In this paper, phase-locking dynamics of 2D VCSEL hexagonal array with an integrated Talbot cavity are numerically investigated based on rate equations aiming at achieving high brightness output. The processes of wavelength synchronization and phase locking under different fill factors ff and fractional Talbot cavity lengths L were addressed comprehensively. Different supermodes of phase-locked VCSEL array were then analyzed from both near-field and far-field pattern, and proved to be well matched with the results of coupled-mode theory. With appropriate configuration the Talbot-VCSEL system can operate in a full in-phase mode eventually, which is beneficial for determining the parameter interval corresponding to the most expected single narrow-lobe far-field pattern. Furthermore, the simulation results also indicate that, considering the parametric interactions the distribution of optical feedback from the fractional Talbot cavity should be consistent as much as possible to facilitate the realization of phase-locked state. Our study could provide a theoretical support to obtain the full in-phase coupled VCSEL array with high performance.
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