We consider a planar waveguide in which there is a confined cholesteric liquid crystal whose helical axis is perpendicular to its plane boundaries. We write the electromagnetic equation for describing the dynamics of the propagating modes inside the guide and solve them numerically. We found the propagating parameter and ratio between magnetic and electric modes versus frequency conforming the band structure of the mentioned modes. We also calculate the profiles electromagnetic field amplitudes and the Poynting vector distributions versus position. We discuss how the transverse electric and magnetic modes are embodied in the eigen modes and their conditions for them to propagate.

我们考虑一个平面波导，其中有一个螺旋轴垂直于其平面边界的受限胆甾型液晶。我们编写了电磁方程来描述波导内传播模式的动力学，并以数值方式求解它们。我们发现磁模式和电模式与频率之间的传播参数和比率符合上述模式的能带结构。我们还计算剖面电磁场幅度和坡印廷矢量分布与位置的关系。我们讨论横向电模式和磁模式如何体现在本征模式中以及它们传播的条件。