Surface and waveguide Josephson plasma waves in slabs of layered superconductors

We discuss the propagation of symmetric and antisymmetric Josephson plasma waves in a slab of layered superconductor clad between two identical dielectrics. We predict two branches of surface waves in the terahertz frequency range, one above and another below the Josephson plasma frequency. Apart from this, there exists a discrete set of waveguide modes with electromagnetic fields oscillating across the slab thickness and decaying exponentially away from the slab. We consider the excitation of the predicted waves by means of the attenuated-total-reflection method. It is shown that for a specific set of the parameters of the structure, the excitation of the waveguide modes is accompanied by the total suppression of specular reflection.

Figure 1

Geometry of the eigenvalue problem.

Figure 2

(a) Numerically calculated dispersion curves for the symmetric eigenmodes in a slab of layered superconductor placed in vacuum. Forbidden regions are shaded. The light line $\Omega =\sqrt{{\varepsilon }_s/{\varepsilon }_d}\kappa$ and the separatrices $\Omega =1$, $\Omega =\gamma$, and $\Omega =\sqrt{1+{\kappa }^2}$ are shown by the thin red (grey) lines. (b) Close-up view of the region of low frequencies for the graph in (a). The plots are given for $\gamma \approx 60$, ${\varepsilon }_s=16$, and $L/{\lambda }_{ab}=10$.

Figure 3

The same as in Fig. 2, but for the antisymmetric eigenmodes.

Figure 4

The same as in Fig. 2, but for the symmetric eigenmodes in a slab of layered superconductor placed between optically dense dielectrics.

Figure 5

Geometry of excitation of symmetric eigenmodes by the “attenuated-total-reflection” method. Here, ${\mathbf{k}}^i$ and ${\mathbf{k}}^r$ are the wave vectors of the incident and reflected waves, respectively.

Figure 6

Reflectivity ${\left|R\right|}^2$ as a function of (a) the incidence angle $\theta$ for given $\Omega =20$, and (b) the frequency $\Omega$ for given $\theta =59.7^{\circ }$. These resonant values of $\theta$ and $\Omega$ determine a point on the dispersion curve in the $(\kappa ,\Omega )$ plane. In Fig. 2, this point is marked by black filled square on the dispersion curve with $n=1$. The optimal thickness of the vacuum gap is $h=0.28{\lambda }_{ab}$. Other parameters are $\gamma =60$, ${\varepsilon }_s=16$, $L/{\lambda }_{ab}=10$, ${\varepsilon }_p=24$, and ${\nu }_{ab}={\nu }_c=5*{10}^{-2}$.

Figure 7

The intensity plot of the reflectivity ${\left|R\right|}^2$ in the $(\theta ,\Omega )$ plane for the same values of the parameters as in Fig. 6. The dispersion curve for the symmetric low-frequency waveguide mode with $n=1$ is shown by the light-blue line in the center of the figure.