2022-08-17 11:00:00

In optimization theory, one clear dividing line between "easy" and "hard" problems is convexity. Convex optimization problems do not have local optima that are not global optima, and multiple decades of development have led to efficient computational machinery for solving convex problems. By contrast, nonconvex problems can have highly oscillatory landscapes, and one must typically use local optimization techniques or black-box algorithms. 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. I will describe how the key constraints in these design problems can be transformed from the typical differential-equation descriptions to infinite sets of local conservation laws, and that the latter have a structure amenable to quadratic and semidefinite programming. I describe how this approach can lead to global bounds ("fundamental limits") for many design problems of interest, and potentially to dramatically new approaches to identifying designs themselves. Next, specific to electromagnetic scattering, I will describe a unique construction of scattering matrices that leads to new methods for identifying fundamental limits across any bandwidth of interest.
Throughout I will emphasize novel applications where we have applied these techniques, including: minimal-thickness perfect absorbers, scaling laws for analog photonics, speed limits in quantum optimal control, and a new theory of the ultimate limits of near-field radiative heat transfer.

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.

2022-09-21 11:00:00

In my talk I will introduce polycyclic aromatic dye molecules as two-level quantum emitters and will review the recent advances of our group in controlling and manipulating their light-matter interaction by shaping their nanoenviroment. A special focus will be given on my PhD work dealing with the coupling of organic molecules to chip-based nanophotonic circuits.
Here, I will discuss the coupling of individual molecules to one-dimensional subwavelength waveguides and the prospects of realizing coupled emitter ensembles by DC-Stark tuning of the molecular resonances. Furthermore, I will demonstrate that the sensitivity of the molecules to electric fields can be used to sense fields in their nanoenviroment. The specific example will be weak charge fluctuations in a gallium phosphide waveguide. I will present a series of experiments that reveal the spatial and temporal correlations of the electric field and show that the temporal correlation scales proportionally with the optical intensity.
In the quest for reaching near deterministic coupling efficiencies, I will introduce ring- and disc-resonators and show the Purcell-enhanced coupling of single molecules to these structures. With our most recent design, a 6 µm diameter disk resonator, I will demonstrate a resonator finesse up to 250 (Q=16000), leading to coupling efficiency of 75%. Furthermore, I will show the controlled manipulation and tuning of molecular resonances via nearby microelectrodes and the simultaneous coupling of two individual molecules to the two counter propagating modes of the disc.

Dominik Rattenbacher studied physics in the "Physics Advanced Program" at the Universities of Erlangen and Regensburg from 2013 to 2018. After a research stay at the Ultrafast and Attosecond Science group of Prof. Hans Jakob Wörner at ETH Zurich, he did his Master thesis on "Spectroscopic investigation of two molecules coupled via a dielectric waveguide" in the Division of Vahid Sandoghdar at the Max Planck Institute for the Science of Light. His PhD work is a direct continuation of this project and aims at coupling several molecules efficiently via nanophotonic circuits.

The Optics and Quantum Electronics Seminar Series is supported by the
Research Laboratory of Electronics (RLE) and the Department of
Electrical Engineering and Computer Science (EECS).