Research on one-dimensional photonic crystals with quantum theory approach

In this paper, we have proposed the spinor wave equation of free and non-free photon, and given the quantum transfer matrix, dispersion relation, quantum transmissivity and quantum reflectivity of one-dimensional photonic crystals with the quantum theory of photon. On that basis, we have studied the effect of different incident angle, refractive index and thickness of medium on quantum and classical dispersion relation, transmissivity and reflectivity. We have found the results of quantum and classical are identical, which indicate the quantum theory approach for photonic crystals is reasonable and true, it will be studied the quantum edge state, quantum Zak phase and Chern number of the quantum topological property for photonic crystals.