Electromagnetic Surface Waves at Anisotropic Interfaces: From Metamaterials to Fractional Quantum Hall Systems

This thesis develops a unified electromagnetic framework for the description of wave propagation and light–matter interaction in complex media characterized by gyrotropy, nonreciprocity, and spatial dispersion. By formulating electromagnetic response in terms of macroscopic constitutive tensors constrained by fundamental symmetry principles, the work establishes a common language for analyzing surface waves in photonic materials and collective excitations in low-dimensional electronic systems. Within linear macroscopic electrodynamics, the implications of time-reversal symmetry, reciprocity, and energy conservation are examined to clarify how these principles restrict admissible response functions. This symmetry-based viewpoint provides a systematic classification of electromagnetic media and reveals how the controlled breaking of specific symmetries leads to nonreciprocal propagation, mode hybridization, and unconventional surface-wave behavior. Applying this framework to anisotropic and gyrotropic materials, the thesis analyzes electromagnetic surface modes supported by interfaces and layered structures. It is shown that the interplay between magnetic-field–induced gyrotropy and hyperbolic anisotropy produces strongly asymmetric dispersion relations, backward-wave propagation, and characteristic field configurations, with direct consequences for directional transport and tunable photonic responses. The same response-function approach is then extended to strongly correlated two-dimensional electron systems in the quantum Hall regime, where low-energy neutral excitations are governed by internal geometric degrees of freedom rather than by simple charge motion. An effective electromagnetic description of these collective modes is developed by deriving a quadrupolar, nonlocal electric susceptibility that captures their coupling to spatial gradients of the electromagnetic field. This susceptibility is intrinsically gyrotropic and spatially dispersive, reflecting the chiral and geometric nature of the underlying electronic state, and enables such collective excitations to be incorporated into Maxwell’s equations within a macroscopic framework. The electromagnetic modes supported by quantum Hall layers and by coupled electronic–metallic systems are analyzed, revealing how collective responses modify dispersion relations and field profiles. To assess experimental accessibility, the influence of these collective modes on electromagnetic resonances is evaluated in engineered near-field environments. While coupling to uniform fields is strongly suppressed, resonator geometries that generate large electric-field gradients are shown to produce appreciable frequency shifts, suggesting viable routes for probing geometric collective excitations through purely electromagnetic measurements.