Fig. 2

Parity-dependent phenomena. a, b The equifrequency contours of the PGMs (ξ = k₀) with odd unit cells and even unit cells, respectively, where the black circles are the equifrequency contours of incident wave in air, the blue circles are the transmission contours of the n = 1 order and the solid (dashed) red circle is the transmission (reflection) contour of the n = −1 order. c, d The simulated acoustic total field patterns of the PGMs (ξ = k₀) with three cells and four unit cells, respectively. In each case, the upper (lower) plot is the case of θ_in = 30° (θ_in = −30°). All the arrows represent propagation directions. In simulations, p = h = λ₀, a = 0.9w and n_j = ρ_j