Wave Chaos Studies and The Realization of Photonic Topological Insulators

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2022

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Wave propagation in various complex media is an interesting and practical field that has a huge impact in our daily life. Two common types of wave propagation are examined in this thesis: electromagnetic wave propagation in complex wave chaotic enclosures, where I studied its statistical properties and explored time-domain pulse focusing, and unidirectional edge modes propagating in a reciprocal photonic topological insulator waveguide.

Several theories, e.g. the Random Matrix Theory and the Random Coupling Model, have been developed and validated in experiments to understand the statistical properties of the electromagnetic waves inside wave chaotic enclosures. This thesis extends the subject from a single cavity to a network of coupled cavities by creating an innovative experimental setup that scales down complex structures, which would otherwise be too large and cumbersome to study, to a miniature version that retains its original electromagnetic properties. The process involves shrinking down the metal cavity in size by a factor of 20, increasing the electromagnetic wave frequency by the same factor and cooling down the cavity by a dilution refrigerator to reduce its ohmic loss. This experimental setup is validated by comparison with results from a full-scale setup with a single cavity and it is then extended for multiple coupled cavities.

In the time domain, I utilized the time-reversal mirror technique to focus electromagnetic waves at an arbitrary location inside a wave chaotic enclosure by injecting a numerically calculated wave excitation signal. I used a semi-classical ray algorithm to calculate the signal that would be received at a transceiver port resulting from the injection of a short pulse at the desired target location. The time-reversed version of this signal is then injected into the transceiver port and an approximate reconstruction of the short pulse is observed at the target port.

Photonic topological insulators are an interesting class of materials whose photonic band structure can have a bandgap in the bulk while supporting topologically protected unidirectional edge modes. This thesis presents a rotating magnetic dipole antenna, composed of two perpendicularly oriented coils fed with variable phase difference, that can efficiently excite the unidirectional topologically protected surface waves in the bianisotropic metawaveguide (BMW) structure recently realized by Ma, et al., despite the fact that the BMW medium does not break time-reversal invariance. In addition to achieving high directivity, the antenna can be tuned continuously to excite reflectionless edge modes to the two opposite directions with various amplitude ratios.

Overall, this thesis establishes the foundation for further studies of the universal statistical properties of wave chaotic enclosures, and tested the limits of its deterministic properties defined by the cavity geometry. It also demonstrated in experiment the excitation of a unidirectional edge mode in a Bianisotropic Meta-waveguide, allowing for novel applications in the field of communications, for example phased array antennas.

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