Robustness of perfect transmission resonances to asymmetric perturbation

We investigate the impact of asymmetric perturbations on the perfect transmission resonances (PTRs) of one-dimensional finite periodic systems. With no perturbations, the scattering region consists of N identical cells, and the transmission spectrum exhibits at least N-1 PTRs in each passband of the Bloch dispersion of the unit cell. By introducing a perturbation, the periodic structure is broken, which a priori results in the elimination of all PTRs. However, we demonstrate that PTRs can still arise under asymmetric perturbations when the unperturbed system possesses mirror symmetry, utilizing the PT symmetry of the unperturbed reflectionless eigenvalue problem. We also reveal an intriguing connection between two seemingly independent PTRs that lies in the symmetry of the unperturbed unit cell: If one PTR is preserved, then a dual one is necessarily also preserved. Our findings offer insights for the design of, for example, a robust antireflection setup at multiple wavelengths or all-optical diode devices.