Graphical Representation of Cavity Length Variations, Δ<i>L</i>, on s-Plane for Low-Finesse Fabry–Pérot Interferometer
Pole-zero maps and Bode plots are commonly utilized in control systems and the study of natural phenomena to visualize their origins and behavior. In this paper, these graphical methods are applied to investigate the behavior of cavity variations, ΔL, in a low-finesse Fabry–Pérot interferometer subj...
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2025-03-01
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| author | Alex Guillen Bonilla José Trinidad Guillen Bonilla María Eugenia Sánchez Morales Héctor Guillen Bonilla Maricela Jiménez Rodríguez Antonio Casillas Zamora |
| author_facet | Alex Guillen Bonilla José Trinidad Guillen Bonilla María Eugenia Sánchez Morales Héctor Guillen Bonilla Maricela Jiménez Rodríguez Antonio Casillas Zamora |
| author_sort | Alex Guillen Bonilla |
| collection | DOAJ |
| description | Pole-zero maps and Bode plots are commonly utilized in control systems and the study of natural phenomena to visualize their origins and behavior. In this paper, these graphical methods are applied to investigate the behavior of cavity variations, ΔL, in a low-finesse Fabry–Pérot interferometer subjected to external perturbations. Both graphical representations are analyzed in the s-plane. The study is theoretically performed, and the theory is corroborated by developing three numerical experiments where small displacements were applied. Based on the theoretical and numerical results, the cavity length variations, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>Δ</mo><mi>L</mi></mrow></semantics></math></inline-formula>, can be studied on the s-plane applying the pole-zero maps and Bode plots. The two methods, including the theory and the experiments, are in agreement. Considering the theoretical and graphical results, pole-zero maps and Bode plots can be applied on the signal demodulation of optical interferometers and quasi-distributed sensors where local sensors are interferometers. |
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| language | English |
| publishDate | 2025-03-01 |
| publisher | MDPI AG |
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| spelling | doaj-art-34416de215e9490a8f7e44c59c50331c2025-08-20T02:09:17ZengMDPI AGSensors1424-82202025-03-01257218210.3390/s25072182Graphical Representation of Cavity Length Variations, Δ<i>L</i>, on s-Plane for Low-Finesse Fabry–Pérot InterferometerAlex Guillen Bonilla0José Trinidad Guillen Bonilla1María Eugenia Sánchez Morales2Héctor Guillen Bonilla3Maricela Jiménez Rodríguez4Antonio Casillas Zamora5Departamento de Ciencias Computacionales e Ingenierías, CUVALLES, Universidad de Guadalajara, Carretera Guadalajara-Ameca Km. 45.5, Ameca 46600, Jalisco, MexicoDepartamento de Electro-Fotónica, Centro Universitario de Ciencias Exactas e Ingenierías, Universidad de Guadalajara, Blvd-M. García Barragán 1421, Guadalajara 44410, Jalisco, MexicoDepartamento de Ciencias Tecnológicas, Centro Universitario de la Ciénega (CUCienéga), Universidad de Guadalajara, Av. Universidad No. 1115, Lindavista, Ocotlán 47810, Jalisco, MexicoDepartamento de Ingeniería de Proyectos, Centro Universitario de Ciencias Exactas e Ingenierías, Universidad de Guadalajara, Blvd-M. García Barragán 1421, Guadalajara 44410, Jalisco, MexicoDepartamento de Ciencias Básicas, Centro Universitario de la Ciénega (CUCienéga), Universidad de Guadalajara, Av. Universidad No. 1115, LindaVista, Ocotlán 47810, Jalisco, MexicoDepartamento de Electro-Fotónica, Centro Universitario de Ciencias Exactas e Ingenierías, Universidad de Guadalajara, Blvd-M. García Barragán 1421, Guadalajara 44410, Jalisco, MexicoPole-zero maps and Bode plots are commonly utilized in control systems and the study of natural phenomena to visualize their origins and behavior. In this paper, these graphical methods are applied to investigate the behavior of cavity variations, ΔL, in a low-finesse Fabry–Pérot interferometer subjected to external perturbations. Both graphical representations are analyzed in the s-plane. The study is theoretically performed, and the theory is corroborated by developing three numerical experiments where small displacements were applied. Based on the theoretical and numerical results, the cavity length variations, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>Δ</mo><mi>L</mi></mrow></semantics></math></inline-formula>, can be studied on the s-plane applying the pole-zero maps and Bode plots. The two methods, including the theory and the experiments, are in agreement. Considering the theoretical and graphical results, pole-zero maps and Bode plots can be applied on the signal demodulation of optical interferometers and quasi-distributed sensors where local sensors are interferometers.https://www.mdpi.com/1424-8220/25/7/2182low-fineness Fabry–Pérot interferometercavity length variations ΔLpole-zero mapsbode plotscomplex plane s |
| spellingShingle | Alex Guillen Bonilla José Trinidad Guillen Bonilla María Eugenia Sánchez Morales Héctor Guillen Bonilla Maricela Jiménez Rodríguez Antonio Casillas Zamora Graphical Representation of Cavity Length Variations, Δ<i>L</i>, on s-Plane for Low-Finesse Fabry–Pérot Interferometer Sensors low-fineness Fabry–Pérot interferometer cavity length variations ΔL pole-zero maps bode plots complex plane s |
| title | Graphical Representation of Cavity Length Variations, Δ<i>L</i>, on s-Plane for Low-Finesse Fabry–Pérot Interferometer |
| title_full | Graphical Representation of Cavity Length Variations, Δ<i>L</i>, on s-Plane for Low-Finesse Fabry–Pérot Interferometer |
| title_fullStr | Graphical Representation of Cavity Length Variations, Δ<i>L</i>, on s-Plane for Low-Finesse Fabry–Pérot Interferometer |
| title_full_unstemmed | Graphical Representation of Cavity Length Variations, Δ<i>L</i>, on s-Plane for Low-Finesse Fabry–Pérot Interferometer |
| title_short | Graphical Representation of Cavity Length Variations, Δ<i>L</i>, on s-Plane for Low-Finesse Fabry–Pérot Interferometer |
| title_sort | graphical representation of cavity length variations δ i l i on s plane for low finesse fabry perot interferometer |
| topic | low-fineness Fabry–Pérot interferometer cavity length variations ΔL pole-zero maps bode plots complex plane s |
| url | https://www.mdpi.com/1424-8220/25/7/2182 |
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