Wave propagation, bi-directional reflectionless, and coherent perfect absorption-lasing in finite periodic PT-symmetric photonic systems

With consideration of parity-time (PT) symmetry, Lorentz reciprocity theorem, and real Bloch phase, we propose a generalized parametric space for any PT-symmetric unit cells that can comprehensively illustrate the PT phase transition, Bloch phase, and necessary conditions of exotic wave scattering in the general finite periodic PT photonic structures. We put forward rigorous and formal expressions of bi-directional reflectionless and coherent perfect absorption and lasing (CPAL) for the finite one-dimensional PT photonic structures. With a new concept of the parametric space, we demonstrate the necessary PT phases of general unit cells, which result in the abnormal bi-directional reflectionless and CPAL effects. Moreover, thanks to parametrization, analytical formulas for complex relative permittivities of the unit cells composed of subwavelength gain–loss heterostructure are derived to provide a guideline for manipulating different PT scattering events. We accordingly study several one-dimensional PT photonic systems to achieve exotic wave scattering enabled by PT-symmetry. We believe this work may offer a theoretical underpinning for studying extraordinary wave phenomena of PT-symmetric photonics and may open avenues for manipulation of light.