Engineering zero modes, Fano resonance, and Tamm surface states in the waveguide-array realization of the modified...

In this article, we developed a generalized coupled-mode theory for mixing an isolated state with a continuum having an intrinsic energy gap, which dubbed as "the bound states in the gapped continuum" (BIGC). We investigated the mixture interaction by mimicking the Su-Schrieffer-Heeger model in an optical coupled waveguide array (WA), and presented a unified engineering mechanism for topologically-protected zero modes, Fano resonance, and Tamm surface states, even though those phenomena are diverse in topological insulators, atomic physics and semiconductors, respectively. By tuning the on-site potential and coupling strength of the isolated state, we found the unified operating characteristics for zero modes, Fano resonance, and Tamm states, with demonstrating their localization, transmission spectra, and distinct evolution dynamics explicitly. As an extension for triple-modes coupling, two special sandwich-like configurations are studied: the isolated-continuous-isolated and continuous-isolated-continuous configurations lead to adiabatic eliminations and domain walls, respectively, revealing possible applications and wide connections in many fields of physics and optics.