Exact modes, hybridization, and polarization rotation of electromagnetic fields propagating in a topological insulating slab

In this work, we study electromagnetic wave propagation in slab waveguides whose core is a topological insulator characterized by a topological magnetoelectric parameter. Topological insulators are materials that are electrically insulating in the bulk but support robust conducting states at their boundaries, protected by time-reversal symmetry. Their electromagnetic response is described by an axionlike term that modifies Maxwell's electrodynamics (ED), leading to rich and unconventional phenomena, as the topological magnetoelectric effect. We find that all modes supported by these structures are all exact hybrid modes with nonvanishing longitudinal field components. This hybridization is a direct consequence of the modified boundary conditions produced by the topological term and is absent in topologically trivial, reciprocal, and nonchiral slab waveguides. Modifications to the propagation condition and ensuing modes are shown for the case of an asymmetric slab; however, the detailed solution of the exact modes, coupling of modes and the dispersion relations is made for the symmetric slab. By solving the full $\mathrm{\ensuremath{\Theta}}$ electrodynamics equations nonperturbatively, we derive the modal dispersion relations and explore polarization rotation and power transfer between modes. Our approach reveals qualitative and quantitative deviations from standard coupled-mode theory and captures different signatures of the topological magnetoelectric response. To compare with other approaches to the subject and owing to the smallness of the $\mathrm{\ensuremath{\Theta}}$ effects, we perform a perturbative analysis of mode propagation, also based on writing a general solution as a superposition of exact modes of $\mathrm{\ensuremath{\Theta}}$-ED but expanding to first nonvanishing order in $\mathrm{\ensuremath{\Theta}}$. Also we apply the methodology of coupled-mode theory. This last approach is predicated on building solutions as superpositions of modes of ordinary electrodynamics that fail to satisfy the boundary conditions imposed by the $\mathrm{\ensuremath{\Theta}}$ term but compensate at the expense of modifying the field profiles. These findings provide a comprehensive framework for light control in topological photonics and potential routes to experimentally probe the magnetoelectric effect in guided settings.