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Date of Award
Doctor of Philosophy (PhD)
Whispering-gallery-mode (WGM) optical microresonators, in which light propagates along the circular rims due to the total internal reflection, have attracted broad attention in the past two decades. Owing to the ultrahigh quality factor and the small mode volume, WGM resonators can significantly enhance light-matter interactions, benefiting many applications such as optical communications, microlasers, opto-mechanics, frequency comb, and cavity quantum electrodynamics. Recently, WGM microresonators have proven to be an excellent platform to study non-Hermitian physics, due to the ease with which non-Hermiticity can be controlled via gain-loss distribution and modal coupling. Non-Hermitian physics studies open systems such as WGM microresonators with loss and/or gain, described by non-Hermitian Hamiltonians. One striking feature of the non-Hermitian systems is the existence of non-Hermitian degeneracies, also known as exceptional points (EPs), at which both the eigenvalues and the corresponding eigenstates coalesce. This is in stark contrast with conventional Hermitian degeneracies, where only the eigenvalues are degenerate, but the associated eigenstates can still be orthogonal. Many interesting phenomena and applications have been demonstrated at or near the EPs.
In this dissertation, we present the studies of non-Hermitian physics and EPs in two different configurations based on WGM microresonators. The first one is based on two coupled WGM resonators with different losses or with gain and loss. EPs are obtained by tailoring the frequency detuning and the coupling strength (or the loss/gain distribution) between the two resonators. The second one is based on a single WGM resonator interacting with two or more Rayleigh scatterers, which can induce asymmetric backscattering between the clockwise and counterclockwise travelling modes. EPs are obtained by tailoring the sizes and the positions of the scatterers. In particular, we have studied two intriguing characteristics of non-Hermitian systems – the chiral modes at EPs and the complex-square-root topology near (second-order) EPs, which can benefit the applications of WGM microresonators in light transport, laser mode management, and optical sensing. In addition, optical analogues of electromagnetically-induced transparency (EIT) in two coupled WGM microresonators are also studied.
Matthew Lew, Shantanu Chakrabartty, Xuan Zhang, Kater Murch,
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