Effect of symmetry breaking on bound states in the continuum in waveguide arrays

We developed the theoretical framework based on the coupled-mode theory which describes spectral and scattering properties of the photonic analog of an extended Fano-Anderson model???a waveguide array with two additional side-coupled waveguides. The structure supports a rich spectrum of eigenmodes, including bound state in the continuum (BIC) and other bound and leaky modes, which can be classified according to the relation between the self-coupling coefficients and eigenvalues. We focus on the structures with broken vertical symmetry with their band structures revealing interesting phenomena, such as exceptional points and level repulsion, and offer a lossless platform for PT-symmetry phase transition. We interpreted the resonant features in the scattering spectra through a generalized Weierstrass factorization. The resonance related with quasi-BIC arises from the interference between two leaky modes: one of them representing a continuum spectrum and the other (quasi-BIC) discrete state. The reflectance near the resonance can be rewritten into the form of the Fano formula where the shape parameter f can be expressed in terms of the poles associated with the two modes. Our approach provides a flexible framework which allows to interpret and to engineer the resonant properties of more complex systems.

Automated summary

We developed a theoretical framework based on the coupled-mode theory to describe the spectral and scattering properties of an extended Fano-Anderson model in a waveguide array with additional side-coupled waveguides. The structure supports various eigenmodes, including bound state in the continuum (BIC) and other bound and leaky modes, which can be classified based on the relation between the self-coupling coefficients and eigenvalues. This research provides insights into the resonant properties of complex systems and offers a lossless platform for PT-symmetry phase transition.