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Metalens can reconstruct the wavefront of a beam arbitrarily, and on-chip metalenses are more conducive to integration. We now propose a metalens based on silicon substrate. The lens consists of several silicon nitride (Si3N4) waveguides and annular coupling gratings (ACG). It can achieve off-chip far-field focusing at a wavelength of 780 nm. The radii and the grating periods of the ACG can be selected respectively according to Fermat’s Principle and Bragg’s Law. The key to designing the metalens lies in the precise control of the on-chip phase delay and the off-chip phase delay. When the total phase delay caused by the on-chip and off-chip light propagation is an integer multiple of 2π, the metalens can reconstruct a specific wavefront and capture the expected focal point in the off-chip free space. The theoretical calculation and simulation results of the designed metalens are well consistent. From the simulation results, the metalens has a focal spot size of FWHMx = 1.18 μm, FWHMy = 0.76 μm, focal depth of 3.25 μm, focal length of 19.6 μm, and transmission of 25.1% at the focal plane. Moreover, the focal length of the metalens can be controlled flexibly by engineering the radii and the grating periods of the ACG. This metalens is of great significance to the integration of modern optoelectronic devices, and it would promote potential applications in controllable focusing, optical interconnection devices, and biosensor imaging.
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