Direct measurement of an ultrafast sub-bandwidth-limited signal in mid-infrared quantum cascade lasers

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Introduction
Quantum cascade lasers (QCLs) offer an attractive platform for mid-infrared frequency combs, due to their compact, on chip geometry [1,2].Their high output powers of more than 1 W at room temperature as well as the possibility to directly probe the comb repetition rate electronically makes them ideal for sophisticated spectroscopic methods such as dual-comb spectroscopy [3].Due to their short upper-state lifetime, which is about an order of magnitude lower than the cavity round-trip time [4], they favor a quasi-continuous intensity state, which is predominantly frequency modulated, rather than the emission of optical pulses [5].To force the QCL into amplitudemodulated operation, active modelocking has been applied to achieve pulses on the picosecond-scale [6].Alternatively, sub-picosecond pulses have been achieved via external compression of the laser output signal [7].However, while simulations predict the formation of short features in the QCL comb time-domain signal [8,9], thus far intrinsic ultrashort sub-picosecond scale features have not been observed experimentally in mid-infrared QCL frequency combs.
In this work, we use the direct upconversion sampling technique asynchronous upconversion sampling (ASUPS) [10] supported by repetition rate stabilization via RFinjection to experimentally study short time-domain features that appear spontaneously in Fabry-Pérot midinfrared QCLs with a width below the bandwidth-limited pulse retrieved from the corresponding optical spectrum.* e-mail: bschnei@ethz.ch

Results
The time-domain signal for an RF-injected QCL ridge, is shown in Figure 1 a).There are spikes with a spacing corresponding to the cavity round-trip time clearly visible on top of a sinusoidal background modulation caused by the RF-modulation of the device bias.Since ASUPS is only sensitive to periodic components in the signal and aver- ages out any incoherent parts of the output.This means that the observed spikes are stable at least on the millisecond scale with respect to the applied RF-modulation.Subtracting a sinusoidal fit from the signal, as shown in Figure 1 b), further reveals the prominence of the spike as well as the occurrence of smaller intensity oscillations between the spikes.The spike itself has a full width at halfmaximum of 549 fs, which is shorter than the 588 fs of the Fourier-limited pulse calculated based on the optical spectrum in Figure 2 a).The two pulses are superimposed in Figure 2 b), where the experimental trace after subtracting the sinusoidally modulated background is used.We were able to predict the occurrence of such sub-bandwidth limited features in our system, as shown in Figure 2 c), using simulations based on the mean-field model by D. Burghoff [9].

Discussion
Our results clearly show the spontaneous formation of ultrashort features in the time-domain signal of a Fabry-Pérot mid-infrared QCL frequency comb.Even without accounting for additional broadening caused by the convolution of the signal with the probe pulse, the experimentally observed pulse-width is below the bandwidth-limited pulse-width.Whereas the spike sits atop a considerable background intensity, it shows remarkable stability relative to the RF-modulation, since any contributions which are not periodic with the modulation are averaged out by default.In the simulation results, the potential for the formation of sub-bandwidth limited pulses is even more apparent.Tuning of the simulation parameters can allow us further insight into the factors that contribute to the nar-rowing of the spike.These results show promise for potential applications of QCLs in ultrafast spectroscopy and imaging in the mid-IR.Both, optimization of the device properties to enhance these pulsations and external amplification of such generated pulses open up new opportunities for generating QCL-based pulsed laser systems.

Figure 1 .
Figure 1.QCL output signal as measured using asynchronous upconversion sampling (ASUPS) a) as is and b) after subtracting a sinusoidal fit corresponding to the background modulation induced by the RF-modulation used to stabilize the comb repetition rate.

Figure 2 .
Figure 2. a) The QCL spectrum measured under the same conditions as the ASUPS trace.b) Zoom around the spike in the ASUPS trace after subtracting a sinusoidal fit from the original signal superimposed with the Fourier-limited pulse calculated from the spectrum in a).c) Results from a mean-field based simulation of the time-trace, superimposed with the respective Fourier-limited pulse and the fastest Fourier-component based on the spectral envelope.