二维光子晶体禁带理论在浓度测量上的模拟研究

Simulation of Two-Dimensional Photonic Crystal Band Gap in Concentration Measurement

对二维光子晶体的电磁波理论及周期性介质中的Bloch波解做了详细的推导,给出了光子晶体中的禁带存在的理论依据,同时以三角晶格的二维光子晶体为例,采用平面波展开方法对果糖水溶液的浓度进行测定。主要利用硅与果糖溶液介电常数较大的原理,通过数值模拟获得相应的光子禁带图并加以分析。结果表明,以果糖的水溶液作为空气圆孔中的介质材料,当溶液浓度不同时TE模式的光子禁带(PBG)明显变宽,而TM模式不出现光子禁带现象。研究结果及方法对高血糖临床应用有一定的指导作用。

Detailed derivation is conducted to solve the Bloch wave solutions of the electromagnetic wave theory of two-dimensional photonic crystal and periodic media. The theoretical basis for the existence of the band gap in the photonic crystal is given. We measured the concentration of fructose solution in a two-dimensional triangular lattice photonic crystal using plane-wave expansion method. To get the numerical simulation of photonic band diagram for analysis, we take advantage of the large permittivity of silicon and fructose solution. The results show that the photonic band gap （PBG） of TE mode distinctly broadens with the difference of the concentration of the fructose solution but there is no PBG in TM mode, when fructose solution is used as the dielectric material in the air hole. The results of this study and the proposed method may play a guiding role in clinical applications for helping hyperglycemia patients.