Hyungki Andrew Shim

As newly emerging optical devices and metamaterials inundate the photonics community, there is a growing need to understand the limits to device performance. Are current state-of-the-art designs already near the frontiers of what is possible, or can they be further improved with better technology? Addressing such broad, foundational questions calls for a new paradigm, a novel approach to explore the unimaginably vast, physically allowed design space. In this thesis, we will establish fundamental limits to light–matter interactions in the context of wave propagation in free space via beam shaping, scattering phenomena involving designable structures, and intrinsic properties of optical materials.

First, we derive upper bounds to free-space concentration of light, mapping out the limits to the maximal intensity for any spot size and beam-shaping device. We use “inverse design” to discover metasurfaces operating near these limits, achieving up to 90% of maximum possible intensity. We then establish a sum rule for spontaneous emission, a prototypical near-field response, which relates integrated response over all frequencies to a simple electrostatic constant. Going further, we develop an analytical framework to derive upper bounds to near-field response over any bandwidth of interest and material platform. Finally, we derive fundamental limits to the refractive index of any transparent material. To this end, we use the theory of composites to identify metal-based metamaterials that can exhibit small losses and sizeable increases in refractive index over the current best materials.