On the coupling of forward and backward slow waves supported by the waveguide configuration of a dielectric sandwiched between two plasma slabs

We derived a general equation governing the spectra of electrostatic surface plasmons supported by a waveguide structure of two identical plasma slabs separated by a dielectric medium. The plasma slabs are parallel, homogeneous, and have finite thicknesses. The geometry under consideration supports two surface plasmon modes, which we investigated numerically for Polyethylene $\varepsilon_d=2.25$ and vacuum $\varepsilon_d=1$ as central regions. With vacuum as a central region, the two surface plasmon modes become coupled and merge into the well known single mode of quasi-static frequency $\omega=0.707\omega_{\rm p}$. The surface plasmon modes in the presence of a Polyethylene are decoupled and remain nondegenerate over the whole range of $kd$. Therefore, the two plasmon modes propagate independent of each other with distinct quasi-static resonance frequencies, namely, a backward wave with $\omega=0.707\omega_{\rm p}$ corresponding to a single plasma-vacuum interface and a forward wave with $\omega=\frac{\omega_{\rm p}}{\sqrt{3.25}}=0.55\omega_{\rm p}$ corresponding to a single plasma-dielectric interface. Increasing the central region width is found to introduce a delay in reaching the quasi-static resonance frequencies. The effect of collision is to down shift the mode frequencies for long wavelengths and also to down shift the quasi-static frequencies.