Electrical injection-locking dynamics of a frequency-modulated comb

The comb spacing of semiconductor comb lasers can be locked to an external reference by injecting a radio-frequency (RF) signal f inj close to the laser beat note round-trip frequency $f_{rt}^0$ [1] . This allows for controlling $f_{rt}^0$ and reducing its RF line width ∆ f rt . In this work, electrical-injection locking of a frequency-modulated quantum dash comb laser emitting at 1.57 µ m is demonstrated. Its round-trip frequency is $f_{rt}^0 = 20.1{\text{ GHz}}$ (cavity length 2 mm). The locking dynamics, recorded by direct detection of the comb’s output in the RF domain, are depicted in Fig. 1(a) for injection powers P inj from -10 dBm to 8 dBm. From -10 dBm up to 0 dBm, $f_{rt}^0$ and its -3 dB line width ∆ f rt remain unaffected. Within this range, the beat note line width amounts to 80 kHz. By increasing P inj from 0 dBm to 2.5 dBm, a pulling effect towards f inj becomes evident. For P inj > 2.5 dBm, the laser remains locked with ∆ f rt reduced to below 1 Hz, the microwave generator bandwidth. When sweeping f in j across $f_{rt}^0$ at P inj =8 dBm, Fig. 1(b) , two regimes evolve. For f inj outside the locking range of 1.8 MHz, $f_{rt}^0$ remains mostly unaffected with a small pulling effect for f inj close to the locking range. For frequencies inside the locking range ∆ f rt narrows to the bandwidth of the microwave oscillator and f rt follows f inj . Weak mixing side-band signals become apparent outside the locking range. Locking dynamics will be explained in more detail in the presentation. We employ the formalism of injection-locked coupled oscillators [2] and extend it by a noise term to take into account the stochastic origin of timing fluctuations. Results are depicted in Fig. 1(c) and Fig. 1(d) and are in agreement with the experiments. In order to quantify the improvement in phase noise of the comb by electrical injection locking $\left( {{f_{inj}} = f_{rt}^0} \right)$ , we measure phase noise spectra in dependence on P inj . Fig. 1(e) depicts increasing phase noise reduction by up to 20 dB at 100 kHz for increasing electrical injection strength. Simulation results ( Fig. 1(f) ) with a stochastic model [3] , developed for amplitude-modulated semiconductor comb lasers, are in excellent agreement with the experimental findings. Finally, we will show, that by joining both models, the comb laser beat note tuning can be directly linked with the phase noise reduction.