In-Phase Coherent Parallel-Coupled Analysis of Two-Dimensional Vertical-Cavity Surface-Emitting Laser Arrays with Talbot Cavity

Coherent laser output in vertical cavity, surface-emitting laser (VCSEL) arrays has attracted enormous attention owing to its potential applications in various fields. In this article, we utilize a Talbot cavity-phase locking technology to achieve in-phase coherent VCSEL arrays (Talbot-VCSEL). A Talbot cavity parallel coupling model of Talbot-VCSEL arrays is established based on Fresnel diffraction theory and mutual injecting locking theory. The magnitude of parallel-coupled optical feedback can be evaluated using the mutual coupling coefficient Cmn, which can be calculated by this model. Furthermore, by combination of parallel-coupled optical feedback with the laser rate equations, the phase locking dynamic behavior of hexagonal Talbot-VCSEL arrays with different Talbot cavities is analyzed. We demonstrate that the in-phase coherent parallel-coupled laser output in the hexagonal Talbot-VCSEL array with a Talbot cavity length of ZT/4. In the experiment, we designed and fabricated a 19-element hexagonal in-phase coherent Talbot-VCSEL array. It has been shown that the fwhm of the spectrum is 0.15 nm and the far-field distribution exhibits highly in-phase coherent performance, which aligns well with theoretical calculation results. This technique opens a new path to achieve large-scale, highly in-phase coherent VCSEL arrays.