Fig. 1. (a) Unit cell of the photonic crystal (PC). Lattice constant of the PC is a=12.5  mm. The radius and refractive index of the dielectric semicylinder and background are r=3.75  mm, n1=2.9, and n0=1.03, respectively. The lower panel shows the Brillouin zone. (b) Bulk bands of the PC1 with d=2.5  mm, where yellow rectangles highlight the band gaps. (c) Eigen-field profiles of bulk modes at high-symmetry points in the first, second, and third bands. (d), (e) Evolution of the modes at the (d) Γ and (e) X points as a function of d. (f) Evolution of Zx for each band when d increases from 0 to 2.5 mm.

Fig. 2. (a) Schematic of the dislocation and (b) modified dislocation constructed by the PC1. (c) Eigenfrequencies of the modes near the first bulk gap, where the red circle indicates the dislocation mode. The yellow region highlights the bulk gap. (d) Eigen-field profile of dislocation modes in (c). (e) Experimentally measured spectrum when the excitation source is placed around the dislocation. (f)–(h) Similar to (c)–(e), but for the second bulk gap. The blue dots indicate the trivial modes in the second band gap.

Fig. 3. (a) Schematic of the dislocation with a point defect. The yellow circle highlights the point defect with a radius of 5.25 mm. (b), (c) Electric field distribution of two dislocation modes for the structure in (a). (d) Schematic of the dislocation with two shifted dielectric cylinders. The yellow circles highlight the shifted dielectric cylinders with a displacement vector of (−a/5, a/5) and (−a/5, −a/5), respectively. (e), (f) Electric field distribution of two dislocation modes for the structure in (d).

Fig. 4. (a) Calculated edge states, which are highlighted in red and blue. The inset shows the schematic of the edge. Lower panel shows the |Ez| field of two edge states at ky=0. (b) Schematic of the add-drop filter, where the input port is denoted as A, and the output ports are denoted as C and D. (c) Photograph of the sample. (d) Simulated |Ez| field distribution at the frequency of 6.708 GHz. (e) Simulated transmission spectrum of the output ports C and D. (f) Experimentally measured electric field intensity at ports C and D. (g)–(i) Similar to (d)–(f) but for the frequency range in the second bulk gap.

Fig. 5. (a) Bulk band structure of PC2. The inset shows the structure of the unit cell. The lattice constant is a=12.5  mm. The radius and refractive index of the rod are r=3.75  mm and n1=2.9, respectively. (b) Eigen-field profiles at high-symmetry points in the first, second, and third bands.

Fig. 6. (a) Dislocation constructed by PC2. (b) Eigenfrequencies of the modes near the second bulk gap, where the red dots indicate the trivial cavity modes in the gap. The yellow region highlights the bulk gap. (c) Eigen-field profile of two trivial cavity modes in (b). (d)–(f) Similar to (a)–(c), but for the dislocation constructed by PC1.

Fig. 7. (a) Dislocation with the center extended by one more unit cell, as highlighted in red. (b) Eigenfrequencies of the modes in two band gaps. (c), (d) Eigen-field profiles of two dislocation modes.

Fig. 8. Photograph of the experimental setup.