Enhancing the sensitivity of mesoscopic light reflection statistics in weakly disordered media by interface reflections

Abstract: Reflection statistics have not been well studied for optical random media whose mean refractive indices do not match with the refractive indices of their surrounding media. Here, we theoretically study how this refractive index mismatch between a one dimensional (1D) optical sample and its surrounding medium affects the reflection statistics in the weak disorder limit, when the fluctuation part of the refractive index (dn) is much smaller than the mismatch as well as the mean refractive index of the sample (dn << <n>). In the theoretical derivation, we perform a detailed calculation that results in the analytical forms of mean and standard deviation (STD) of the reflectance in terms of disorder parameters (dn and lc) in an index mismatched backscattering system. Particularly, the orders of disorder parameters in STD of the reflectance for index mismatched systems is shown to be lower ( (<dn^2> lc )^1/2 ) than that of the matched systems (<dn^2> lc). By comparing STDs of the reflection coefficient of index matched and mismatched systems, we show that reflectance at the sample boundaries in index mismatched systems can enhance the signal of the STD to the disorder parameters of the reflectance. In terms of biophotonics applications, this result can lead to potential techniques that effectively extract the sample disorder parameters by manipulating the index mismatch conditions. Potential applications of the technique for enhancement in sensitivity of cancer detection at single cell level are also discussed.