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