Low-Finesse Fabry–Pérot Interferometers Applied in the Study of the Relation between the Optical Path Difference and Poles Location

Abstract

Interferometry sensors are frequently analyzed by applying the Fourier transform because the transformation separates all frequency components of its signal, making its study on a complex plane feasible. In this work, we study the relation between the optical path difference (OPD) and poles location theoretically and experimentally, using the Laplace transform and a pole-zero map. Theory and experiments are in concordance. For our study, only the cosine function was considered, which is filtered from the interference pattern. In experimental work, two unperturbed low-finesse Fabry–Pérot interferometers were used. First, a Fabry–Pérot interferometer that has a cavity length of ~ 1.6 mm was used. Its optical path difference was 2.33 mm and the poles were localized at points ± i 12 . rad/nm. Secondly, a Fabry–Pérot interferometer with a cavity length of ~ 5.2 mm was used, and its optical path difference was 7.59 mm and the poles were localized at points ± i 40.4 rad/nm. Experimental results confirmed the theoretical analysis. Our proposal finds practical application for interferometer analysis, signal processing of optical fiber sensors, communication system analysis, and multiplexing systems based on interferometers.