# Two Polarization Comb Dynamics in VCSELs Subject to Optical Injection
Optical injection of comb is used: first as a method to select and amplify a desired line in an optical frequency comb, but more recently as a technique to induce rich nonlinear laser dynamics, such as relaxation oscillation frequency locking [24], harmonics frequency locking [24] and Devil's staircase resonance [25]. However, to date, the full potential of this technique for broadband optical comb generation has only recently been addressed, with an in-depth analysis and mapping of nonlinear comb dynamics [26; 27]. In addition, in a very recent work, we have experimentally taken advantage of polarization dynamics in VCSEL to extend the comb's bandwidth and improve the power per comb lines referred to as carrier to noise ratio (CNR) [28]. It is shown that polarization switching induced by orthogonal optical injection plays a key role in the control of the comb properties (bandwidth and CNR) through the generation of two combs with orthogonal polarization. This work was restricted to a single-mode VCSEL with birefringence of \(\sim\)18 GHz and does not consider the full potential of the VCSEL parameters. The literature provides a lot of research on the optical injection dynamics in VCSEL with orthogonal polarized light [7; 10; 29; 30; 31; 32; 33; 34; 35]. The parallel (orthogonal) injection is the injection of light with linear polarisation parallel (orthogonal) to the free-running VCSEL linear polarisation direction. Although parallel optical injection in VCSELs shows similarities to optical injection in the conventional single-polarization edge-emitting laser, very interesting additional polarization dynamics have been reported recently [36; 37; 38; 39; 40]. The excitation of the polarization modes has been found to bifurcate to periodic, complex or chaotic dynamics with orthogonal polarization. The question of how parallel optical frequency comb injection in VCSELs induces additional nonlinear polarization dynamics is of great interest and has not been addressed so far. In this paper, we analyze, in detail, nonlinear dynamics and polarization properties in VCSELs subject to optical frequency comb injection. More specifically, we provide an in-depth experimental and theoretical description of the bifurcation scenarios when the polarization of injection comb is parallel to that of the VCSELs. We show that a variation of the injection parameters together with the bias current allows enabling the excitation of the normally depressed polarization mode accompanied by the generation of two combs with orthogonal polarization directions. The appearance of the two polarization combs is directly linked to the evolution of the injection current. Indeed, for a fixed injection current, comb generation performance is limited by the increase in injected comb spacing, but the increase in bias current allows overcoming this limitation. Experimental and numerical simulations highlight that the injection current is an addition parameter to control comb properties. Beyond this, the injection parameters are used to tailor the comb properties in a VCSEL in our previous work [28]; here, we take advantage of linear dichroism and birefringence to improve comb properties in the VCSEL. We also contrast experimentally and theoretically the comb dynamics in the cases of parallel and orthogonal optical injection when varying injection parameters, i.e., the comb spacing and injection strength and most importantly the injection current in the VCSEL. More specifically, we provide an in-depth bifurcation analysis of polarization comb dynamics when varying VCSEL parameters. The bifurcation diagrams show that VCSEL parameters can be used to suppress the comb in the normally depressed polarization mode or to tailor power in each polarization comb.