Fig. 5. Nonreciprocal acoustic wavefront manipulation for extraordinary refraction.

In the FD (forward direction), the normal plane incident wave is converted into an extraordinary refracted plane wave with an angle of 45°. The time-reversed wave of this refracted plane wave is the incident wave in the BD (backward direction) with an angle of 45° which is converted into an extraordinary refracted plane wave with an angle of −45°, which is not the time-reversed wave of the incident one in the forward direction, demonstrating the non-reciprocity of the JAM. a The phase profiles along the y-direction for the FD and BD, which are φ₁ = 83.3 y rad and φ₂ = 166.6 y rad, respectively. b Corresponding height h₁ and h₂ for the FD and BD, respectively. c FD and d BD simulated (Sim.) and experimental (Exp.) acoustic pressure distribution at 6430 Hz.