Slab dielectric waveguide with randomly fluctuating refractive indices

Abstract

Abstract The three-layer slab dielectric waveguide is perhaps the most basic structure for designing optical and electronic devices. Deterministic results, assuming constant refractive indices, on the propagation of an electromagnetic wave within this structure are well known and they are reported in papers and textbooks, however to the best of the authors knowledge, there are no works reported in the literature on the stochastic propagation. In order to describe the stochastic propagation, we propose a model in which the refractive indices are variables fluctuating randomly. Our main objective is to show the student the significant difference between the deterministic and stochastic response of the system, when constant or random refractive indices are considered. In particular the dispersion curves, the distribution of the fields and the energy flow are presented and discussed. Our results show that the asymmetry factor associated with the dispersion curves can be easily modified by means of the magnitude of the induced fluctuation. Another interesting property shows that both TE0 and TM0 fundamental modes propagate only for small fluctuations. In the core of the guide, the amplitude of the electric and magnetic fields exhibits damped oscillations due to the randomness of the system. The energy flow is high in the substrate region, but it is vanishing in the cladding region. We conclude that those deterministic results are a particular case of our stochastic results.