New polarization rotation and exact TEM wave solutions in topological insulators

TL;DR

This paper analyzes θ-electrodynamics in topological insulators to reveal purely transverse TEM waves that propagate with a linear dispersion $k = k_0 \sqrt{\epsilon \mu}$ and exhibit a polarization rotation driven solely by topological magnetoelectric boundary conditions. Using cylindrical geometries with one or more θ-interfaces, the authors derive exact field solutions, show a rotation of the plane of polarization inside TI regions (e.g., $\cos \varphi_{int} = (1+Z_\theta^2)^{-1/2}$ with $Z_\theta = \tilde{\theta} Z/2$), and demonstrate omnidirectional confinement of the TEM field in TI shells. They further quantify power transmission and identify geometry- and θ-dependent regimes where TI layers enhance or confine energy, including a ~1% gain in region 2 for certain configurations at $\theta_2=27\pi$. Overall, the work provides a new, observable signature of the topological magnetoelectric effect and demonstrates potential optical-fiber-like control of light using TI-based structures, with implications for photonics and TI-based devices.

Abstract

In the context of $θ$ electrodynamics we find transverse electromagnetic wave solutions forbidden in Maxwell electrodynamics. Our results attest to new evidence of the topological magnetoelectric effect in topological insulators, resulting from a polarization rotation of an external electromagnetic field. Unlike Faraday and Kerr rotations, the effect does not rely on a longitudinal magnetic field, the reflected field, or birefringence. The rotation occurs due to transversal discontinuities of the topological magnetoelectric parameter in cylindrical geometries. The dispersion relation is linear, and birefringence is absent. One solution behaves as an optical fiber confining exact transverse electromagnetic fields with omnidirectional reflectivity. These results may open new possibilities in optics and photonics by utilizing topological insulators to manipulate light.

Figures (3)

• Figure 1: In (a) we show a generic cylindrical geometry. Only three media $\mathcal{M}_i$ are shown (each characterized by $\epsilon_i, \mu_i, \theta_i$). In this example $\theta_1 = 0$, so $\Sigma_{23}$, located at $R_2$ is the only $\theta$-interface and $\boldsymbol{\nabla} \theta = (\theta_3 - \theta_2)\delta(\rho - R_2)\boldsymbol{\hat{\rho}}$. In (b, c) different $\boldsymbol{\nabla} \theta$ configurations are shown in which an EM wave propagates in the $\hat{\mathbf{z}}$ direction. Antiparallel (b) and Parallel (c) refer to the directions of $\boldsymbol{\nabla}\theta$ (red). The transverse $\mathbf{E}_{\perp}$-fields are shown in blue.
• Figure 2: The color map is a density plot of the temporal average of the total Poynting vector in the interior and exterior regions relative to that of the background EM field, $\langle S_{z0} \rangle=c E_{0}^{2}/8\pi Z$. The streamlines are the total $\mathbf{E}$ field-lines. The contour plots show contours of constant relative Poynting vector. Panels (a-d) correspond to $Z=1$ and $\theta =3\pi, 11\pi, 19\pi, 27\pi$, respectively.
• Figure 3: In all cases $Z=1$. In (a) and (b), $\theta_1=0=\theta_3$ and $\theta_2=27 \pi$ inside the TI. In (a) $\chi=0.45$ and in (b) $\chi = 0.82$. In (c,d) we show the power transmitted through regions 1 and 2: $P_{1}^{\theta_2}$ and $P_{2}^{\theta_2}$, respectively for $R_2=10 \mu m$. For $\theta_2=0$, the corresponding powers: $P_{1,2}^{\theta_2=0}$, are shown in solid black line. For $\theta_2 = 27 \pi$, in the inset of (c) we show $\Delta P_{1}$ . The vertical lines are $\chi_{a} = 0.45$ which defines the geometry of the configuration in (a), and $\chi_{1M}$ that maximizes the difference. The inset of (d) shows $\Delta P_{2}$ with the values $\chi_2^\ast$ and $\chi_{2M}$ shown.