Dissertation Defense - Hanwen Zhang, “Resonances and Fundamental Bounds in Wave Scattering”

 
Abstract:
In nanophotonics, light is manipulated by interactions with designed subwavelength structures, fully harnessing wave interference and creating large responses that are unimaginable in ray optics. This talk will discuss new theoretical frameworks for analyzing scattering via resonances and for identifying fundamental limits to designed scattering response.
 
First, we develop a new resonance-based construction of scattering matrices in open electromagnetic systems. 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 denote “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.
 
Second, for arbitrary scattering matrices, we obtain power-concentration bounds for wave scattering by generalizing classical brightness theorem to wave scattering. We show that power per scattering channel generalizes brightness, and the rank of an appropriate density matrix generalizes etendue to states with arbitrary coherence. 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.
 

Finally, adapting recently developed techniques for electromagnetic-response bounds to quantum dynamics, we develop a general framework for identifying fundamental bounds in quantum control.  We show that an integral-equation-based formulation of conservation laws in quantum dynamics leads to fundamental limits for quantum control scenarios. We demonstrate the utility of our bounds in three prototype systems– three-level driving, decoherence suppression, and maximum-fidelity gate implementations – and show that our bounds are tight or nearly so in each case. Global bounds complement local-optimization-based designs, illuminating performance levels that may be possible and those that cannot be surpassed.

Join from PC, Mac, Linux, iOS or Android: https://yale.zoom.us/j/95253082161
    Or Telephone：203-432-9666 (2-ZOOM if on-campus) or 646 568 7788
    Meeting ID: 952 5308 2161
    International numbers available: https://yale.zoom.us/u/ae7aN3GYm
 
The committee members are:
Prof. Owen Miller
Prof. John Schotland
Prof. Doug Stone
 
Event time: 
Friday, April 8, 2022 - 10:00am
Department: 
Applied Physics
Advisor: 
Owen Miller