# An Optimal Control Approach to Gradient-Index2 Design for Beam Reshaping

@article{Adriazola2022AnOC, title={An Optimal Control Approach to Gradient-Index2 Design for Beam Reshaping}, author={J Marco Adriazola and Roy H. Goodman}, journal={Journal of the Optical Society of America A}, year={2022} }

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…

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SHOWING 1-10 OF 30 REFERENCES

Quantum optimal control in a chopped basis: Applications in control of Bose-Einstein condensates

- PhysicsPhysical Review A
- 2018

We discuss quantum optimal control of Bose-Einstein condensates trapped in magnetic microtraps. The objective is to transfer a condensate from the ground state to the first-excited state. This type…

Optimal control of Bose-Einstein condensates in three dimensions

- Physics
- 2015

Ultracold gases promise many applications in quantum metrology, simulation and computation. In this context, optimal control theory (OCT) provides a versatile framework for the efficient preparation…

Simplified freeform optics design for complicated laser beam shaping.

- PhysicsApplied optics
- 2017

A modified ray-mapping method is presented to simplify the freeform optics design for complicated optical field control and achieve a challenging task of producing two prescribed beam profiles on two successive target planes.

Optimal control technique for many-body quantum dynamics.

- PhysicsPhysical review letters
- 2011

We present an efficient strategy for controlling a vast range of nonintegrable quantum many-body one-dimensional systems that can be merged with state-of-the-art tensor network simulation methods…

Reduction-based strategy for optimal control of Bose-Einstein condensates.

- Computer SciencePhysical review. E
- 2022

This work proposes a control method based on first reducing the problem, using a Galerkin expansion, from a partial differential equation to a low-dimensional Hamiltonian ordinary differential equations system, and applies a two-stage hybrid control strategy that allows it to greatly reduce excitations both in the reduced model and the full GPE system.

Optimal quantum control of Bose-Einstein condensates in magnetic microtraps

- Physics
- 2007

Transport of Bose-Einstein condensates in magnetic microtraps, controllable by external parameters such as wire currents or radio-frequency fields, is studied within the framework of optimal control…

Numerical design of three-dimensional gradient refractive index structures for beam shaping.

- PhysicsOptics express
- 2020

A numerical design method is demonstrated for gradient refractive index (GRIN) beam shapers embedded in a medium and the solution is found using phase retrieval and a paraxial scalar wave beam propagation model.

Gradient-index design for mode conversion of diffracting beams.

- PhysicsOptics express
- 2016

A numerical GRIN design method is presented, where diffraction effects are considered in solving for the refractive index profile and reduced beam distortion is demonstrated in comparison to a purely geometric design method.

Computational techniques for a quantum control problem with H1-cost

- Computer Science
- 2008

A systematic comparison of L2- versus H1-based minimization shows that the choice of the appropriate functional space matters and has many consequences in the implementation of some optimization techniques.

Introduction to Fourier optics

- Physics
- 1968

The second edition of this respected text considerably expands the original and reflects the tremendous advances made in the discipline since 1968. All material has been thoroughly updated and…