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

Jimmie Adriazola and Roy Goodman. Journal of the Optical Society of America A, 2022.
Apr 25, 2022·
Jimmie Adriazola
Jimmie Adriazola
Roy Goodman
Roy Goodman
· 0 min read
Abstract
We address the problem of reshaping light in the Schrödinger optics regime from the perspective of 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 reshape the intensity distribution of Schrödinger 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.
Type
Publication
Journal of the Optical Society of America A, 39(5), 907
publication published
optics optimal control
Jimmie Adriazola
Authors
Jimmie Adriazola
Presidential Postdoctoral Fellow, Arizona State University

In addition to studying applied mathematics and physics, Jimmie plays jazz guitar in local venues.

Jimmie’s dissertation research focused on the application of methods of optimal control to designing structures for the control of nonlinear waves in optics and BECs. He also worked as a research assistant in the NJIT Physics Department with professors John Federici and Ian Gatley.

Roy Goodman
Authors
Roy Goodman
Professor, Associate Chair for Graduate Studies, Department of Mathematical Sciences

I am a professor in the Department of Mathematical Sciences at NJIT. My research applies methods of dynamical systems to (conservative, dispersive) nonlinear wave equations arising, for example, in optics and fluid mechanics. I am interested in dynamical and bifurcation phenomena, and I use techniques from Hamiltonian mechanics and perturbation theory, as well as extensive computations. My current research in vortex dynamics is supported by the NSF under DMS-2206016.

I led the effort to start the SIAM New York-New Jersey-Pennsylvania Section (SIAM NNP) and was its first president in 2023-2024. I have handed over the reins to a new leadership group.