  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.
