Quantum theory of photonic crystals
Xiang-Yao Wu, Ji Ma, Xiao-Jing Liu, Jing-Hai Yang, Hong Li, Si-Qi, Zhang, Hai-Xin Gao, Xin-Guo Yin, San Chen
TL;DR
This paper introduces a quantum theoretical framework for analyzing one-dimensional photonic crystals, deriving quantum dispersion and transmissivity, and comparing them with classical results, with potential extensions to higher dimensions.
Contribution
It presents a novel quantum approach to photonic crystal analysis, including quantum transform matrix and dispersion relation, aligning with classical results and enabling studies of higher-dimensional structures.
Findings
Quantum and classical dispersion relations are identical.
Quantum transmissivity matches classical transmissivity.
The approach can be extended to 2D and 3D photonic crystals.
Abstract
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.
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