Optimal control approach to gradient-index design for beam reshaping

We address the problem of reshaping light in the Schrödinger optics regime from the perspective of the optimal control theory. In technological applications, Schrödinger 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 Schrödinger dynamics, optimally reshapes the intensity distribution of Schrödinger eigenfunctions from one end of the waveguide to the other. This work considers reshaping problems found in work by 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.