Contribution of evanescent waves to the effective medium of disordered waveguides

TL;DR

This paper investigates how evanescent waves influence the effective optical properties of disordered waveguides, revealing their significant impact on the effective refractive index but not on average transmittance or reflectance.

Contribution

It demonstrates the crucial role of evanescent modes in determining the effective refractive index in disordered waveguides, supported by theoretical and numerical analysis.

Findings

Evanescent modes significantly affect the real part of the effective refractive index.

Statistical averages of transmittance and reflectance are unaffected by evanescent modes.

Theoretical predictions align well with numerical simulations.

Abstract

We consider a wave propagating through a thin disordered slab inside a wire or waveguide of finite width. In the dense weak scattering limit, the statistics for the complex reflection and transmission coefficients (the coherent field) is found to depend dramatically on the contribution of evanescent modes or closed channels, leading to an effective refractive index whose real part is quite sensitive to the closed channels inclusion. In contrast, evanescent modes play no role in the statistical average of transmittances and reflectances. The theoretical predictions, based on the perturbative Born series expansion, are in excellent agreement with numerical simulations in disordered wires.