  Optical metasurfaces performing analog image processing - such as spatial
differentiation and edge detection - hold the potential to reduce processing
times and power consumption, while avoiding bulky 4F lens systems. However,
current designs have been suffering from trade-offs between spatial resolution,
throughput, polarization asymmetry, operational bandwidth, and isotropy. Here,
we show that dispersion engineering provides an elegant way to design
metasurfaces where all these critical metrics are simultaneously optimized. We
experimentally demonstrate silicon metasurfaces performing isotropic and
dual-polarization edge detection, with numerical apertures above 0.35 and
spectral bandwidths of 35 nm around 1500 nm. Moreover, we introduce
quantitative metrics to assess the efficiency of these devices. Thanks to the
low loss nature and dual-polarization response, our metasurfaces feature large
throughput efficiencies, approaching the theoretical maximum for a given NA.
Our results pave the way for low-loss, high-efficiency and broadband optical
computing and image processing with free-space metasurfaces.
