PhD Oral Exam - Alexis Hotte-Kilburn, Physics

When studying for a doctoral degree (PhD), candidates submit a thesis that provides a critical review of the current state of knowledge of the thesis subject as well as the student’s own contributions to the subject. The distinguishing criterion of doctoral graduate research is a significant and original contribution to knowledge.

Once accepted, the candidate presents the thesis orally. This oral exam is open to the public.

Abstract

Photonic lattices are often described with tight-binding and coupled-mode Hamiltonians. Their spatially extended modes, however, can produce band structures that depart from nearest-neighbour models. We isolate numerically calculated photonic bands and represent their real squared normalized frequencies with reduced tight-binding-style harmonic models. For holey photonic-crystal waveguides and linear dielectric-pillar arrays, the one-band and Su–Schrieffer–Heeger-type reduced models reproduce the selected band curves very accurately. We then use model-order and sensitivity tests to determine how much harmonic content is reproducibly supported and when the smaller fitted coefficients become unstable. Parameter sweeps show how effective index, radius, width, and feature distance change identifiable spectral combinations. For the two-band SSH problem, the eigenvalues determine a squared-frequency centre and splitting magnitude; phase or eigenvector information is additionally needed for a unique off-diagonal factor or topological invariant. We apply the same effective-model perspective to a passive stub-ring lattice that supports a flat middle band. In the simulated equal-coupling design, this band has a normalized bandwidth of 〖6.65x10〗^(-5), and destructive interference leaves the connector-ring amplitude dark. We use controlled detuning and Gaussian onsite disorder to diagnose flat-band broadening, and a normalized finite-chain local scattering calculation to show how the chosen ports couple to the flat-band sub- space. Together, these results show how squared frequency harmonic models and temporal coupled-mode models for the resonator array connect photonic geometry to band-design diagnostics while retaining distinct physical interpretations.