running QCLs was not composed of one isolated pulse per roundtrip [15,16].
The physics of multimode behaviour observed in those lasers is described by spatial hole-burning and the Risken-Nummedal-Graham-Haken (RNGH) instability [15,16], rather than by stable mode locking.
Our devices were processed into ridge waveguides with multiple electrically independent sections, see Fig. 1b and a processing description in Methods.Radiofrequency (RF) signals were injected into a short 120 µm to 160 µm-long section at one end of the 2.6 mm-long laser ridge via a bias tee to modulate the pumping current in the section.The current-voltage (I-V) and light-current (L-I) characteristics of a 16µmwide-ridge device when the ridge is pumped in continuous wave with no RF modulation at 77K are shown in Figure 2a.The differential resistance of the RF section above threshold is R ≈ 30 Ω.Given the estimated capacitance across the insulation layer C ≈ 0.05 pF, the RC-limited frequency response extends to ~100 GHz, far above the roundtrip frequency of the laser cavity.The actual microwave power delivered to the device measured by a network analyzer was about 30% of the input power, which indicates a significant impedance mismatch between the source and the device.The largest contribution to the impedance mismatch is the inductance caused by the bond wire, estimated to be about 1 nH.(See Supplementary Information 1) Figure 2b shows the optical spectra of the device, measured with a Fourier transform infrared spectrometer (FTIR), as a function of the RF modulation frequency, for a DC pumping current of 340 mA which is about 1.1 times the laser threshold.The RF input power was kept constant at 35 dBm.The laser emission is single mode when no gain modulation is applied.At a gain modulation frequency corresponding to the laser roundtrip frequency of 17.86 GHz we observe significant spectral broadening.The spectrum exhibits many longitudinal modes with an approximately Gaussian envelope.
With a slightly detuned RF frequency from resonance, the laser spectrum becomes narrower.When the RF frequency is tuned further away from resonance (<17.36GHz or >18.11GHz), lasing stops.The RF power is able to suppress the lasing up to 355 mA of pumping current.As we shall see, stable mode-locked pulses are formed for pumping close to threshold; gain can overcome loss only if the RF frequency is tuned to resonance, and the laser generates a train of isolated short pulses which reach the modulated section at each round-trip at its gain maximum.When the laser is pumped at higher DC current (1.45 times the laser threshold), the optical spectra show similar resonance behaviour, but the RF modulation is no longer sufficiently strong to suppress the lasing when the detuning between the RF modulation frequency and the cavity round-trip frequency is large (Fig. 2c).
The laser emission is characterized using a second-order interferometric autocorrelation (IAC) technique [24] using a two-photon quantum well infrared photodetector (QWIP) [25,26].A description of the autocorrelator setup is given in Methods.For the case of stable, isolated periodic pulses, the ratio between the interference maximum and the background should be 8 to 1 [16].Fig. 3a shows the IAC trace obtained when the QCL is pumped at 340 mA and the RF modulation is applied at the cavity resonance frequency of 17.86 GHz.The observed peak-to-background ratio is 8:1, indicating stable mode-locking and the circulation of an isolated pulse per roundtrip in the cavity.The pulse width, estimated from the width of the interference fringes, is approximately 3 ps.This value is approximately a factor of two larger than the width of a Fourier-transform limited pulse duration calculated from the optical spectrum in Fig. 1a.The estimated energy per pulse is close to 0.5 pJ.The observed IAC in Fig. 3a is in good agreement with a simulated IAC trace shown in Fig. 3d for the same ratio p = 1.1 of the pumping current to the threshold current.
When the DC pumping is increased to 450 mA, the peak-to-background ratio of the IAC is no longer 8:1, but rather 8:2.5, as shown in Fig. 3b.This indicates that the laser output does no longer consist of isolated pulses separated by the roundtrip time, but rather of overlapping pulses with a continuous-wave component.Further increasing the laser pumping current to 500 mA with fixed RF power decreases the peak-tobackground ratio of the IAC even more to 8:4, see Fig. 3c.
We also measured the microwave spectrum of the laser output with applied RF modulation.The laser output was sent directly to a 20 GHz bandwidth QWIP [27] and the resulting photocurrent was displayed on a spectrum analyzer.The microwave spectrum of the laser output at DC pumping of 340 mA is shown in the inset of Fig. 3a.
A narrow peak with a FWHM of ~3 kHz was observed at the RF modulation frequency, which indicates phase coherence between the modes for more than 10 6 roundtrips.This beat note is also at least an order of magnitude narrower than any previously observed beat note from multimode QCLs [19,23].
Figures 4a-c show the IAC for a 12 µm-wide laser with various RF power levels when the laser was pumped constantly at 265 mA (about 1.08 times the laser threshold).
The pulse quality degrades dramatically as the RF input power decreases from 35 dBm to 12 dBm.Thus, operating near threshold and applying sufficiently large RF modulation are two necessary conditions to achieve stable mode-locking in our devices.
For fixed input RF power (35 dBm) the IAC shows a similar behaviour to that of the 16 µm wide device as the DC pumping is increased.
Modulating the injection current of the QCLs leads to the modulation of the gain.
In that case, the standard active mode-locking formalism of loss modulation which does not take the gain dynamics into account cannot be applied [18].To understand the pulse regimes in our system, we use a simple model based on one-dimensional Maxwell-Bloch equations in a Fabry-Perot cavity, where the active medium is described by an open twolevel system.This model has been shown to successfully describe the dynamics in QCLs without active modulation [15,16].Details of the equations and the simulation parameters can be found in the Supplemental Information 2.
In our model, we assume that the whole laser is DC pumped at , where th  denotes the pumping at threshold, and p the pumping ratio.To model the active modulation in the short section, a sinusoidal term is added to the pumping: , where m is the modulation amplitude, and f R is the cavity roundtrip frequency.Fig. 3d-f shows the simulated IACs for fixed modulation amplitude m=5 with different pumping ratio p, and Fig. 4d-f show the simulated IACs for fixed pumping ratio p=1.1 with different modulation amplitude m.For p=1.1 and m=5, the peak-to-background ratio of the IAC is 8:1, and the ratio gradually decreases with higher DC pumping p and smaller modulation amplitude m, which follows the experimental trend.Note however that there remain quantitative discrepancies with experiments, which show a faster decrease of the IAC ratio with increasing p and decreasing m.In order to predict the exact level to which the background in the IAC is rising, given certain pumping and modulation conditions, will need a much more detailed description of the gain as a function of pumping conditions and laser operation, then the two level model allows [18].
In both experiment and simulation, we observe side lobes in the IACs beside the main interference peak.The side lobes come from the multiple spikes in the intensity profile, as seen in the insets of Fig. 3d-f and Fig. 4d-f.Those spikes are caused by spatial hole-burning (SHB) in the laser gain created by standing waves in the cavity.
The gain grating introduced by SHB interferes with active mode locking as it couples the longitudinal modes and reduces the phase locking imposed by the gain modulator.
As a result, the modes develop nonlinear phases that lead to a waveform with multiple spikes.Note that in the experimental IACs, the 12 µm-wide device has more pronounced lobes than the 16 µm-wide one.This is consistent with our previous observation that SHB is less significant in wider devices because multiple transverse modes tend to wash out the gain grating formed by SHB [16].
In conclusion, we have demonstrated the first unequivocal stable mode-locking in QCLs via active gain modulation.As revealed by IAC, isolated periodic pulses as short as 3 ps can be generated in the vicinity of the laser threshold.Experimental data and numerical simulations show that the parameter window for stable mode-locking is determined both by the DC pumping current and the RF modulation power.Further pulse shortening and increase in pulse energy can be achieved by increasing gain lifetime and modulation amplitude.
The material was processed into 2.

