Fig. 1. Parameter space for mass density ρ and bulk modulus K:　(a) Metamaterials with negative effective mass density, ρ < 0, K > 0; (b) natural materials, ρ > 0, K > 0; (c) double-negative metamaterials, ρ < 0, K < 0; (d) metamaterials with negative effective bulk modulus, ρ > 0, K < 0 弹性模量ρ和体弹性模量K的参数空间图　(a) 负质量密度超构材料, ρ < 0, K > 0; (b) 天然材料, ρ > 0, K > 0; (c) 双负超构材料, ρ < 0, K < 0; (d) 负体弹性模量超构材料, ρ > 0, K < 0

Fig. 2. (a) Snell’s law; (b) generalized Snell’s law.(a)斯涅耳定律; (b)广义斯涅耳定律

Fig. 3. Three typical forms of acoustic metasurfaces and their physical effects:　(a) Reflective metasurfaces; (b) transmissive metasurfaces; (c) absorbing metasurfaces; (d) the self-bending beam; (e) acoustic holographic imaging; (f) perfect sound absorber at low frequency声学超构表面的三种典型形式及其物理效应　(a)反射型超构表面; (b)透射型超构表面; (c)吸收型超构表面;(d)自弯曲波束调控; (e)声学全息成像; (f)低频完美吸声体

Fig. 4. Sound absorbing metamaterial:　(a) Membrane-type structure; (b) Helmholtz resonator structure; (c) Fabry-Pérot resonator structure; (d) optimized broadband sound absorption spectrum吸声超构材料　(a)薄膜型结构; (b)亥姆赫兹共振结构; (c) Fabry-Pérot共振结构; (d)优化的宽频吸声谱

Fig. 5. (a) Acoustic superlens with negative refractive; (b) holey-structured metamaterial lens; (c) fin-shaped acoustic lens; (d) membrane-type metamaterial.(a)负折射声学超透镜; (b)管道结构透镜; (c)扇形声学透镜; (d)薄膜结构超材料

Fig. 6. (a) Acoustic topological Chern insulator by incorporating the circulating flow and its projected energy band; (b) acoustic topological insulator based on hybridized modes and its projected energy band; (c) three-dimensional topological acoustic crystals with glide symmetry and its projected energy band.(a)引入环流的声学陈绝缘体及其投影能带; (b)基于模式杂化的声学拓扑绝缘体结构及其投影能带; (c)引入滑移对称性的三维拓扑声子晶体及其投影能带