Quantum theory of photonic crystals

• We have firstly presented a new quantum theory to study one-dimensional photonic crystals.
• We give quantum dispersion relation and quantum transmissivity.
• We find the classical and quantum dispersion relation and transmissivity are identical.
• We find the position and width of band gaps are identical for classical and quantum transmissivity.

In this paper, we have firstly presented a new quantum theory to study one-dimensional photonic crystals. We give the quantum transform matrix, quantum dispersion relation and quantum transmissivity, and compare them with the classical dispersion relation and classical transmissivity. By the calculation, we find the classical and quantum dispersion relation and transmissivity are identical. The new approach can be studied two-dimensional and three-dimensional photonic crystals.