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Differentiation has widespread applications, particularly in image processingfor edge detection. Significant advances have been made in using nanophotonicstructures and metamaterials to perform such operations. In particular, arecent work demonstrated a topological differentiator in which the transferfunction exhibits a topological charge, making the differentiation operationrobust to variation of operating conditions. The demonstrated topologicaldifferentiator, however, operates in the reflection mode at off-normalincidence and is difficult to integrate into compact imaging systems. In thiswork, we design a topological differentiator that operates isotropically intransmission mode at normal incidence. The device exhibits an optical transferfunction with a symmetry-protected, topological charge of $\pm 2$ and performssecond-order differentiation. Our work points to the potential of harnessingtopological concepts for optical computing applications.

Isotropic Topological Second-Order Spatial Differentiator Operating in Transmission Mode