Design of Random and Stationary Sources and Media for Structuring Light on Propagation and Scattering

The dissertation incorporates a series of investigations relating to the design of coherence states for stationary, random sources, and correlation functions of spatially random, stationary media, for modulation of far fields radiated or scattered from them to the far zone, and, hence, for structuring of any observable statistical properties. In particular, we reveal how the coherence states of sources affect their far-zone radiated properties, including the spectral density, the scintillation index, and the intensity correlation function. Furthermore, we also present results that address how the spatial structuring of the refractive index correlation function of a three-dimensional (3D) medium influences the far-zone scattered spectral density of light. In so doing we have developed several novel, bona fide mathematical models for random stationary sources and media. The first part of this thesis is dedicated to modeling of stationary 3D media. Our major contributions include modeling of media that produce a strongly peaked intensity profile off the scattering axis. Further, by extending the 2D laser coherent modes to those of a 3D medium, the Deterministic Mode Representation (DMR) method is introduced based on the eigenmode expansion of a broad class of stationary random media. This method is envisioned to find applications to fine modeling and matrix-based reconstruction of correlations of spatially random media. The second part of this thesis attributes to modeling of several novel classes of beam-like, partially coherent, stationary sources of Schell class, including Lorentz-correlated, Fractional Multi-Gaussian-correlated, and crescent-like sources. Specifically, we investigate, both analytically and experimentally, the evolution of beams radiated from the above-mentioned sources passing through the ABCD optical systems and atmospheric turbulence. The detailed synthesis procedures of these sources with the help of the Spatial Light Modulators (SLM) are outlined. In addition, we also achieve experimental realization of the Im-Bessel-correlated beam via superposition of its coherent modes by using an SLM. These results are of importance for beam shaping, in Free Space Optical Communications and LIDAR sensing. The third and the fourth parts of the thesis are concerned with two important natural media - atmospheric turbulence and soft biological tissues - being particular examples of the refractive index correlation functions that can influence the light statistics in a certain, well-defined manner. The third part of the thesis discusses sensing of correlation properties of the boundary-layer, non-classic atmospheric turbulence by laser light, in a single pass. In particular, a robust method is proposed to assess the anisotropy information of turbulence by using the two-point intensity correlation function of the optical beam obtained from experiments. The possibilities for sensing of non-classic, anisotropic turbulence via the Enhanced-Back Scatter (EBS) mechanism of collimated laser light in double passage mono-static link with a retro-reflector are also experimentally examined. The final portion of the thesis includes in-depth investigations of laser light interaction with soft biological tissues, modeled as turbulent-like, stationary media. Since such media have been little explored so far for light propagation problems we first examine the important issue of a threshold depth at which the transition from weak to strong optical turbulence occurs, by examining the scintillation index of a plane wave. We also study the scintillation index of a spherical wave and of a Gaussian beam. Furthermore, an analytical method is introduced to solve both direct and inverse problems of weak scattering of light from a soft biological tissue. The results are of importance to optical sensing techniques for soft tissue diagnostics