Fig. 1. (a) Sketch of an isolated cross-shaped silicon structure. Fixed parameters include ly=700  nm, wy=150  nm, h=400  nm, and wx=140  nm. (b) Simulation unit cell of a periodical cross-shaped structure array, consisting of a cross-shaped particle, substrate, and coating layer. The thicknesses of the substrate and coating layer are 200 and 500 nm, respectively, and Px=Py=1  μm. (c) Sketch of the dipolar moments induced in the two arms of the cross-shaped particle. The gray-colored area depicts the top view of the particle. (d) Sketch of the proposed refracting metasurface. The three cross-shaped elements in the structure are marked as C1, C2, and C3, respectively. Fixed parameters are the same as in (a). The refractive index of the substrate is set as 1.45, while the refractive index of the coating layer is set as 1.4. The refractive index of the silicon is set as 3.5. The ordinate origin is set as the center of the cross particle for (a) and (b), while it is set as the center of the cross particle C2 for the structure in (d).

Fig. 2. (a) Scattering cross sections of ED and MD components varying with x arm length lx. (b) ED and MD resonant wavelengths as a function of lx for an isolated cross-shaped particle.

Fig. 3. (a) Spectral reflection and (b) spectral phase as a function of the structure parameter lx in Fig. 1(b).

Fig. 4. Electric field magnitude distributions |E|2 at the (a) first reflection peak and (b) second reflection peak in Fig. 3(a). Electric field vector distribution at the (c) first reflection peak and (b) second reflection peak in Fig. 3(a). The incident electric field is along the negative x direction. The variable lx is set as 0.27 μm. (a)–(d) are the electric field distributions at the y=0 plane.

Fig. 5. (a)–(c) Electric field distributions of the periodically arranged cross-shaped structures E1, E2, and E3, respectively, at 1.507 μm. (d) Electric field distribution of one unit cell of the metasurface configuration 1, consisting of three elements, namely E1, E2, and E3. (a)–(d) depict the electric field distributions at the y=0 plane. (e) Phase distribution of the metasurface configuration 1 at 1.493 μm. Three unit cells (UCs), marked as UC1, UC2, and UC3, are plotted to have a comfortable aspect ratio for the figure. (f) Spectral transmission for the proposed three configurations.

Fig. 6. (a) Top view of the metasurface configuration 1. (b) Top view of the metasurface configuration 2. The parameters of each element stay unchanged, while only the spaces d1 and d2 between three elements change from 1 to 0.86 μm. (c) Top view of the metasurface configuration 3. Element parameters lx are optimized. The optimized parameters lx of the three elements are 0.3, 0.4, and 0.56 μm, respectively. (d) Calculated phase distribution of the second configuration of the metasurface; the operating wavelength is 1.495 μm. (e) Calculated phase distribution of the third configuration of the metasurface; the incident wavelength is 1.521 μm.

Fig. 7. (a) Transmissive response of the metasurface varying with the element spacing d. Black dotted line marks the applied working wavelength. (b) Phase response along the x direction inside a metasurface unit cell varying with the element spacing d at working wavelength. The parameters lx of the three elements are 0.3, 0.4, and 0.56 μm, respectively.

Fig. 8. Far-field transmitting intensity (T.I.) for the three configurations at different diffraction angles. The transmitting intensity is normalized to the total transmission intensity.

Fig. 9. Phase distribution of the Huygens’ metasurfaces consisting of different element numbers. (a) Four-element Huygens’ metasurface. (b) Five-element Huygens’ metasurface. (c) Six-element Huygens’ metasurface. Each figure consists of two unit cells to better show the anomalous deflection effect. The spacing between neighboring elements in these three configurations is set as 0.86 μm for simplicity. Other parameters are listed in Table 2.