  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 a PT 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 system made of a gain, a gap, and a loss media
in deeply subwavelength is derived to achieve various exotic PT functionality.
This work could offer an alternative route to design versatile optical and
photonic PT devices.
