Differentiation has widespread applications, particularly in image processing for edge detection. Significant advances have been made in using nanophotonic structures and metamaterials to perform such operations. In particular, a recent work demonstrated a topological differentiator in which the transfer function exhibited a topological charge, making the differentiation operation robust to variations in operating conditions. The demonstrated topological differentiator, however, operates in reflection mode at off-normal incidence and is difficult to integrate into compact imaging systems. In this work, we design a topological differentiator that operates isotropically in transmission mode at normal incidence. The device exhibits an optical transfer function with a symmetry-protected topological charge of ±2 and performs second-order differentiation. Our work points to the potential of harnessing topological concepts for optical computing applications.
