Wave Propagation in Randomly Perturbed Weakly Coupled Waveguides

Abstract

We present an analysis of wave propagation in a two step-index, parallel waveguide system. The goal is to quantify the effect of scattering at randomly perturbed interfaces between the guiding layers of high index of refraction and the host medium. The analysis is based on the expansion of the solution of the wave equation in a complete set of guided, radiation and evanescent modes with amplitudes that are random fields, due to scattering. We obtain a detailed characterization of these amplitudes and thus quantify the transfer of power between the two waveguides in terms of their separation distance. The results show that, no matter how small the fluctuations of the interfaces are, they have significant effect at sufficiently large distance of propagation, which manifests in two ways: The first effect is well known and consists of power leakage from the guided modes to the radiation ones. The second effect consists of blurring of the periodic transfer of power between the waveguides and the eventual equipartition of power. Its quantification is the main practical result of the paper.

Slab cholesteric waveguide with randomly fluctuating propagation constant

“…By using a stochastic technique of estimators for coupling coefficients, a study of a planar waveguide with perturbed walls has been performed by Swierk and Heimrath [24]. The propagation of electromagnetic waves in random waveguides in rectangular cross section with randomly fluctuating electric permittivity has been studied by Alonso and Borcea [25]. Whereas, the polarization effects in random media with small fluctuations of the electric permittivity, and randomness of amplitudes on the electric and magnetic fields, have been analyzed by Borcea and Garner [26].…”

“…Whereas, the polarization effects in random media with small fluctuations of the electric permittivity, and randomness of amplitudes on the electric and magnetic fields, have been analyzed by Borcea and Garner [26]. In a more recent work, these same authors quantified the effect of scattering at randomly perturbed interfaces between the guiding layers of high index of refraction and the host medium [27].…”

A ghost imaging modality in a random waveguide

“…This makes it possible to use the wave propagation theory developed in [1]. The results should extend qualitatively to three dimensions, to other reflecting boundary conditions such as sound hard [1], to open (radiating) random boundaries studied in [2], and to electromagnetic waves studied in [3,4]. Waveguides with slowly changing cross-section can be considered as well, especially if the cross-section increases in the forward direction of wave propagation.…”