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

José Trinidad Guillen Bonilla; Héctor Guillen Bonilla; Verónica María Rodríguez Betancourtt; María Eugenia Sánchez Morales; Juan Reyes Gómez; Antonio Casillas Zamora; Alex Guillen Bonilla

doi:10.3390/s20020453

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

Sensors (Basel). 2020 Jan 13;20(2):453. doi: 10.3390/s20020453.

Authors

José Trinidad Guillen Bonilla^{1

2}, Héctor Guillen Bonilla³, Verónica María Rodríguez Betancourtt⁴, María Eugenia Sánchez Morales⁵, Juan Reyes Gómez⁶, Antonio Casillas Zamora³, Alex Guillen Bonilla⁷

Affiliations

¹ Departamento de Electrónica, Centro Universitario de Ciencias Exactas e Ingenierías (C.U.C.E.I.), Universidad de Guadalajara, Blvd. M. García Barragán 1421, Guadalajara 44410, Mexico.
² Departamento de Matemáticas, Centro Universitario de Ciencias Exactas e Ingenierías (C.U.C.E.I.), Universidad de Guadalajara, Blvd. M. García Barragán 1421, Guadalajara 44410, Mexico.
³ Departamento de Ingeniería de Proyectos, Centro Universitario de Ciencias Exactas e Ingenierías (C.U.C.E.I.), Universidad de Guadalajara, Blvd. M. García Barragán 1421, Guadalajara 44410, Mexico.
⁴ Departamento de Química, Centro Universitario de Ciencias Exactas e Ingenierías (C.U.C.E.I.), Universidad de Guadalajara, Blvd. M. García Barragán 1421, Guadalajara 44410, Mexico.
⁵ Departamento de Ciencias Tecnológicas, Centro Universitario de la Ciénega (CUCienéga), Universidad de Guadalajara, Av. Universidad No. 1115, LindaVista, C.P., Ocotlán 47810, Mexico.
⁶ Departamento de Ciencias químicas, Universidad de Colima, Las Víboras, Coquimatlan 28045, México.
⁷ Departamento de Ciencias Computacionales e Ingenierías, Centro Universitario de los Valles (CUValles), Universidad de Guadalajara, Carretera Guadalajara-Ameca Km. 45.5, Ameca 46600, Mexico.

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 ±i12. 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 ±i40.4 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.

Keywords: Fabry–Pérot interferometer; Laplace transform; interferometry sensors; pole-zero map; relation between the optical path difference (OPD) and poles location.