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.

中文翻译：

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用于基于连续体中准束缚态的光学模拟计算的拉普拉斯超表面

空间函数的拉普拉斯运算（各向同性二阶微分）是大多数物理方程和信号处理中必不可少的数学计算。以光学模拟计算的方式实现拉普拉斯运算最近引起了人们的注意，但具有高空间分辨率的紧凑设备仍然难以实现。在这里，我们介绍了一个拉普拉斯超曲面，它可以对入射光场图案执行拉普拉斯运算。通过激发连续谱中的准束缚态，获得了具有波长尺度空间分辨率的近乎完美的各向同性二阶微分的光学传递函数。这样的拉普拉斯超曲面已经用一维和二维空间函数进行了数值验证，结果与理想的拉普拉斯操作的结果非常吻合。此外，图像中相关对象的边缘检测已经用拉普拉斯超曲面进行了演示。我们的结果为超表面在光学模拟计算和图像处理中的应用铺平了道路。