Global Frequency Locking of Networks of Coherently Coupled Lasers

Nonlinear dynamics of networks of coupled oscillators is a subject of great interest in various disciplines ranging from electrical circuits and chemical reactions to biological cells and social systems. A universal property of such networks is a self-organized oscillation at a common frequency, which is often referred to as synchronization. Here, we investigate the frequency locking of a network of coupled lasers. In this regard, we introduce a first-order nonlinear coupled-mode model for optical oscillators representing semiconductor lasers. We show that two coupled oscillators with different individual frequencies can be synchronized in frequency when the mutual coupling rate exceeds a critical level. The threshold coupling is calculated and explored in the parameter space of the system. Next, we investigate synchronization in one- and two-dimensional arrays of lasers with uniform nearest neighbor coupling and explore the synchronization threshold as a function of the size of the network. Finally, we discuss that a more complex network topology is required in order to enforce global synchronization in a large network of coupled lasers.