Tamm surface states in a finite chain of defects in a photonic crystal

We present detailed theoretical and numerical studies of surface states of a coupled defect chain of finite length in a photonic crystal. By comparatively studying three such structures with zero, one, and two defects on the photonic crystal surface, respectively, we found that the transmission characteristics of the structure depend on the termination of the defect chain in the host crystal. The peak frequencies and the number of peaks are related to the boundary conditions of the coupled defects. Our numerical simulations in conjunction with analytical treatment using the coupled mode theory fully establish the analogy between the surface states in photonic crystals and the Tamm states in solids. We also point out how the results of the localized surface states in this one-dimensional model system can be generalized to two- or three-dimensional systems where surface states become surface waves.