The graphs show the range of θ over which homogeneous waves can propagate for ε_1s = 3.3856, ε_3s = 2.25, ε_1f = 4, |ε_3f| = 2.7889. The range extends from θ = 0° up to each of the curves in the figure. As ϕ increases, there is little change when ε_3f > 0. When ε_3f < 0, there is a rapid increase in the range until, at a particular value ϕ = ϕ_crit, homogeneous waves can propagate at all angles of θ up to 90°. With the parameters given in the text ϕ_crit = 39.9° (shown by the dotted line). The upper right hand curve shows the decreasing range of θ when φ increases beyond ϕ = ϕ_crit.