Photonic band-gap transmission map of graphene in a defective optical structure

Interaction of graphene with a defect layer of a 1D defective photonic structure correspondingly could open a Dirac gap in its nonlinear energy dispersion. Also, an excitonic gap could be created upon applied strong magnetic fields at low temperatures. Now, the exact solution for the transmission of the allowed defective states under the influence of a homogeneous magnetic field requires providing a new scheme for the transfer matrix method to cover the circularly polarized propagation of the light in THz regime. In this paper, through an easy-to-follow framework for obtaining the distinct expression of the related transfer matrix method, it is observed that the hybrid defective states in the suggested optical structure undergo an unconventional transmission map as function of Dirac gap. Moreover, it is shown that mapping the transmission spectrum in the frequency space reveals peculiar results for narrow-band transport of the defective states. Finally, it is demonstrated that the transmission spectrum shows plateaus as a function of the applied magnetic field analogues to the situations observed for the conductance of a 2D electron gas system in the quantum Hall effect regime. This almost simple suggested design which can be fully controlled marks the first optical counterpart of quantum Hall effect in optics.