Structural stability and array modes of odd number cyclic vertical cavity semiconductor laser arrays

Abstract

Arrays of Vertical Cavity Surface Emitting Lasers (VCSELs) were prepared by patterning the reflectivity of the laser's back mirror.1 The latter was accomplished by the deposition of metal layers on top of the Bragg mirror, employing a predefined spatial pattern. High quality and very large laser arrays were obtained using this method.2 The cyclic arrays of this paper are “real" two-dimensional (2D) arrays, since cyclic boundary conditions cannot be implemented in one dimension. Cyclic (ring) arrays are of practical interest since, by applying symmetry consideration, it is obvious that the near field (NF) and the far field (FF) intensity patterns of the dominant mode should have the same number of intensity lobes. This is in contrast to rectangular arrays, where the number of FF lobes is always 4. As a consequence, array illumination by multiple beams can be generated using the ring arrays. Odd number ring arrays are of a special interest, since the regular anti-phase mode cannot be supported by odd cyclical symmetry. Thus, spontaneous symmetry breaking is expected. The study presented in this paper explores the self modes of such arrays, their structural stability, and manifests the linear mechanism for spontaneous symmetry breaking with its general implications.