Spatial waveguide mode separation for acoustic waves in a meta-slab composed of subunits with graded thicknesses

A meta-slab composed of subunits with graded thicknesses is proposed for spatially separating the zeroth- and first-order acoustic waveguide modes according to the generalized Snell's law. The phase velocity for the first-order mode depends on the waveguide thickness, whereas that for the zeroth-order mode does not. This enables the required phase-shift gradients of the meta-slab to be obtained for spatially separating the two waveguide modes. To design the meta-slab, analytic solutions are derived for the transmission coefficients and phase shifts of the incident acoustic waves with the two modes propagating through the subunits. Numerical simulations with transient finite-element analyses are implemented to demonstrate the propagation of the two waveguide modes. Sinusoidal signal and tone-burst excitations are applied in the analyses. The latter case shows that the two waveguide modes can be successfully separated in space by the designed meta-slab.