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 (Δn) is much smaller than the mismatch as well as the mean refractive index of the sample (Δn ≪〈n〉). In the theoretical derivation, we perform a detailed calculation that results in the analytical forms of the mean and standard deviation (STD) of the reflection coefficient in terms of disorder parameters (〈(Δn)2〉1/2 and its correlation length lc) in an index mismatched backscattering system. Particularly, the orders of disorder parameters in STD of the reflection coefficient for index mismatched systems are shown to be lower (∼(〈Δn2〉lc)1/2) than that of the matched systems (∼〈Δn2〉lc). By comparing STDs of the reflection coefficient values of index matched and mismatched systems, we show that reflection coefficient at the sample boundaries in index mismatched systems can enhance the signal of the STD to the "disorder parameters" of the reflection coefficient. In terms of biophotonics applications, this result can lead to potential techniques that effectively extract the sample disorder parameters by manipulating the index mismatched conditions. Potential applications of the technique for enhancement in sensitivity of cancer detection at the single cell level are also discussed.
- Statistical optics
- medical and biological imaging
ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Condensed Matter Physics