Jacobian Methods for Dynamic Polarization Control in Optical Applications

TL;DR

This paper models dynamic polarization control (DPC) using Jacobian-based control theory, providing a detailed analysis and proposing an efficient, reset-free algorithm inspired by robot kinematics for high-speed optical applications.

Contribution

It introduces a Jacobian framework for DPC, analyzes the Stokes vector gradient, and develops a novel null-space control algorithm for improved polarization manipulation.

Findings

Identifies the Jacobian structure of DPC control

Proposes a reset-free, efficient control algorithm

Demonstrates potential for customized DPC algorithms

Abstract

Dynamic polarization control (DPC) is beneficial for many optical applications. It uses adjustable waveplates to perform automatic polarization tracking and manipulation. Efficient algorithms are essential to realizing an endless polarization control process at high speed. However, the standard gradientbased algorithm is not well analyzed. Here we model the DPC with a Jacobian-based control theory framework that finds a lot in common with robot kinematics. We then give a detailed analysis of the condition of the Stokes vector gradient as a Jacobian matrix. We identify the multi-stage DPC as a redundant system enabling control algorithms with null-space operations. An efficient, reset-free algorithm can be found. We anticipate more customized DPC algorithms to follow the same framework in various optical systems.