Abstract
We consider an optical ring cavity with distributed nonlinear elements and investigate the effect of delay using linear stability analysis. The lowest threshold for stability of the system is found and described by the spatial Lyapunov exponent α as α=0. When the system is lowest stability threshold, the delay has no effect on the system's stability. We also discuss the short delay approximation. In this regime, the stability threshold prediction is larger than that the system should have, and this also verifies that delay will induce instability.
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