Dependence on the longitudinal wavenumber k of the phase speed v_ph for a static cold slab with a symmetric Epstein density profile. The asterisks represent the results obtained with BVPSUITE by numerically solving the eigen-value problem, while the dashed red lines represent the analytic results, Eqs. (A.3) and (A.4). Here a density ratio ρ₀/ρ_∞ of 5 is adopted.