Slab cholesteric waveguide with randomly fluctuating propagation constant

Abstract

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.