The quantum transmission characteristic of one-dimensional photonic crystals

In this paper, we have given the quantum transfer matrix, quantum dispersion relation, quantum transmissivity and reflectivity of one-dimensional photonic crystals with the quantum theory of photon. We have studied the quantum transmission characteristic of different structure one-dimensional photonic crystals, which include mirror and nonmirror structures, with and without defect, and the defects are active and inactive media. On that basis, we compared the dispersion relation, transmissivity and reflectivity of quantum with classical for one-dimensional photonic crystals, and found they are identical, which indicate the quantum theory approach of photonic crystals is true, it can further study the quantum topological property of photonic crystals, such as quantum Zak phase, Chern number and quantum edge state and so on.