Asymmetric topological pumping in nonparaxial photonics.

The study of topological photonics was initially inspired by the quantum-optical analogy between the Schrodinger equation for electron wave function and the paraxial Helmholtz equation for light. Here, we reveal a novel phenomenon in topological pumping in arrays of nonparaxial optical waveguides, where the quantum-optical analogy becomes no longer valid. We predict theoretically and demonstrate experimentally an unexpected topological pumping when the injected field transfers from one edge of the waveguide arrays to the other edge in the nonreciprocal fashion. Our finding could pave the way to a new field of nonparaxial topological photonics, and it suggests novel topological effects in optics and photonics driven by nonparaxiality.