Date of Award
Doctor of Philosophy (PhD)
In this thesis, we develop a framework for analyzing light-matter interaction by resonances, explore power concentration limits in wave scattering, and discover fundamental bounds of quantum state controls via pulse engineering. We use quasinormal modes to develop an exact, ab initio generalized coupled-mode theory from Maxwell’s equations. This quasinormal coupled-mode theory, which we de- note “QCMT”, enables a direct, mode-based construction of scattering matrices without resorting to external solvers or data. We consider canonical scattering bodies, for which we show that a conventional coupled-mode theory model will necessarily be highly inaccurate, whereas QCMT exhibits near-perfect accuracy. We generalize classical brightness theorem to wave scattering, showing that power per scattering channel generalizes brightness, and obtaining power-concentration bounds for systems of arbitrary coherence for general linear wave scattering. The bounds motivate a concept of “wave ́etendue” as a measure of incoherence among the scattering-channel amplitudes and which is given by the rank of an appropriate density matrix. The bounds apply to nonreciprocal systems that are of increasing interest, and we demonstrate their applicability to maximal control in nanophotonics, for metasurfaces and waveguide junctions. Through inverse design, we discover metasurface elements operating near the theoretical limits. We show that an integral-equation-based formulation of conservation laws in quantum dynamics leads to a systematic framework for identifying fundamental limits to any quantum control scenario. We demonstrate the utility of our bounds in three scenarios – three-level driving, decoherence suppression, and maximum-fidelity gate implementations – and show that in each case our bounds are tight or nearly so. Global bounds complement local- optimization-based designs, illuminating performance levels that may be possible as well as those that cannot be surpassed.
Zhang, Hanwen, "Resonances and Fundamental Bounds in Wave Scattering" (2022). Yale Graduate School of Arts and Sciences Dissertations. 689.