## 2 Experimental Setup and Results
(**b**) L-I curve. Inset is the optical spectrum at 280 mA. (**c**) Optical linewidth versus the pump current. The reflector in (**a**) is tilted in the yaw direction. The tilt angle is zero when the reflector is well aligned with the optical path and is positive when the reflector is tilted in the arrow direction. Figure 2: (**a**) Temporal waveform and (**b**) electrical spectrum of the P1 oscillation at 300 mA. The tilt angle of the reflector is \(-1.05^{\prime}\). Figure 3a shows that the amplitudes of the fundamental signal in the electrical spectrum are mostly in the range of 50 to 65 dB, which yields an average value of 57.2 dB. The amplitude does not show clear dependence on either the tilt angle of the reflector or on the pump current of the laser. Through least-square fitting of the electrical signal using the Voigt function, we obtain the electrical linewidth as illustrated in the inset of Figure 3b. For the statistics of the linewidth, 20 sweeps of measurement are averaged for every tilt angle with a resolution bandwidth (RBW) of 2.0 kHz. It is demonstrated that the electrical linewidths for different tilt angles in Figure 3b are mostly in the range of 1.5 to 2.0 kHz, with an average value of 1.7 kHz. It is remarked that these extracted linewidths are below the RBW of 2.0 kHz. However, a smaller RBW leads to an electrical signal deviating from the Voigt shape. In this case, the fundamental signal peak splits into several sub-peaks due to the long-term instability of the experimental setup, such as the variation of the feedback length or phase [40]. This P1 frequency instability will be quantified in future work. On the other hand, the frequency stability can be improved by stabilizing the feedback mirror position using a piezoelectric transducer. Similar to the peak amplitude in Figure 3a, the electrical linewidth is almost independent of the tilt angle and of the pump current as well. Surprisingly, the electrical linewidth of the P1 oscillations is about four orders of magnitude smaller than the optical linewidth of the free-running laser. Because the electrical spectrum is a beat note of the optical spectrum, the ultra-narrow electrical linewidth suggests that the main optical mode is highly coherent with the P1-induced optical sidebands. Unluckily, these sidebands are not visible in the optical spectrum due to the resolution limit of the FTIR (2.4 GHz). Future work may measure such optical sidebands based on the absorption resonance of certain gas molecules [41; 42]. The high coherence of the optical sidebands is similar to that with direct current modulation or with external modulation. It is remarked that semiconductor lasers subject to optical injection produce P1 oscillations as well [43; 44]. However, the coherence of the optical sidebands with optical injection is usually low and varies significantly depending on the injection condition [9; 11]. Figure 4 extracts the modulation depth of the electrical signal from the AC temporal waveform in Figure 2a, along with the tracked DC voltage. The modulation depths are mostly in the range of 1.0% to 3.5%. The dependence of the modulation depth on the tilt angle of the reflector is not obvious, possibly due to the uncertainty of the measured tilt angle, including the calibration error of zero angle and the backlash of the kinematic stage. On the other hand, the modulation depth shows little dependence on the pump current. Figure 3: (**a**) Amplitude and (**b**) linewidth of the fundamental electrical signal for pump currents of 280, 290, and 300 mA. Inset is an example of the electrical linewidth fitting using the Voigt function. Because the P1 frequency is governed by the external cavity frequency, the modulation frequency of the QCL can be easily tuned by changing the feedback length. As shown in Figure 5, the P1 frequency is tuned from 147.1 MHz at the feedback length of about 102 cm up to 627.3 MHz at the length of about 24 cm, which is the lower length limit of our experimental setup.