  In this paper, we propose an unfitted Nitsche's method for computing wave
modes in topological materials. The proposed method is based on Nitsche's
technique to study the performance-enhanced topological materials which have
strongly heterogeneous structures (e.g., the refractive index is piecewise
constant with high contrasts). For periodic bulk materials, we use
Floquet-Bloch theory and solve an eigenvalue problem on a torus with unfitted
meshes. For the materials with a line defect, a sufficiently large domain with
zero boundary conditions is used to compute the localized eigenfunctions
corresponding to the edge modes. The interfaces are handled by Nitsche's method
on an unfitted uniform mesh. We prove the proposed methods converge optimally,
and present numerical examples to validate the theoretical results and
demonstrate the capability of simulating topological materials.
