# Optical Injection Locking for Generation of Tunable Low-Noise Millimeter Wave and THz Signals
## 4 Results and Discussion  
### Injection Locking with a Single Laser  
In order to measure the locking range of the laser, i.e., the range within which the slave laser locks to a tone of the injected comb without retuning, a modified setup as shown in Figure 5a was used. The phase modulator was replaced with a Mach-Zehnder modulator (MZM) to generate only two optical tones, and a variable optical attenuator was added to control the power of the injected light. The MZM was biased at the null point  
Figure 4: Electrical spectra for (**a**) comparison of two free-running lasers and two locked lasers and (**b**) linewidth estimation of two locked lasers. Figure 3: Microscope photograph of a section of the chips, showing one of the used lasers and identifying the relevant on-chip laser components. MIR—multimode interference reflector; PS—phase shifter; SOA—semiconductor optical amplifier; DBR—distributed Bragg reflector. to suppress the carrier and modulated with a sinusoidal wave with a frequency of \(f_{RF}\) in the range of 15-18 GHz, which produces two optical tones with a spacing of 30-36 GHz. This configuration produces two optical tones with spacing equal to \(2f_{RF}\). The slave laser was thermally tuned to match one of the external optical tones. The incident light was controlled through an optical coupler and achieving the locking state was monitored by analyzing the electrical signal from the photodiode and direct measurement of the optical signal. Detuning of the master signal was achieved by changing the RF frequency of the source, and injected power was tuned by means of the VOA. Figure 5b shows the measured locking range as a function of injection ratio \(P_{inj}/P_{0}\), where \(P_{inj}\) is the power of a master signal and \(P_{0}\) is the power of the slave laser, for two different currents feeding SOA\({}_{1}\). As can be seen, a locking range of about 2 GHz is achieved with an injection ratio of \(-20\) dB. The shape of the locking range is in good agreement with predictions based on analytical estimation of the locking range [24; 41]:  
\[-k\sqrt{1+\alpha^{2}}\sqrt{\frac{P_{inj}}{P_{0}}}=w_{min}<\Delta w<w_{max}=k \sqrt{\frac{P_{inj}}{P_{0}}} \tag{2}\]  
where \(\Delta w=w_{max}-w_{min}\), \(k\) is the coupling coefficient, and \(\alpha\) is the linewidth enhancement factor. In order to confirm that slave laser performance stays the same for different locking points within the locking range, phase noise (PN) of the output electrical signal resulting from beating the slave laser with the remaining second tone from the master on the PD can be analyzed as an indicator for locking quality, as it is related to the linewidth of the optical tone [42]. The measured PN when using Laser 1 (see Table 1) is shown in Figure 5c for different frequency offsets of the master tone and an injection ratio of \(-18\) dB, showing that for all measured frequency offsets, the shape and level of the phase noise profile remains the same. This observation can be explained by the fact that locking is similar for any different locking point within a limited locking range. Figure 5: (**a**) Experimental setup for measuring the locking characteristics of a single laser; (**b**) measured (dots) and theoretical (solid) locking range of a single laser for two different feeding currents; (**c**) phase noise power spectral density of the RF tone resulting from heterodyning of the injection-locked slave laser with the second master tone for different master laser frequency offsets. Another important aspect of injection locking is the quality of locking for different injected powers. Minimization of the injected ratio is desirable in order to increase suppression ratio between amplified tone and residual lines of the OFC. Similarly, in complex systems, it is possible to use a single master laser to lock arrays of slave lasers, which also decreases the available power to each copy of the signal, forcing locking at small injection ratios.