We analyze the chirality of dispersion relations and propagation lengths of two fundamental modes (m=0 and 1) in single silver nanowire coated by chiral TDBC. The systems of both Ag nanowires only coated by left TDBC (ALM) and right TDBC (ARM) are considered, respectively. Finite-difference time-domain method is used to do the mode analysis. The results show that the dispersion relations curves of both ALM and ARM are similar to magnetic hysteresis loops. There is a dip in the propagation length of ALM or ARM versus the incident frequency at the resonant frequency of left TDBC or right TDBC. The propagation length is reduced shapely in chiral TDBC due to the dissipation of TDBC. The difference of the propagation length \(|\Delta L|\) becomes larger with the incident frequency far away from the resonant frequency of chiral TDBC for these two modes. The maximum difference of the real part of the effective index between ALM and ARM (\(\Delta n'\)) is the linear function of m and the radius of Ag nanowire. With the radius decreasing from 100nm to 10nm, the propagation length for m=0 decreases and the propagation length for m=1 increases. Also, the maximum difference of the propagation length for m=1 increases. The maximum normalized difference between Ag nanowires coated by left TDBC and right TDBC in both the dispersion relation for \(m=0\) (0.024) and the propagation length for \(m=1\) (0.16) are quite larger than the one of only chiral TDBC (1/3000). According to our analysis, chiral molecules can be distinguished in either the dispersion relation or the propagation length, and our proposed structure has potential applications in chiral molecules detecting.

我们分析了手性TDBC包覆的单银纳米线中两个基本模式（m = 0和1）的色散关系的手性和传播长度。分别考虑了仅被左TDBC（ALM）和右TDBC（ARM）包覆的两种银纳米线的系统。时域有限差分法用于模式分析。结果表明，ALM和ARM的色散关系曲线与磁滞回线相似。在左TDBC或右TDBC的谐振频率处，ALM或ARM的传播长度相对于入射频率有所下降。由于TDBC的耗散，传播长度在手性TDBC中呈形状减小。传播长度之差\（| \ Delta L | \）对于这两种模式，当入射频率远离手性TDBC的共振频率时，它变得更大。ALM和ARM之间的有效索引的实部最大差异（\（\ Delta n'\））是m的线性函数和Ag纳米线的半径。随着半径从100nm减小到10nm，m = 0的传播长度减小，m = 1的传播长度增加。而且，对于m = 1 ，传播长度的最大差增大。左TDBC和右TDBC包覆的Ag纳米线之间的最大归一化差在\（m = 0 \）（0.024）的色散关系和\（m = 1 \）的传播长度上（0.16）远远大于唯一的手性TDBC（1/3000）之一。根据我们的分析，手性分子可以通过色散关系或传播长度来区分，并且我们提出的结构在手性分子检测中具有潜在的应用。