Critical angle, θ_C (Eq. (24)), Brewster angle, θ_B (Eq. (25)), and Phase inversion angle, θ_P (Eq. (29)), as a function of the density contrast, ρ_c. Below the Critical angle (red solid line) there is no transmission of energy perpendicular to the interface (grey area), whereas for angles above the Critical there is transmission in the positive x-direction. The Brewster angle (blue solid line) shows the situation of perfect transmission (which is tantamount to no reflection) for different density contrasts.