Confined Electromagnetic Waves in Media Composed of Topological Insulators

Abstract

Topological insulators (TIs) are quantum materials combining insulating bulk properties with conductive surface states protected by time-reversal symmetry. Their unique electromagnetic behavior originates from the topological magnetoelectric effect encoded in an axion-like $θ$-term ($θ$ = $π$ mod 2$π$). This $θ$-electrodynamics modifies Maxwell's equations specifically at material interfaces through altered boundary conditions, preserving conventional bulk electrodynamics while enabling surface-mediated optical effects like polarization rotation and hybrid wave modes. This thesis explores electromagnetic wave confinement in TI-based waveguides. Key advances include: (1) Controlled modification of reactive and dissipated energies through polarization engineering in waveguide geometries; (2) Experimental realization of transverse electromagnetic (TEM) waves violating Earnshaw's theorem via $θ$ discontinuities in coaxial TI structures, demonstrating unique polarization rotation mechanisms and low-loss propagation through bent fibers; (3) TEM wave confinement with fewer than two conductors using imaginary $θ$ parameters, explained through self-consistent surface charge dynamics; (4) First-principles identification of hybrid TE-TM modes in TI slab waveguides, contrasting with conventional magnetoelectric material responses. These findings establish how surface boundary condition modifications from $θ$ enable new electromagnetic solutions despite unchanged bulk equations. The demonstrated phenomena -- including modified propagation modes, non-trivial polarization dynamics, and unconventional confinement -- suggest photonic applications in polarization control and optical routing. By connecting topological electrodynamics with waveguide physics, this work provides both fundamental insights and practical design principles for topological photonic systems.