Experimental implementation of a non-ideal three-waveplate array as a polarization disturbance corrector

Polarization disturbance is a significant source of error in polarization-based experiments, where an input state is unpredictably transformed into an unintended state due to the birefringence of optical media. A solution to this problem is the implementation of a polarization disturbance corrector based on a three-waveplate array. In this work, we propose a theoretical framework to derive the analytical expressions of the correction parameters for a three-waveplate array with retardance (η1,η2,η3), along with an experimental method that requires only a single polarization measurement basis. The proposed theoretical framework, based on the mathematical treatment of polarization and its relation with the mathematical structure of the SU(2) Lie group, reveals the fundamental role of the transformations performed by a three-waveplate array in correcting polarization disturbances while analytical expression are deduced. Furthermore, we validate the theoretical derived expressions by implementing a three-waveplate array with retardances close to (π/2,π/2,π) in an experimental scenario, successfully compensating for polarization disturbance introduced by a single-mode optical fiber. The experimental results were evaluated through the calculation of polarization state fidelities, achieving values approaching unity. The experimental method presented in this work enables a precise correction to polarization disturbance as well as an enhancement of the robustness of experiments involving polarization against external variables that affect birefringent media. Our work sets the theoretical and experimental foundations for developing automated optical correction systems with precise polarization control in polarization-based experiments.