Engineering zero modes, Fano resonance and Tamm surface states of 'bound states in the gapped continuum'

In this article, we developed a generalized coupled-mode theory for mixing an isolated state with the gapped continuum to unify the engineering mechanism of gap-protected zero modes, Fano resonance and Tamm surface states, even though those phenomena are diverse in numerous branches of physics and optics. By tuning the on-site potential and coupling strength of/with the isolated state, we found the operating characteristics from zero modes, Fano resonance and to Tamm modes, with explicitly demonstrating their localization, transmission spectra and distinct evolution dynamics of the 'bound states in the gapped continuum' (BIGC). As an extent, we designed two sandwich-like structures in the BIGC framework: (1) the 'isolated-continuous-isolated' (ICI), which leads to adiabatic elimination technique and topologically-protected edge states, and (2) the 'continuous-isolated-continuous' (CIC), which results into the domain wall dynamics. Finally, we proposed the optical waveguide array (WA) modelling of the modified Su-Schrieffer-Heeger dimerized lattice to achieve those interesting engineering processes, and meanwhile to shed light on the generalization of bound states in the continuum into photonics and condensed matters.