Edge modes in two-dimensional electromagnetic slab waveguides: Analogs of acoustic plasmons

We analyze planar electromagnetic waves confined by a slab waveguide formed by two perfect electrical conductors. Remarkably, two-dimensional (2D) Maxwell equations describing transverse electromagnetic modes in such waveguides are exactly mapped onto equations for acoustic waves in fluids or gases. We show that interfaces between two slab waveguides with opposite-sign permeabilities support 1D edge modes, analogous to surface acoustic plasmons at interfaces with opposite-sign mass densities. We analyze this type of edge mode for the cases of isotropic media and anisotropic media with tensor permeabilities (including hyperbolic media). We also take into account non-Hermitian edge modes with imaginary frequencies or/and propagation constants. Our theoretical predictions are feasible for optical and microwave experiments involving 2D metamaterials.