FiguresFigure 1 . 8 ,
photolithography and a metal layer (Ti/Au; 20 nm/300 nm) was then deposited to provide electrical contact.The top Ti/Au contact and the underlying heavily doped InP

Figure 2 .
Figure 2. Laser characteristics.(a) The current-voltage (I-V) and output powercurrent (L-I) characteristics of the 16 µm wide QCL with no RF modulation.The laser threshold is at 310 mA.A, B, C denote the currents (I=340 mA, 450 mA &

Figure 3 .
Figure 3. Pulse characterization of the 16 µm-wide QCL output with 35 dBm of applied modulation at various DC pumping levels and corresponding simulations.(a), (b), (c) Interferometric autocorrelation traces (IACs) of the QCL pumped at 340 mA (1.1 times the laser threshold), 450 mA (1.45 times the laser threshold) and 500 mA (1.61 times the laser threshold), respectively.Inset (a): Microwave spectrum of photocurrent generated by the laser at 340 mA.Inset (b): detail of the interference fringes from 0.1 ps to 0.5 ps.All measurements

Figure 4 .
Figure 4. Pulse characterization of the 12 µm-wide QCL output at 265 mA with various RF input powers and corresponding simulations.(a), (b), (c) Interferometric autocorrelation traces (IACs) of the QCL with 35 dBm, 28 dBm & 12 dBm of RF input powers, respectively.All measurements were performed at a heat sink temperature of T=77 K and RF modulation frequency at 17.415 GHz.(d), (e), (f) Simulated IACs with modulation amplitude m=5, 3.5 & 0.5, respectively, with fixed DC pumping p=1.1.Insets show the corresponding intensity profile of one round-trip.