Generalized parametric space, parity symmetry of reflection, and systematic design approach for parity-time-symmetric photonic systems

Based on the reciprocity theorem, we put forward a generalized parametric space for arbitrary transfer matrix with parity-time (PT) symmetry. Through this parametric space, one can extract complete information involving PT-symmetric phases, reflectances, transmittances, and known extraordinary scattering phenomena. We demonstrate a PT-symmetric heterostructure with coherent perfect absorption-lasing, anisotropic transmission resonance, and parity symmetry of reflection coefficients at the frequencies of interest. In addition, with the parametric space and the analytical formula, the corresponding complex dielectric permittivities for a simple PT-symmetric system made of a gain, an air gap, and a loss media in deeply subwavelength is derived to achieve various exotic PT-symmetric functionality. This work could offer an alternative route to design versatile optical and photonic PT-symmetric devices.