In this work, we present a stochastic theoretical analysis of an electromagnetic wave propagating inside a planar slab waveguide filled with a cholesteric material. In this system, the propagation constant of the wave is assumed to be a randomly fluctuating parameter. By means of the van Kampen systematic expansion method, Maxwell’s electromagnetic equations with random coefficients, and appropriate boundary conditions, are obtained. Numerical examples of the effects of the randomness on the propagating constant, on the ratio between magnetic and electric modes, on the field profiles, and on the energy flow are given. The results show that the stochastic waveguide can support multiple Transverse Magnetic (TM) or Transverse Electric (TE) modes with the same cutoff frequency, and furthermore, they support a distribution of electric and magnetic fields with phase shift. Our results are consistent with those of an isotropic waveguide.

在这项工作中，我们对在填充有胆甾型材料的平面平板波导内传播的电磁波进行了随机理论分析。在这个系统中，假设波的传播常数是一个随机波动的参数。通过van Kampen系统展开法，得到了具有随机系数和适当边界条件的麦克斯韦电磁方程。给出了随机性对传播常数、磁模式和电模式之间的比率、场分布和能量流的影响的数值示例。结果表明，随机波导可以支持多个具有相同截止频率的横磁 (TM) 或横电 (TE) 模式，此外，它们支持具有相移的电场和磁场分布。我们的结果与各向同性波导的结果一致。