Phonons, as classical quasiparticles, possess both wave-like and particle-like characteristics. In low-temperature or complex crystals, the wave nature of phonons profoundly influences the thermal transport properties of materials. Additionally, the wave behavior of phonons holds broad prospects in applications such as damage detection in materials, addressing the mismatch issue in optoelectronic and low-temperature superconducting chips. These scenarios require precise control over the wave behavior of phonons.

The generalized Snell's law, proposed in 2011, provides new ideas and methods for controlling wave propagation. By structurally designing the phase of light or sound waves, anomalous deflection, focusing, cloaking, mode conversion to surface waves, and other novel properties of sound or light waves have been achieved. Currently, the control of phonon wave behavior primarily relies on Bragg scattering and is mainly concentrated in the MHz~GHz frequency range. The main direction of research is to achieve control over the transmission angle and energy of lattice waves in the THz frequency range using subwavelength-scale structures.