## Abstract

Statistical properties of light waves reflected from a one-dimensional (1D) disordered optical medium [n(x) = n_{0} + dn(x), <dn(x)>=0] have been well studied, however, most of the studies have focused on the situation when the mean refractive index of the optical medium matched with the outside medium, i.e., n_{0} = n_{out} =1. Further, considering dn(x) as a Gaussian color noise refractive index medium with exponential spatial correlation decay length l_{c} and k as the incident wave vector, it has been shown that for smaller correlation length limit, i.e., kl_{c} <<1, both the mean reflection coefficient <r> and std of r, σ(r), have same value, and they follow the relation <r>= σ(r) ∝ <dn^{2}> l_{c}. However, when the refractive index of the sample medium is different from the outside medium, the reflection statistics may have interesting features, which has not been well studied or understood. We studied the reflection statistics of a 1D weakly disordered optical medium with the mean background refractive index n_{0} being different from the outside medium n_{out} (≠n_{0}), to see the effect of mismatching (i.e., value of n_{0} - n_{out}) on the reflection statistics. In the mismatched case, the results show that the mean reflection coefficient <r> follows a form similar to that of the matched refractive-index case, i.e., <r(dn, l_{c})>∝ <dn^{2}> l_{c}, with a linear increased shift, which is due to 1D uniform background reflection from a slab. However, σ(r) is shown to be σ(r) ∝ (<dn^{2}>l_{c})^{1/2}, which is different from the matched case. This change in std of r is attributed to the interference between the mismatched-crerated edge mediated multiple scattering that are coupled with the random scattering. Applications to light scattering from random layered media and biological cells are discussed.

Original language | English (US) |
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Pages (from-to) | 185-190 |

Number of pages | 6 |

Journal | Optics Communications |

Volume | 393 |

DOIs | |

State | Published - Jun 15 2017 |

### Funding

This work was partly supported by NIH grants (Nos. R01EB003682, R01EB016983, R01CA128641 and U54CA143869), a NSF grant no CBET-0937987, a FedEx Institute of Technology Grant, and a Faculty Research Grant from the University of Memphis.

## Keywords

- Backscattering
- Cancer detection
- Scattering theory
- Weakly disordered biological media

## ASJC Scopus subject areas

- Electronic, Optical and Magnetic Materials
- Atomic and Molecular Physics, and Optics
- Physical and Theoretical Chemistry
- Electrical and Electronic Engineering