# Graphical Representation of Cavity Length Variations, ΔL, on s-Plane for Low-Finesse Fabry–Pérot Interferometer

## TL;DR

This paper uses graphical methods to study cavity length changes in a low-finesse Fabry–Pérot interferometer under external disturbances.

## Contribution

Applying pole-zero maps and Bode plots on the s-plane to analyze cavity variations in optical interferometers.

## Key findings

- Cavity length variations can be visualized using pole-zero maps and Bode plots on the s-plane.
- Theoretical and numerical results agree on the behavior of cavity length changes under perturbations.
- These graphical methods are applicable to signal demodulation in optical interferometers and quasi-distributed sensors.

## Abstract

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, ΔL, 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.