For finite 2D photonic structures, the per-area edge circulation index converges to the bulk gap Chern number as the domain grows, conditional on unproved Green function bounds.
Applications of Chebyshev polynomials and Toeplitz theory to topological metamaterials
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We survey the use of Chebyshev polynomials and Toeplitz theory for studying topological metamaterials. We consider both Hermitian and non-Hermitian systems of subwavelength resonators and provide a mathematical framework to explain some spectacular properties of metamaterials.
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Bulk-edge correspondence in finite photonic structure
For finite 2D photonic structures, the per-area edge circulation index converges to the bulk gap Chern number as the domain grows, conditional on unproved Green function bounds.