Optimal sparse networks for synchronization of semiconductor lasers

Abstract: The inevitable random frequency differences among semiconductor lasers present an obstacle to achieving their collective coherence, but previous worked showed that fully (all-to-all) coupled networks can still be synchronized even in the weakly coupling regime. An outstanding question is whether sparsely coupled network structures exist that lead to strong synchronization. This paper gives an affirmative answer: optimal sparse coupling configurations can be found which enables near-complete synchronization. Quite surprisingly, with respect to synchronization, certain sparse networks can outperform fully coupled networks, when the weights of coupling are placed dominantly on the laser pairs with large frequency differences. The counterintuitive phenomenon can be explained by a thermodynamic potential theory that maps the time-delay-induced phase dynamics to an energy landscape. These findings suggest a scalable and cost-effective approach to achieving robust, steady-state synchronization of semiconductor lasers in the presence of disorder and noise.