Statistical insight into the correlation of geometry and spectral emission in network lasers

Optically active networks show feature-rich emission that depends on the fine details of their geometry and find diverse applications in random lasers, sensing devices, and photonics processors. In these and other systems, a thorough and predictive characterization of how the network geometry correlates with the resulting emission spectrum would be highly important; however, such an outright description is still lacking. In this work, we take a step toward filling this gap by using the well-known Steady-state Ab initio Laser Theory equations to carry out an extensive set of statistical analyses and establish connections between the random network geometry and their ultimate emission spectrum. Our results show that edge crowding (abundance of short edges in the network) is key to tuning the uniformity of the modal intensity distribution of the emission spectrum. A statistical framework for the comprehensive understanding of the network statistical properties is highly significant to establish precise design rules for network-based photonic devices and intelligent systems.