  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 exhibits a topological charge, making the differentiation operation
robust to variation of operating conditions. The demonstrated topological
differentiator, however, operates in the 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 $\pm 2$ and performs
second-order differentiation. Our work points to the potential of harnessing
topological concepts for optical computing applications.
