## 3 Self-injection Locking of a DFB Laser  
The experimental set-up for the injection locking of a DFB laser (model number LSDLD155-5-5-0-2-SMFA with current driver LDTC0520) is sketched in Figure 2. The output beam of a DFB laser passes through an optical circulator, and collimated into free-space to pass he FPMC. The transmission is then sent back into the laser via a 90:10 fiber beam splitter. The transmission into the FPMC is measured to be \(\sim\)86%. A series of half-wave plates (HWP) and quarter-wave plates (QWP) are applied to ensure that the light beam is injected back to the DFB laser with the same polarization output. An optical spectrum analyzer (OSA) is used to characterize the laser spectrum. Figure 3a plots the measured laser wavelength as a function of the driving current before (black) and after (red) the injection locking. Before locking, the laser output is directed to OSA without the feedback loop. The threshold current of the free-running DFB laser is \(\sim\)11.3 mA. When the laser is injection-locked, the threshold (10 mA) is lower than the free-running case, due to the extra external feedback. It can be seen that, before the injection locking, the laser wavelength increases with the driving current, while after locking, the output wavelength is stabilized to the FPMC resonance (1550.24 nm). This indicates that the output power of the locked laser can be modulated without varying its wavelength, which is beneficial for telecommunication applications. Figure 3b compares the lasing wavelength (red) and the FPMC resonance (black) at different FPMC temperature. To control the temperature of the FPMC, it is put inside an oven with temperature-control accuracy of 0.01 \({}^{\circ}\)C. It can be seen that, after the locking, the laser wavelength follows the variation of the change of FPMC resonance. In this measurement, the current is set 24.8 mA, which is far above the threshold (5 mA). Figure 3c compares the measured laser spectrum before and after injection locking, and the result shows that the sidebands of the free-running laser can be suppressed by \(\sim\)9 dB. Figure 3d displays the laser output wavelength, measured after the 10% port of the 90:10 fiber beam splitter, as a function of laser temperature. In the free-running case, the laser wavelength increased as the temperature of the laser diode (black line), mainly due to the refractive index dependence of the temperature. However, when the laser is locked, the output wavelength is stabilized. Figure 2: Sketch of experimental setup. FPMC, Fabry-Perot microcavity; QWP, quarter-wave plate; HWP, half-wave plate; BS, beam-splitter; PD, photodetector. OSA, optical spectrum analyzer. The free-running DFB laser we used has a relatively large linewidth, which can be reduced by the self-injection locking with the FPMC. We used heterodyne detection [32; 33] to measure the beat note between the locked laser and the high-performance reference external cavity diode laser (Santec TSL-710, 200 kHz linewidth). For the free-running case shown in Figure 4a (blue curve), the captured oscilloscope trace of the beating signal is a distorted sinusoidal function. Figure 4b shows the measured beat spectrum using an electric spectrum analyzer (resolution bandwidth 50 Hz). A sharp peak at 102.5 MHz is clearly visible, corresponding the beat frequency between the free-running laser and Laser 1 (zoom-in of the marked regime shown in inset picture). The measured FWHM linewidth is 7.1 MHz, indicating the free-running laser linewidth at this level. When the laser is locked, the temporal waveform appears more regularly, as shown in Figure 4c. Figure 4d shows the measured beat spectrum using the same electric spectrum analyzer setting. The beat-note linewidth is fit to be 402 kHz FWHM (assuming Lorentzian shape), which is orders of magnitude narrower than the free-running case. In this measurement, the temperature was 23.997 \({}^{\circ}\)C and the current was 24.8 mA.