Coherent control of nonreciprocal optical properties of the defect modes in 1D defective photonic crystals with atomic doping

We investigate the spectral properties of photonic crystals, lacking parity-time (PT) symmetry, using scattering matrix formalism. We show using the symmetry properties of matrices that a defective photonic crystal, doped with three-level atoms, breaks PT symmetry. For the two defect modes lying in the band gap region, both the reflection and the absorption become nonreciprocal, while the transmission remains reciprocal. We show that the relevant energy spectra do not exhibit exceptional points, thereby invalidating its necessity to achieve nonreciprocity in reflection and absorption. We further demonstrate how this non-reciprocity can be coherently controlled using the driving field and dissipation rates of the atoms.