An Optimal Control Approach to Gradient-Index Design for Beam Reshaping

TL;DR

This paper applies optimal control theory to design the refractive index profile in Schr"odinger optics, enabling precise reshaping of light intensity distributions in waveguides, with demonstrated numerical success.

Contribution

It introduces an optimal control framework for beam reshaping in Schr"odinger optics, integrating quantum control tools for improved computational solutions.

Findings

Numerical demonstrations show effective beam reshaping.

The optimal control approach outperforms traditional methods.

The method is applicable to existing waveguide reshaping problems.

Abstract

We address the problem of reshaping light in the Schr\"odinger optics regime from the perspective of optimal control theory. In technological applications, Schr\"odinger optics is often used to model a slowly-varying amplitude of a para-axially propagating electric field where the square of the waveguide's index of refraction is treated as the potential. The objective of the optimal control problem is to find the controlling potential which, together with the constraining Schr\"odinger dynamics, optimally reshape the intensity distribution of Schr\"odinger eigenfunctions from one end of the waveguide to the other. This work considers reshaping problems found in work due to Kunkel and Leger, and addresses computational needs by adopting tools from the quantum control literature. The success of the optimal control approach is demonstrated numerically.