Dual-Polarized Broadband Laplace Differentiator via Quasi-Bound States in the Continuum Empowered by Nonlocal Metasurfaces

Directly performing optical analog computations and image processing in space, such as optical differential operations and image edge detection, is a burgeoning area. To avoid the bulkiness and low efficiency of traditional 4f filtering systems, one can utilize Green's function and metasurfaces for advanced wavefront control. However, some metasurface differentiators can be hindered by issues like polarization sensitivity, restricted bandwidth, low resolution, and the need for additional polarization devices or digital post-processing, potentially degrading their performance and operation efficiency. In this work, a dual-polarization Laplace differentiator is engineered to address these issues based on nonlocal hollow metasurface. The optical transfer function (OTF) required by the Laplace operation can be obtained by exciting different quasi-bound states in the continuum (Q-BIC) modes with distinct angular dispersion capabilities under p- and s-polarized illumination, respectively. This Laplace differentiator not only directly realizes 2D second-order edge detection in a dual-polarization channel but also features a numerical aperture (NA) with an upper limit close to 0.42 and a broadband range reaching 165 nm. Such an efficient, high-quality dual-polarization and bandwidth image edge detection approach offers powerful imaging techniques for applications in machine vision, microscopic imaging, and image processing.