Topological theory for perfect metasurface isolators

We introduce a topological theory of perfect isolation: perfect transmission from one side and total reflection from the other side simultaneously. The theory provides an efficient approach for determining whether such a perfect-isolation point exists within a finite parameter space. Herein, we demonstrate the theory using an example of a Lorentz nonreciprocal metasurface composed of dimer unit cells. Our theory also suggests that perfect-isolation points can annihilate each other through the coalescence of opposite topological charges. Our findings could lead to novel designs for high-performance optical isolators.