Reflection statistics of weakly disordered optical medium when its mean refractive index is different from an outside medium

TL;DR

This paper analyzes how the reflection properties of a weakly disordered optical medium differ when its mean refractive index is not equal to that of the outside medium, revealing unique statistical behaviors in such mismatched conditions.

Contribution

It provides a theoretical analysis of reflection statistics in weakly disordered media with mismatched refractive indices, highlighting differences from matched cases and considering correlation effects.

Findings

Average reflectance proportional to disorder variance and correlation length

Standard deviation of reflectance scales with square root of disorder variance and correlation length

Differences from matched index case in statistical behavior of reflection

Abstract

Based on the difference between mean background of an optical sample refractive index n_0 and an outside medium, n_out, different than n_0, we study the reflection statistics of a one-dimensional weakly disordered optical medium with refractive index n(x)=n_0+dn(x). Considering dn(x) as color noise with the exponential spatial correlation decay length l_c and k as the incident wave vector, our results show that for the small correlation length limit, i.e. k*l_c<1, the average value of reflectance, r, follows a form that is similar to that of the matched refractive-index case n_0=n_out, i.e., <r(dn, lc)> proportional to <dn^2>l_c. However, the standard deviation of r is proven to be std(r(dn,l_c)) proportional to sqrt(<dn^2>l_c), which is different from the matched case. Applications to light scattering from layered media and biological cells are discussed