Route to Chaos in a Unidirectional Ring of Three Diffusively Coupled Erbium-Doped Fiber Lasers

Abstract

We numerically investigate the dynamics of a ring consisting of three unidirectionally coupled Erbium-Doped Fiber Lasers (EDLFs) without external pump modulation. The study focuses on the system behavior as the coupling strength is varied, employing a six-dimensional mathematical model that includes three variables for laser intensities and three variables for population inversions of all lasers. Our primary objective is to understand the system evolution towards chaos from a stable equilibrium in the ring, considering the impact of increasing coupling strength. To analyze the system’s behavior, we employ various techniques such as time series analysis, power spectra, Poincaré sections, bifurcation diagrams, and Lyapunov exponents. During the transition to chaos, the system undergoes a Hopf bifurcation and a series of torus bifurcations. An essential aspect of this study is the exploration of a rotating wave propagating along the ring, where the wave nature (periodic, quasiperiodic, or chaotic) depends on the coupling strength. Additionally, we observe the coexistence of periodic and chaotic orbits within a specific range of the coupling strength. However, for very strong coupling, this bistability disappears, resulting in a monostable system with a single limit cycle. This regime exhibits potential for applications that demand short laser pulses with a substantial increase in peak power, reaching nearly 20 times higher levels compared to the continuous mode when the lasers are uncoupled. This discovery holds particular importance for optical communication systems, especially considering the attenuation optical signals experience when transmitted over long distances.