Oscillation analysis for a quasi-ring optical network

We study a two-channel quasi-ring network composed of two reconfigurable optical add-drop multiplexers (ROADMs) equipped with dynamic gain equalizers (WSS/DGEs) and two constant gain controlled optical amplifiers. We conduct an equilibrium and stability analysis on the quasi ring network because it is the simplest scenario in which optical channel power can oscillate within a loop. Due to the difference of time scale between pump control and channel power equalization, we treat the amplifiers in the loop as static nonlinear function mappings. Based on this mapping and considering transmission delay, we show that a specific type of channel flattening control by a output-average tracking WSS/DGE can cause oscillations in the quasi-ring network. Theoretical results are validated using numerical simulations.