We investigate the light propagation characteristics that depend on strong dispersion response in two-ring resonant structure. Strong dispersion response brings obvious effective phase shift change in resonant arm of Mach-Zehnder interferometer. We propose that two-ring coupled Mach-Zehnder interferometer exhibits sharp asymmetric Fano line shape. It mainly decided by the combined action of a π/2 phase bias in reference arm and effective phase shift in resonant arm. It can greatly enhance the sensitivity of sensor. It allows for measuring effective refractive index change down to 10-9 refractive index units.