一维光子晶体光学特性的复平面波展开法研究

Study on the optical properties of one-dimensional photonic crystals with the complex plane wave expansion method

应用复平面波展开法对一维光子晶体的光子带隙,透射特性进行了分析.通过对色散关系和透射系数的数值计算发现一维光子晶体周期结构个数以及折射率分布对光学晶体透射系数以及光子带隙的影响.对于含有整数个周期结构的光子晶体有共振点出现在光子帯隙外的频率范围内,共振点的个数比周期结构个数少1.带隙倾斜斜率等于折射率的比值.折射率比值越大,带隙的范围越大.

The complex plane wave expansion method is used to investigate photonic band gaps and transmission properties of one-dimensional periodic structure photonic crystals. The numerical analysis on dispersion relations and transmission coefficients shows how the number of periodic structures and the distribution of refractive indexes influence transmission coefficients and photonic band gaps. There occur resonance points outside band gaps in the crystals with integral periodic structures, and the num- ber of the resonance points is one less than that of periodic structures. For a given monochromatic light incident on a multilayer film of different thicknesses which contains two kinds of media, the slope of band gaps equals the ratio of refraction indexes of the two media. The higher ratio results in a wider band gap.