Fig. 1: Working principle of meta-imager for arbitrary convolution operation.

a Sketch for the imaging process of a single imaging lens with an Airy-spot-like point spread function (PSF). b Mechanism of meta-imager composed of a metalens and complex-amplitude meta-modulator. The PSF_meta of this meta-imager can be reshaped into an arbitrary pattern, which can be used as the kernel of the convolution operation. The spacer exists between the metalens and the meta-modulator. The position (x₀, y₀) and (x₃, y₃) stand for the coordinates of object and image spaces, respectively. c Simulated (curves) and experimental (dots) amplitude modulation by using geometric metasurfaces made of dielectric c-Si nanobricks with different lengths L, where the height H = 300 nm and the width W = 110 nm. Considering the fabrication error, we provide the simulated L-dependent amplitude profiles if the width W (from 105 nm to 115 nm) has deviated with a step size of ±2.5 nm. The simulation about the amplitude modulation is implemented in a finite-difference time-domain model with the periodic boundaries along x and y direction, and perfect-matching layers along z-direction. In our simulation, the periods (p_x and p_y) of metasurfaces are taken to be 250 nm, which is below the operating wavelength (λ = 633 nm). The experimental amplitude (calculated as the square of polarization conversion efficiency) and length L (directly measured from the SEM images) of the nanobricks are derived from five individual samples, which exhibit similar behavior. The insert presents the configuration of a unit cell in geometric metasurfaces. d Phase modulation is determined by the rotation angle of nanobricks. One hundred twenty-eight-level phase modulation is employed to obtain a high-accuracy meta-modulator. The insert illustrates the orientation-rotated nanobricks with a rotating angle θ. e Optical and SEM (insert) images of our fabricated metalens, where the nanobriks have the dimension of W = 110 nm and L = 170 nm