Analytic theory of an edge mode between impedance surfaces

An eigenmode analysis is presented of the electromagnetic field which occurs between two complementary surface impedances. The analysis is based on the generalized reflection method which is a generalization of the Sommerfeld-Maliuzhinets technique. Numerical results are presented and validated against independent comsol simulations. Also, the characteristic impedance and phase velocity are defined and calculated for further investigation of the structure.

Figure 1

(a) Impedance wedge with obliquely incident plane wave. The angle between impedance faces is $\theta$. (b) Line wave structure shown in Ref. [9] when $\theta =\pi$.

Figure 2

Integration path $\gamma$.

Figure 3

Absolute value of the determinant defined in Eq. (17) when sweeping $cos\beta$ (blue line) and eigenvalue $cos\beta$ calculated by comsol (red line) for (a) $Z_1=-i{Z}_0/\sqrt{3}, Z_2=\sqrt{3}i{Z}_0$; (b) $Z_1=-i{Z}_0/\sqrt{2}, Z_2=2i{Z}_0$; and (c) $Z_1=-i{Z}_0/2, Z_2=2\sqrt{2}i{Z}_0$.

Figure 4

(a) Absolute value and (b) phase of normalized electric field $E_z/E_z(k_0\rho =0.1)$ (blue line for analytic solution and green dots for comsol simulation) and normalized magnetic field $Z_0{H}_z/E_z(k_0\rho =0.1)$ (red line for analytic solution and yellow dots for comsol simulation), when $\varphi =\pi /3$.

Figure 5

(a) Absolute value and (b) phase of normalized electric field $E_z/E_z(\varphi =\pi /2)$ (blue line for analytic solution and green dots for comsol simulation) and normalized magnetic field $Z_0{H}_z/E_z(\varphi =\pi /2)$ (red line for analytic solution and yellow dots for comsol simulation) when $k_0\rho =0.5$.

Figure 6

Normalized electric field $|E_z/E_z(k_0\rho =0)|$ calculated by (a) analytic method and (b) comsol simulation.

Figure 7

Normalized magnetic field $|H_z{Z}_0/E_z(k_0\rho =0)|$ calculated by (a) analytic method and (b) comsol simulation.

Figure 8

$|E_z/\left(H_z{Z}_0\right)|$ calculated by (a) analytic method and (b) comsol simulation.

Figure 9

Real part of the transverse electric field calculated by (a) applying Eq. (19) and (b) comsol simulation is plotted.

Figure 10

(a) Normalized phase velocity $v_p/c$ and (b) normalized characteristic impedance $Z_c/Z_0$ are plotted as functions of $Z_1$ and $Z_2$.