Coherent 2-dimensional VCSEL arrays

Coupled 2-dimensional (2D) arrays of vertical cavity surface emitting lasers (VCSELs) have been pursued for more than two decades [1-4]. Recently, VCSEL arrays defined by introducing an etched photonic crystal (PhC) into the top facet [5] or with multiple implantation apertures [6] have demonstrated coherently coupled in-phase operation. Moreover, we have found that variable phase between the array pixels is possible and influences the coherence and far field pattern, where the latter can enable beam steering applications. Conventional VCSELs emitting nominally at 850 nm have 2D PhC patterns etched into their top facet to define transversely coupled laser arrays as depicted in Fig. 1 [5,7]. The PhC pattern confines light to the defect regions where lasing occurs. Evanescent optical coupling between the elements of the array can be engineered by the parameters of the holes or spaces in the photonic crystal between the lasing defect regions to achieve in-phase operation [5,7]. Arrays as large as 4×4, such as shown in Fig. 1(a) have operated in out-of-phase emission. Proton implantation may also be used to define individual elements in the coupled array. A 3-element triangular array and device cross-section is shown in Fig. 2. This approach adds no fabrication complexity to that of a conventional implant VCSEL. Because the implant provides electrical confinement without adding optical loss, the lasers tend to lock in-phase. In-phase far-field patterns for 2×1 and 3-element arrays are shown in Fig. 3 at 1.4 times threshold. Changing the current injection to one laser in the array causes the coherence and relative phase between the emission of the two lasers to change [8]. The phase difference may be determined using antenna array theory combined with far field beam patterns [9]. Fig. 4(a) shows that the magnitude of the complex coherence (proportional to visibility) is maximum near the in-phase condition for a 2×1 PhC VCSEL array. The change in relative phase between defects results in a change in the far field angle of the peak emission. Fig. 4(b) shows the variation in angle of the far-field lobe as a function of current injection into an in-phase coupled array. Because the relative phase variation is retained when the array current is pulsed, electronic (rather than thermal) effects create the induced refractive index changes which lead to phase shifting [8]. By separately controlling the injection into the 3-element array shown in Fig. 2(a), up to 7° maximum beam steering in 2-dimensions has been achieved [10]. Finally, modal analysis theory has been developed to describe the coupling between lasers. Each mode of our lasing system is expected to be fully spatially coherent and orthogonal with the other lasing modes. For the case of the 2×1 arrays we can analyze the modal behavior with 2 eigenvalue equations expressed in terms of the cross-spectral density between the two possible modes. The cross spectral density can be related to the intensity and the complex degree of coherence [11]. Through measurements of the far-field visibility and local intensity measurements, the relative contribution of each eigenmode to the coupled array emission can be determined. In Fig. 5 the ratio of the weaker to the stronger eigenvalue and the magnitude of the complex degree of coherence are plotted with respect to current to one of the lasers, while the other laser current is fixed at 3.1 mA. In the case of equal current injection, only one mode is lasing, and the coherence is high. As the difference between current injection to each laser increases, the second mode gains strength. As would be expected when two orthogonal modes are lasing, coherence decreases. As both modes continue to increase in relative strength, eventually frequency splitting arises, which matches well to predictions from our theory.