Probing the Upper Limits to Light-Matter Interactions: from Spontaneous Emission to Superresolution

Date of Award

Fall 10-1-2021

Document Type


Degree Name

Doctor of Philosophy (PhD)



First Advisor

Miller, Owen


As newly emerging optical devices and metamaterials enrich the photonic landscape, there is a growing need to understand the limits to optical response. Are current, physical-intuition-based designs already near the frontiers of what is possible, or can they be significantly further improved? New approaches are needed to explore the vast, physical design space. In this thesis, we will establish fundamental limits to light-matter interactions at three levels: in free space, where beam-shaping can be used for wide-ranging applications including superresolution, for arbitrary scattering structures, where we develop new tools for identifying "power-bandwidth limits" to near-field optical response, and, finally, at the level of the optical properties of natural or designed materials themselves. 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. For sub-diffraction-limited optical beams, our bounds suggest the possibility for orders-of-magnitude intensity enhancements compared with existing demonstrations. We use "inverse design" to discover metasurfaces operating near these limits, achieving up to 90% of the global bounds. Moving from wave propagation to scattering phenomena, we 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. Our framework connects the classic complex-analytic properties of causal fields with newly developed energy-conservation principles. We also extend our bounds to multifunctional, tunable devices that allow for multiple frequencies as well as active tuning. Finally, we derive fundamental limits to the refractive index of any material, given only the underlying electron density and either the maximum allowable dispersion or the minimum bandwidth of interest. While our bounds are closely approached by a wide range of natural materials with small to modest dispersion, nature does not provide the highly dispersive, high-index materials that our bounds suggest should be possible. 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.

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