Fig. 1. The sunflower-type crystal and its combination structures. (a) Radius of crystal with glass as dielectric (elastic) cylinders, r₁ = 0.5a; (b) radius of crystal with water as dielectric (elastic) cylinders, r₂ = 0.3a; (c) upper–lower combination structure; (d) inner–outer combination structure. The parameters of glass (gray) and water (blue) are as follows: relative dielectric constant ε_r1 = 3.75 and ε_r2 = 78.5; bulk modulus K₁ = 3.7 × 10¹⁰ and K₂ = 2.2 × 10⁹; density ρ₁ = 2500 kg m⁻³ and ρ₂ = 1000 kg m⁻³. The zoom-in schematics of these four structures are attached to the upper right corners.

Fig. 2. Projected band structures. Interface states are expressed in red lines, and bands of square lattice are expressed in green lines [with glass as dielectric cylinders in (a) and elastic cylinders in (b)] and blue lines [with water as dielectric cylinders in (a) and elastic cylinders in (b)]: (a) PCs; (b) PnCs.

Fig. 3. Electric field (sound pressure field) distribution when electromagnetic (elastic) waves propagate in the combined structure of two types of PCs (PnCs). (a) PCs at f = 30.6 GHz; (b) PnCs at f = 0.96 MHz. The material of bigger cylinders is glass, and the background material is water. The material of smaller cylinders is water, and the background material is glass. The parameters of glass and water are shown in Fig. 1.

Fig. 4. Transmission spectra of models shown in Figs. 1(a) and 1(b). (a) PCs; (b) PnCs. Transmission spectra of the model shown in Fig. 1(c) [the radius of upper (lower) cylinders is r₁ = 0.5a (r₂ = 0.3a)]: (c) PCs; (d) PnCs.

Fig. 5. Considering Fig. 1(c) as the model, the field distributions of the upper–lower combination structure of sunflower-type crystals. (a) PCs at f = 30.54 GHz; (b) PnCs at f = 0.96 MHz.

Fig. 6. Transmission spectra of models shown in Fig. 1(d) [the radius of outer (inner) cylinders is r₁ = 0.5a (r₂ = 0.3a)]. (a) PCs; (b) PnCs.

Fig. 7. Considering Fig. 1(d) as the model, the field distributions of the inner–outer combination structure of sunflower-type crystals. (a) Electric field of PCs at f = 30.54 GHz; (b) sound pressure field of PnCs at f = 0.96 MHz.

Fig. 8. Transmission spectra of PCs and PnCs with a defect and a metal barrier. (a) PCs; (b) PnCs.

Fig. 9. Field distributions of the inner–outer combination structure of sunflower-type crystals with (a), (b) a defect and (c), (d) a metal barrier. (a) Electric field of PCs at f = 30.54 GHz; (b) sound pressure field of PnCs at f = 0.96 MHz; (c) electric field of PCs at f = 30.54 GHz; (d) sound pressure field of PnCs at f = 0.96 MHz.

Fig. 10. Field distributions of output from angles of 120°, 90°, and 60°. (a) Electric field of PCs at f = 30.54 GHz; (b) sound pressure field of PnCs at f = 0.96 MHz.