Instabilities and spatial complexity in a laser

We discuss the emergence of spatial structures in a ring laser model with transverse effects. The emphasis of this study is on the development of a description that can capture the essential features of transverse dynamics without the need for large-scale numerical efforts. We introduce an extension of the uniform field limit and derive a set of modal equations that we solve with conventional numerical methods. Our solutions show evidence of transverse mode competition in the laser dynamics, leading to both time-dependent and multimode stationary (cooperative frequency-locking) behaviors. In the time-dependent regime we analyze the resulting spatial structures and suggest a scheme for the investigation and characterization of spatial complexity.