Electromagnetic radiation mediated by topological surface states

Abstract

We study electromagnetic radiation from classical sources near a planar interface separating a topological and a trivial insulator, modeled within axion electrodynamics. The system features a piecewise constant $θ$-term that encodes the magnetoelectric response of topological surface states. Treating this coupling perturbatively, we derive analytical corrections to the standard Liénard-Wiechert potentials and obtain modified radiation fields in the far zone. As applications, we analyze the emission from linear antennas and the bremsstrahlung radiation of accelerated charges near the interface. For antennas, the surface Hall response breaks axial symmetry and produces azimuthal modulations that grow with the electrical length, leading to distinct scaling behaviors in the total and angular radiated power. {For accelerated charges, the emitted intensity is uniformly reduced by a factor $1 - (σ_{\mathrm{Hall}} / 2εv)^2$, which we interpret as a process-specific attenuation of the radiative strength due to interference with its image magnetic monopole inside the topological medium.} These results reveal how topological surface states mediate measurable modifications to classical radiation, establishing a link between axion electrodynamics, topological phases, and field theories with spatially varying couplings.

Figures (5)

• Figure 1: Geometry of a semi-infinite topologically insulating media separated by the plane $z=0$ from a trivial insulator. Both media have the same permittivity and permeability.
• Figure 2: a) Zeroth-order propagator $G _{\omega} (\mathbf{r},\mathbf{r}')$ in homogeneous space, describing direct propagation between two points. b) First-order corrections $G ^{(1)} _{0i} (\mathbf{r} , \mathbf{r}' , \omega)$ and $G ^{(1)} _{ij} (\mathbf{r} , \mathbf{r}' , \omega)$, obtained as a single convolution of two $G _{\omega} (\mathbf{r},\mathbf{r}')$ propagators with the integration restricted to the interface at $z=0$. This term accounts for a single interaction with the topological surface states, which host the effective Hall current induced by the jump in $\theta$. c) Second-order corrections $G ^{(2)} _{0i} (\mathbf{r} , \mathbf{r}' , \omega)$ and $G ^{(2)} _{ij} (\mathbf{r} , \mathbf{r}' , \omega)$, involving a double convolution of three $G _{\omega} (\mathbf{r},\mathbf{r}')$ propagators, with both integrals performed over the same interface. This contribution represents multiple scattering events mediated by the surface states, highlighting their cumulative effect on the electromagnetic propagation.
• Figure 3: Geometry of a linear antenna of length $L$ placed at a distance $z_0$ from a planar interface ($z=0$) separating a topological medium from a dielectric medium. a) Simple antenna. b) Center-fed antenna.
• Figure 4: Density plot of the dimensionless integrated deviation $I_{\hbox{\scriptsize s}}(\xi,\ell)$ versus the scaled distance $\xi=z_0/\lambda$ and electrical length $\ell=L/\lambda$. Dashed lines indicate the loci of maximal intensity obtained from the numerical evaluation of the exact integral and coincide with the estimated maximum intensities at $\xi_1 \approx 0.3049$, $\xi_2 \approx 0.8096$, and $\xi_3 \approx 1.3107$. The ridge structure originates from phase interference encoded in the Bessel-function dependence of the integrand.
• Figure 5: Density plot of the dimensionless integrated deviation $I_{\hbox{\scriptsize c}}(\xi,\ell)$ as a function of the scaled distance $\xi=z_0/\lambda$ and the electrical length $\ell=L/\lambda$ for the center-fed antenna. The plot exhibits a sequence of quasi-periodic bright bands in $\ell$, whose positions shift smoothly with $\xi$, reflecting the interplay between the multilobed classical radiation pattern of the center-fed dipole and the angular modulation induced by the topological interface. The dotted lines indicate the estimated maxima corresponding to the vertical ridges ($\ell =2.95$, $3.96$, $4.97$). The red crosses indicate the numerically determined maxima $\xi _{1, \ell}$, in good agreement with the analytical predictions discussed in the text.