Modulation instability in long distance -OTDR system

Recent trends in long distance phase-sensitive optical time-domain reflectometer (phi-OTDR) have led to a proliferation of studies on modulation instability (MI). However, most of these studies overlook the inaccuracies of MI gain spectrum based on the linear stability analysis of the nonlinear Schro center dot dinger equation in the case of long distance over about 10 km. Here, we conducted a comprehensive exploration of MI characteristics in the phi-OTDR system, including the effects of input power, detection distance, and background noise on the MI evolution process. Experiments confirmed the presence of an intrinsic spectral component of MI surrounding the signal in long-distance detection, which has not been reported previously. Further, we proposed a fitting expression using numerical simulation to determine the optimal input power for the phi-OTDR system. Compared to traditional threshold formulas, it does not require complex theoretical derivations and demonstrated significantly higher accuracy, particularly in systems with ultra-long detection distances. The deviation was less than 10%, demonstrating its potential as a more precise and simplified method of determining optimal input power. This could help improve the efficiency and reliability of these systems, leading to further advancements in the field of MI research.