Solid State & Optics Seminar
sponsored by “The Flint Fund Series on Quantum Devices and Nanostructures”
Date : Wednesday, 11/9/22
Time: 1:00PM
Location: YQI Seminar Room
Speaker: Prof. Owen Miller, Yale University
Title: Physical design meets convex optimization: Hidden structure in Maxwell’s (and Schrodinger’s) equations
Abstract:
In optimization theory, one clear dividing line between “easy” and “hard” problems is convexity. In convex optimization problems, all local optima are global optima, which can be found by efficient computational algorithms. By contrast, nonconvex problems can have highly oscillatory landscapes, and one must typically resort to local optimization techniques or black-box approaches. Nanophotonic design problems, and many design problems across physics, reside squarely in the latter category of nonconvex optimization problems.
Or do they? I will show that there is a surprising amount of mathematical structure hidden in the typical differential equations of physics, and that this structure enables new connections to modern techniques in convex optimization. The key differential-equation constraints can be transformed to infinite sets of local conservation laws, which have a structure well-suited to quadratic and semidefinite programming. This approach offers a general framework for global bounds (“fundamental limits”) for many design problems of interest. It also appears to offer a dramatically new approach to the design process itself.
Spectral degrees of freedom have further hidden structure. Material optical susceptibilities are Drude-Lorentz oscillators not (only) because of single-electron quantum perturbation theory, but more generally as a consequence of causality. We can use this to identify upper bounds to refractive index, and design metamaterial structures that can approach them. We also propose a striking generalization: in electromagnetic scattering, the scattering “T” matrix can be decomposed into fictitious, matrix-valued (spatially nonlocal) Drude-Lorentz oscillators. For any EM scattering problems, the only controllable degrees of freedom are the matrix-valued oscillator strengths. This natural encoding of causality and passivity offers new insights into what is possible in nanophotonics.
Throughout I will emphasize novel applications where we utilize these techniques, including: maximum spontaneous-emission enhancements, scaling laws for analog photonics, optimal quantum control, and a theory of the ultimate limits of near-field radiative heat transfer.
Bio:
Owen Miller is an Asst. Prof. of Applied Physics and Physics at Yale. His research interests center around developing large-scale computational and analytical design techniques for discovering novel structures and new phenomena in nanophotonics. He is the recipient of AFOSR and DARPA young investigator awards, as well as the Yale Graduate Mentor award.