Fig. 1. Schematic of the homogeneous metasurface composed of rectangular crystalline silicon posts based on silica film.

Fig. 2. (a) Transmission and phase of the periodic c-silicon posts with 190 nm unit cell size and 220 nm height for different cross-section lengths at the wavelength of 751 nm. (b) Magnetic field amplitudes in the x–z plane (Hxz) for w=120  nm and w=180  nm at wavelength of 751 nm. (c) Vertical view of the compactly arranged silicon posts. (d) Vertical view of the period formed by filling the gaps between the silicon posts.

Fig. 3. Schematic of the proposed silicon phase-gradient metasurface composed of trapezoidal antenna arrays on a quartz substrate.

Fig. 4. Simulated phase and the electric field amplitude variation for silicon nanoantenna thickness h=290  nm. (a) Simulated phase variation along the x direction of the super cell for wavelengths of 740–780 nm; (b) full 2π phase shift along the x direction of the super cell for typical wavelengths of 740, 751, 760, and 770 nm; (c) intensity of the transmission, reflection, and absorption; and (d) the transmission of every layer of the metasurface.

Fig. 5. (a) Simulated transmission efficiency normalized to input energy and the transmission energy of the quartz substrate for wavelengths of 740–780 nm. (b) Far-field transmission efficiency (normalized to input energy) for different anomalous refraction angles (θr) at wavelength of 751 nm, where the inset shows the E-field (Ey) distribution for the refracted light with the propagation being signified by a red arrow at wavelength of 751 nm.

Fig. 6. (a) Schematic of assumptive unit cell composed of rectangular silicon post arrays on quartz substrate. (b), (c) Simulated transmission and reflection of the unit cell with various thickness h of silicon posts for wavelengths of 720–780 nm (the marked dashed lines indicate the variation of transmission and reflection at wavelength of 751 nm). (d) Transmission, reflection, and absorption of the unit cell at wavelength of 751 nm.

Fig. 7. Transmission efficiency with the fixed geometric parameters of the silicon trapezoidal antennas. (a) Simulated transmission efficiency normalized to input energy and the transmission energy of the quartz substrate for wavelengths of 720–780 nm, and (b) far-field transmission efficiency (normalized to input energy) for different anomalous refraction angles (θr).

Fig. 8. (a) Calculated total transmission at different values of w1. (b) Calculated desired anomalous refraction efficiency at different values of w1.