Confined Electromagnetic Waves in Media Composed of Topological Insulators

TL;DR

This paper investigates how topological insulators alter electromagnetic wave behavior at interfaces, enabling novel waveguiding modes, polarization effects, and confinement mechanisms with potential applications in photonics.

Contribution

It introduces new electromagnetic wave confinement and polarization control methods in topological insulator-based waveguides, leveraging topological boundary conditions for innovative photonic functionalities.

Findings

Demonstrated TEM wave violation of Earnshaw's theorem via $ heta$ discontinuities

Achieved low-loss wave propagation through bent fibers using topological effects

Identified hybrid TE-TM modes in TI slab waveguides

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 $\theta$-term ($\theta$ = $\pi$ mod 2$\pi$). This $\theta$-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 $\theta$ 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 $\theta$ 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 $\theta$ 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.