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Updated: Jun 4, 2025

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Published on: June 8, 2018

Many photonic design problems are sparse QCQPs.

Shai Gertler¹, Zeyu Kuang¹, Colin Christie¹

¹Department of Applied Physics and Energy Sciences Institute, Yale University, New Haven, CT 06511, USA.

Science Advances

|January 1, 2025

Summary

This summary is machine-generated.

This study transforms complex photonic design problems into solvable sparse quadratic programs. This breakthrough enables the use of convex optimization to find optimal designs for wave physics, including metasurfaces.

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Area of Science:

Physics
Engineering
Applied Mathematics

Background:

Photonic design involves optimizing objectives like beam formation under Maxwell's equations.
These optimization problems are typically nonconvex and NP-hard, making global optima difficult to find.

Purpose of the Study:

To reformulate photonic design problems into a tractable mathematical framework.
To enable the application of convex optimization techniques to wave physics design.

Main Methods:

Transformed photonic design optimization into a sparse-matrix, quadratically constrained quadratic program (QCQP).
Applied convex optimization techniques, specifically semidefinite programming, to solve the sparse QCQPs.

Main Results:

Successfully computed fundamental limits for large-area metasurfaces.
Identified photonic designs that approach global optimality.

Conclusions:

The proposed sparse QCQP formulation makes photonic design problems solvable with convex optimization.
The approach is extensible to other fields governed by bilinear differential equations, such as structural optimization and fluid dynamics.