Abstract

We investigate theoretically the interplay between polarization switching (PS) and nonlinear dynamics in a vertical-cavity surface emitting laser (VCSEL) subject to orthogonal optical injection from a master laser (ML). The free- running VCSEL is biased such that only the horizontal (x) linearly polarized fundamental (LP) mode is excited. The injected VCSEL is then modeled using an extension of the Spin Flip Model (SFM). We perform a bifurcation analysis using continuation techniques that allow tracking bifurcation of both stable and unstable solutions. The results are presented in Fig. 1 as a mapping in which qualitatively different bifurcation lines are depicted in the detuning (Am) vs. injection strength (E_inj) plane. A saddle-node (SN), two Hopfs (H₁ and H₂) and two first period-doubling bifurcations (PD¹₁ and PD¹₂) have been resolved. The supercritical and subcritical parts of each bifurcation line are plotted in black and gray respectively. The black dots are the switching points (PS) from x to y polarization when increasing the injection strength. Both SN and Hi are bifurcations of stationary solutions and have been previously discussed in details for edge emitting lasers [1], The supercritical parts of SN and H₁ bound the zone of stable injection-locking regime. We have therefore focused our discussion on the second Hopf bifurcation H₂ which, to the best of our knowledge, has not been reported for optically injected EEL. We show that the role played by H₂ is twofold. First it appears, from the stability analysis, that the upper part of the stable injection-locking zone is bounded by H₂ and not by the saddle-node- Hopf point G as it is the case for EEL [1], Second, we find that the smallest injection strength necessary to achieve PS is located on H₂ and corresponds to an abrupt change in the PS curve (see the arrow in Fig. 1). In addition to H₂, our results reveal that the presence of chaotic attractors such as those bounded by PD\ and PD¹₂ may affect the switching mechanism in a more complicated way (see the corresponding changes in the slope of the PS curve in Fig. 1). A Torus bifurcation (not shown in Fig. 1) that arises at the intersection between Hi and H₂ and then extends toward positive detuning contributes also to the complexity of PS in that zone. More interestingly, we observe that the resulting E-shape of the switching line agrees, qualitatively, with recent experiments [2].

© 2007 IEEE