Abstract

Although the complex Landau-Ginzburg equation has played an important role in the study of fluid dynamics and has been widely investigated, much still remains unknown due to the complex nature of this PDE. Studies of optical turbulence or spatial-temporal chaos have recently been reviewed by Arecchi,^[1] in addition to other reports in related fields such as optical vortices, pattern formation and spatial-temporal complexity and intermittency.^[2] In this work, we suggest that instabilities observed experimentally^[3,4] in linear semiconductor laser arrays and 2-D surface emitting lasers can, in fact be interpreted as optical hydrodynamical phenomena similar to those observed in other laser system. If we define h to be the physical spacing between adjacent elements, for h→0, the complex amplitude becomes a continuous function both of time and space and Eq. (2) of Ref. ⁵ can rewritten for two-dimensional Surface emitting lasers as which is exactly complex Landau-Ginzburg equation, where p is the pump current above the threshold.

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