Electrical engineering

Physics

Isotropy

Fourier analysis

Green's function for the three-variable Laplace equation

Mathematics

Laplace's equation

Transfer function

Partial differential equation

Laplace transform

Fourier transform

Two-sided Laplace transform

Optics

Engineering

Mathematical analysis

Computer science

Inverse Laplace transform

Quantum mechanics

Wavelength

Fractional Fourier transform

Photonics Research

Laplace operation, the isotropic second-order differentiation, on spatial functions is an essential mathematical calculation in most physical equations and signal processing. Realizing the Laplace operation in a manner of optical analog computing has recently attracted attention, but a compact device with a high spatial resolution is still elusive. Here, we introduce a Laplace metasurface that can perform the Laplace operation for incident light-field patterns. By exciting the quasi-bound state in the continuum, an optical transfer function for nearly perfect isotropic second-order differentiation has been obtained with a spatial resolution of wavelength scale. Such a Laplace metasurface has been numerically validated with both 1D and 2D spatial functions, and the results agree well with that of the ideal Laplace operation. In addition, the edge detection of a concerned object in an image has been demonstrated with the Laplace metasurface. Our results pave the way to the applications of metasurfaces in optical analog computing and image processing.

Laplace metasurfaces for optical analog computing based on quasi-bound states in the continuum