Fig. 1. Designed structure for exciting BSWs. (a) Schematic of the structure composed of three layers: Si (top), SiO2 (middle), and Si substrate (bottom). (b) Dispersion relation of the structure described by absorption as a function of incidence angle under TE polarization. The white dashed line indicates the wavelength of 1.55 µm. The absorption spectrum of the structure as a function of incidence angle at 1.55 µm is plotted in the top subfigure. (c) Electric field distribution of the structure at incidence angle of 24.98° at 1.55 µm under TE polarization. The white curve refers to the electric field. The real part of the refractive index of the structure is plotted in the top subfigure. (d) Schematic of the mechanism of the OAM sorting methods. Only one nanoslit is considered. The phase along the semi-ring nanoslit has a linear dependence on the azimuthal angle φ. (e) Schematic of the designed BSW structure with five semi-ring shaped nanoslits. (f) Schematic of the geometric parameters of the BSW structure.

Fig. 2. On-chip sorting of OAM beams with different TCs using BSW structures. (a) Schematic of the designed BSW structure with five semi-ring shaped nanoslits. The structure was illuminated vertically by the OAM beam with circular polarization from the bottom. (b) Electric field intensity (|E|2) of the BSW structure under incident OAM beam with TC of one. The edge length of the square region surrounded by the white dashed line is 3 µm. (c) Spatial phase patterns of OAM beams with TCs of two, four, six, eight, and ten (from top to bottom) (left) and the electric field intensity of the BSW structures under the corresponding incident OAM beams (right). All the subfigures share the same scale bar. The white dashed line indicates the position where Y=0. The green dashed line indicates the peak position of the focal points. (d) Normalized electric field intensity along the white dashed lines in (c) under incident OAM beams with TCs of one to ten. (e) Linear fitting of the peak positions of the focal points as a function of the TCs of incident OAM beams. R2 for this linear fitting is 0.999.

Fig. 3. On-chip sorting of OAM beams with different TCs using metallic structures. (a) Schematic of the metallic structure with five semi-ring nanoslits. This structure consists of an Au film (top) and a SiO2 substrate (bottom). The structure was illuminated vertically by the OAM beam with circular polarization from the bottom. (b) Electric field intensity (|E|2) of the metallic structure under incident OAM beam with TC of one. The edge length of the square region surrounded by the white dashed line is 3 µm. (c) Spatial phase patterns of OAM beams with TCs of one, two, three, four, and five (from top to bottom) (left) and electric field intensity of the metallic structure under the corresponding incident OAM beams (right). All the subfigures share the same scale bar. The white dashed line indicates the position where Y=0. The green dashed line indicates the peak position of the focal points. (d) Normalized electric field intensity along the white dashed lines in (c) under incident OAM beams with TCs of one to five. (e) Linear fitting of the peak positions of the focal points as a function of the TCs of incident OAM beams. R2 for this linear fitting is 0.997.

Fig. 4. Comparison of the electric field intensity (|E|2) of the metallic structure and the BSW structure under incident OAM beams. (a) Electric field intensity of the metallic structure under incident OAM beams with TCs of one, seven, and eight. Subfigures in (a) share the same color scale bar. (b) Electric field intensity of the BSW structure under incident OAM beams with TCs of 1, 35, and 36. Subfigures in (b) share the same color scale bar. The green dashed lines in (a) and (b) indicate the position where Y=0. The white curves in (a) and (b) refer to the electric field intensity along the green dashed line. (c) Electric field intensity of the focal points on metallic structure (SPP, orange) and BSW structure (cyan) under incident OAM beams with TCs of one to seven. Electric field intensity of the focal points on BSW structure over that on metallic structure is also plotted. (d) Electric field intensity of the focal points on metallic structure (SPP, black) under incident OAM beams with TCs of one to seven and electric field intensity of the focal points on BSW structure (red) under incident OAM beams with TCs of 1 to 35.

Fig. 5. On-chip sorting of two OAM beams simultaneously. (a) Electric field intensity of the BSW structure under the incident OAM beam with TC of −3. The edge length of the square region surrounded by the white dashed line is 2 µm. (b) Spatial phase patterns of OAM beams with TCs of 1 and −3 (from top to bottom) (left) and electric field intensity of the BSW structure under the incidence of two OAM beams with TCs of 1 and −3 (right). The edge length of the square region surrounded by the white dashed line is 2 µm. (c) Electric field intensity of the BSW structure under the incidence of two OAM beams with TCs of 1 and −3 (top), and the electric field intensity along the green dashed line (bottom). (d) Electric field intensity of the BSW structure under the incidence of two OAM beams with TCs of 3 and −3 (top), and the electric field intensity along the green dashed line (bottom). (e) Electric field intensity of the BSW structure under the incidence of two OAM beams with TCs of 5 and −3 (top), and the electric field intensity along the green dashed line (bottom); (c)–(e) share the same color scale bar. The green dashed line indicates the position where Y=0. The purple dashed lines indicate the peak positions of the two focal points.

Fig. 6. Comparison of BSW structures with different semi-ring shaped nanoslits. (a) Electric field intensity of the BSW structure with five semi-ring nanoslits. The structure was illuminated by a circularly polarized OAM beam with TC of one from the bottom. The edge length of the square region surrounded by the white dashed line is 2 µm. (b) Schematic of the BSW structures with one to six semi-ring shaped nanoslits (top) and the electric field intensity of the corresponding structures (bottom) under incidence of an OAM beam with TC of one. All the subfigures share the same scale bar. (c) Normalized electric field intensity of the region around the peak positions of focal points as a function of nanoslit numbers.

Fig. 7. Electric field intensity of the metallic structure under incident OAM beams with TCs of 2, 4, 6, 9, 10 and 12. The green dashed line indicates the position where Y=0. The white curve refers to the electric field intensity along the green dashed line. All figures share the same color scale bar.

Fig. 8. Electric field intensity of the BSW structure under incident OAM beams with TCs of 10, 20, 30, 37, 38, and 40. The green dashed line indicates the position where Y=0. The white curve refers to the electric field intensity along the green dashed line. All figures share the same color scale bar.

Fig. 9. (a), (b) Electric field intensity of the metallic structure along the Y=0 line under incidence of OAM beams with TCs of 1 to 7 with a broader X-axis scale (a) and a narrower X-axis scale (b). (c), (d) Electric field intensity of the BSW structure along the Y=0 line under incidence of OAM beams with TCs of 1 to 35 with a broader X-axis scale (c) and a narrower X-axis scale (d).

Fig. 10. Electric field intensity of the artificial structure under incident OAM beams with TCs of 5, 10, 12, 13, 14, and 15. The green dashed line indicates the position where Y=0. The white curve refers to the electric field intensity along the green dashed line. All figures share the same color scale bar. The radius of the outermost semi-ring nanoslit is 12.2 µm.

Fig. 11. Electric field intensity of the artificial structure with larger radius under incident OAM beams with TCs of 5, 15, 25, 26, 27, and 28. The green dashed line indicates the position where Y=0. The white curve refers to the electric field intensity along the green dashed line. All figures share the same color scale bar. The radius of the outermost semi-ring nanoslit is 18.36 µm.

Fig. 12. Electric field intensity (|E|2) and electric field components (|E|, |Ex|, |Ey|, and |Ez|) of the BSW structure under incident OAM beams with TC of five. The bottom three figures share the same color scale bar.

Fig. 13. Electric field intensity (|E|2) and electric field components (|E|, |Ex|, |Ey|, and |Ez|) of the metallic structure under incident OAM beams with TC of five. The bottom three figures share the same color scale bar.