This paper presents a method to obtain spectral ring-down information simultaneously via double-looped Mach-Zehnder interferometry. The symmetric split-step Fourier method was used to simulate the pulse propagation through the fiber loop to check fiber-induced effects on the pulse. The loop was built with a segment of fiber, output coupler, and fiber Bragg grating. The fiber Bragg grating was used as an artificial sample. We found that the pulse spectrum is not distorted as the pulse propagates the fiber loop. We have also demonstrated the possibility to extract the ring-down signals from spectrum variation via simulation. This approach can be applied to sample detection which requires high sensitivity and high spectral resolution.