# Two Polarization Comb Dynamics in VCSELs Subject to Optical Injection
## 2 Experimental Polarization Dynamics
### Impact of the Injected Comb Spacing
Such single-polarization comb has the same repetition rate as the injected one. Figure 3 shows the polarization resolved optical spectra for comb dynamics in Figure 2d-f. Figure 3 confirms that the total VCSEL output combs shown in Figure 2d-f are formed by two combs with orthogonal polarization. In the optical spectrum of X-PM (Y-PM), we observed some comb lines at the frequency position of Y-PM (X-PM). This is due to the extension ratio of the polarization controllers. We have shown in Figure 2 the possibility of two orthogonal combs generation from polarization mode competition in a single-mode VCSEL. As discussed earlier in the introduction, the tunability of the optical frequency comb is a key property for many applications. In order to demonstrate tuning capability, we show in Figure 4 bifurcation scenarios inducing two polarization comb dynamics for the same detuning \(\Delta\
u=1.6\) GHz when increasing the injected comb spacing to \(\Omega=2\) GHz. Similarly for \(\Omega=1\) GHz comb injection, the VCSEL output at low injected power shows the free-running operation, which bifurcates to nonlinear wave mixing due to a modulation involving detuning and injected comb spacing. In agreement again with Figure 2, wave-mixing results in a two polarization combs generation. Most importantly, despite the comparable power of the two polarization combs, the numbers of lines in X-PM and Y-PM have significantly decreased compared to \(\Omega=1\) GHz comb injection case. Indeed, the number of frequency lines in each polarization mode has decreased to achieve 3 at \(-30\) dB from the maximum. It is important to notice that the two polarization comb dynamics are observed in a very small area of injection parameters for \(\Omega=2\) GHz comb injection. We have checked by using polarization resolved optical spectra that these total combs are formed by two micro-comb with orthogonal polarization in single-mode VCSEL, as shown in Figure 5. A small increase in the injected power destabilizes VCSEL to more complex dynamics in each polarization mode, as shown in Figure 4d. We have checked that the size of the two polarization comb region shrinks when increasing the injected comb spacing until it disappears at \(\Omega=4\) GHz. Figure 6 shows how to overcome this limitation. Similarly to \(\Omega=1\) GHz comb injection, complex polarization dynamics bifurcates to the single-polarization comb in X-PM. This polarized comb has an important noise pedestal and, therefore, deteriorating the comb performances. Interestingly, we have also checked that the two polarization comb dynamics in the single-mode VCSEL under parallel optical injection are not observed when the bias current is below \(I=6\) mA. In contrast, when the polarization of the injected comb is orthogonal to that of VCSEL, the two polarization comb dynamics is always observed, whatever the bias current is. Figure 3: Polarization resolved-optical spectra corresponding to an example of two polarization comb dynamics similar to Figure 2d–f for detuning \(\Delta\
u=1.6\) GHz and injected power \(P_{inj}=20\) μW. (**a–c**) correspond to the optical spectra of Y-PM, X-PM and the superposition of Y-PM and X-PM, respectively. Figure 2: Bifurcation scenarios resulting in the excitation of the depressed polarization mode. These optical spectra are obtained for detuning \(\Delta\
u=1.6\) GHz and injected comb spacing \(\Omega=1\) GHz when increasing the injected power, \(P_{inj}\). (**a**) Stable output at \(P_{inj}=3\) μW, (**b,c**) wave mixing at \(P_{inj}=16\) μW and \(P_{inj}=32\) μW, respectively, (**d**) two polarization comb at \(P_{inj}=48\) μW, (**e,f**) two polarization harmonics comb at \(P_{inj}=80\) μW and \(P_{inj}=96\) μW, respectively, (**g**) two polarization complex dynamics at \(P_{inj}=128\) μW and (**h,i**) X-polarization comb at \(P_{inj}=144\) μW and \(P_{inj}=240\) μW, respectively.