基于Berreman 4×4矩阵对胆甾相液晶Bragg反射带宽的模拟研究

利用Berreman 4×4矩阵和Matlab编程模拟了胆甾相液晶的反射光谱,分析了螺旋数(液晶厚度)、基板的折射率、双折射、折射率色散、固定螺距、梯度螺距和入射角等因素对反射光谱带宽的影响。结果表明,要得到理想的Bragg反射带宽,液晶层的厚度即螺旋数N需达到N≥10;基板折射率会影响最大反射率,基板折射率ng与寻常光折射率no相比,ngno时,最大反射率比较低,ng越小越影响明显,当ng≥no时,具有很好的反射率;折射率的色散和大的入射角会使带宽变窄,而大的双折射Δn和螺距P可以得到较宽的反射带宽,但拓宽效果有限。通过梯度螺距的函数表达式,理论模拟了具有螺距梯度的胆甾相液晶的反射带宽,其对于胆甾相液晶宽波反射的实验研究具有一定的意义。

Simulation research on Bragg reflection bandwidth of cholesteric liquid crystal based on Berreman 4×4 matrix

This research simulates the reflection spectrum of cholesteric liquid crystal by Berreman 4×4 matrix and Matlab program, and analyses the factors that affect the bandwidth of reflection spectrum, such as pitch number (thickness of liquid crystal), refractive index of substrate, birefringence, dispersion of refractive index, fixed pitch, pitch gradient, incident angle and so on. The result illustrates that in order to get an ideal Bragg reflection bandwidth, the thickness of the liquid crystal, the pitch number N, must reach N≥10; The substrate refractive index can impact the maximum reflection, which will be relatively low when the substrate refractive index n_gis smaller than the common light reflection and the affection is more obvious as the n_g becomes smaller when n_g≥n_o,a pefect reflection can be attained.The dispersion reflection and big incident angle will make the bandwidth become narrow, while large birefringence Δn and pitch P lead to broader bandwidth, but the broadening effects is finite. The reflection bandwidth of the pitch gradient cholesteric liquid crystal was simulated theoretically by giving the function expression of pitch gradient, which makes sense for the experimental study of broadband reflection of cholesteric liquid crystal.