Measurements of diffuse backscattering Mueller matrices of turbid media

We report on the development of a method that records spatially dependent intensity patterns of polarized light that arise from illuminating a turbid media with a polarized laser beam and being diffusely backscattered. Our technique employs polarized light from a He-Ne laser () which is focused onto the surface of the scattering medium. A surface area of approximately 2×2 cm centered on the light input point is imaged through polarization analysis optics onto a CCD camera. The Mueller matrix is reconstructed by 49 intensity measurements with various orientations of polarizer and analyzer. The measured Mueller matrix of polystyrene spheres was compared with the theory result of incoherent scattering of light by spheres. The experimental and theory results are in excellent agreement. It appears that the azimuthal patterns of the Mueller matrix are determined by the symmetry of the turbid media.     

Polarization characteristics of backscattering of turbid media based on Mueller matrix

Mueller matrix is one approach to characterizing optical polarization of the turbid media. We have simulated the two-dimensional images of Mueller matrix based on single-scattering approximation model and implemented experiments to verify the simulations. By comparing the experimental results to the theoretical simulations, we have obtained some conclusions. When the particle size is smaller than the wavelength, the linearly polarized light propagating through the turbid media of Rayleigh scatterers has better polarization-maintaining ability. Whereas when the particle size is larger than the wavelength, the circularly polarized light propagating through the turbid media of Mie scatterers has better polarization-maintaining ability. Moreover, the radial dependence of the element patterns becomes weak as the transport mean free path decreases. This study can help us understand to the fundamental principle of optical polarization.     

Correlated coherent states and the problem of wave propagation in randomly inhomogeneous media

Radiophysics and Quantum Electronics -     

Approximate calculation of coherent backscattering for semi-infinite discrete random media

We describe an approximate method for the calculation of all characteristics of coherent backscattering for a homogeneous, semi-infinite particulate medium. The method allows one to transform a system of integral equations describing coherent backscattering exactly into a system of linear algebraic equations affording an efficient numerical solution. Comparisons of approximate theoretical results with experimental data as well as with benchmark numerical results for a medium composed of nonabsorbing Rayleigh scatterers have shown that the method can be expected to give a good accuracy.     

Identifying coherent structures in nonlinear wave propagation

Nonlinear wave phenomena are often characterized by the appearance of "solitary wave coherent structures" traveling at speeds determined by their amplitudes and morphologies. Assuming that time intervals exist in which these structures are essentially noninteracting, a method for identifying the number of independent features and their respective speeds is proposed and developed. The method is illustrated with a variety of increasingly realistic specific applications, beginning with a simple nonlinear but analytically tractable Gaussian model, continuing with (numerically generated) data describing multisoliton solutions to the Korteweg-de Vries equation, and concluding with (numerical) data from a realistic simulation of nonlinear wave interactions in plasma turbulence. These studies reveal both strengths and limitations of the method in its present incarnation and suggest topics for future investigations.     

Estimation of light transport parameters in biological media using coherent backscattering

The suitability of using the angular peak shape of the coherent backscattered light for estimating the light transport parameters of biological media has been investigated. Milk and methylene blue doped milk were used as tissue phantoms for the measurements carried out with a He-Ne laser (632.8 nm). Results indicate that while the technique accurately estimates the transport length, it can determine the absorption coefficient only when the absorption is moderately high (α>1 cm⁻¹) for the long transport lengths typical of tissues. Further, the possibility of determining the anisotropy factor by estimating the single scattering contribution to the diffuse background is examined.     

Electromagnetic wave propagation in random media

The propagation of a narrow frequency band beam of electromagnetic waves in a medium with randomly varying index of refraction is considered. A novel formulation of the governing equation is proposed. An equation for the average Green function (or transition probability) can then be derived. A Fokker-Planck type equation is contained as a limiting case. The results are readily generalized to include the features of the random coupling model and it is argued that the present problem is particularly suited for an analysis of this type.     

Anomalous wave propagation in quasiisotropic media

Based on boundary conditions and dispersion relations, the anomalous propagation of waves incident from regular isotropic media into quasiisotropic media is investigated. It is found that the anomalous negative refraction, anomalous total reflection and oblique total transmission can occur in the interface associated with quasiisotropic media. The Brewster angles of E- and H-polarized waves in quasiisotropic media are also discussed. It is shown that the propagation properties of waves in quasiisotropic media are significantly different from those in isotropic and anisotropic media.     

Modeling of wave propagation in inhomogeneous media

We present a methodology providing a new perspective on modeling and inversion of wave propagation satisfying time-reversal invariance and reciprocity in generally inhomogeneous media. The approach relies on a representation theorem of the wave equation to express the Green function between points in the interior as an integral over the response in those points due to sources on a surface surrounding the medium. Following a predictable initial computational effort, Green's functions between arbitrary points in the medium can be computed as needed using a simple cross-correlation algorithm.     

Small amplitude wave propagation in stratified media

Four mutually connected first order linear differential equations for a system of two waves — constituting a set of mathematical models are developed. Small amplitude wave propagation through stratified media have been studied using the mathematical models. Limiting wave solutions are identified as WKB solutions.One of the authors (M.Khan) acknowledges the support of the University Grants Commission (India).     

Spectrum of coherent backscattering of light by two atoms

The inelastic spectrum of coherent backscattering of laser light by two atoms was theoretically studied. For an intense laser field, there are frequency domains of either constructive or destructive self-interference of inelastically scattered photons. The emergent spectral features were interpreted by considering coherent backscattering as a pump-probe experiment. The text was submitted by the author in English.     

Visualization of scattering media upon backscattering of a linearly polarized nonmonochromatic light

The method of polarization visualization of multiply scattering macroinhomogeneous media, based on analysis of the spatial distributions of polarization characteristics of a linearly polarized radiation backscattered from a medium, is discussed. The effect of optical characteristics of the medium and the scattering geometry on the quality of the images obtained in the case of visualization of an absorbing heterogeneity immersed into a multiply scattering medium is considered. The comparative analysis of the quality of formed images was performed with the use of different polarization characteristics of the backscattered radiation as a visualization parameter. The theoretical interpretation of the obtained experimental results is given within the framework of the phenomenological approach based on the concept of the distribution of the effective optical paths of partial components of the scattered optical field. To calculate the probability density of the effective optical paths, the statistical simulation method was used.     

Partially coherent Airy beam and its propagation in turbulent media

The properties of partially coherent Airy beam propagating in turbulent media are investigated. Firstly the variations in the intensity profile and the location of the Airy beam peak with respect to dislocation and width parameters are examined. On the source plane, it is shown that there is a threshold value of the dislocation parameter which determines whether the beam peak will lie on the negative or positive side of the axis. The changes in source beam power and source beam size with respect to dislocation and width parameters are also examined. Then analysis is made for partially coherent Airy beam propagating in turbulence against variations in propagation distance, dislocation and width parameters, structure constant and partial coherence. It is found that the peak of the Airy beam will always shift to the right for increasing propagation distance. But this shift will become less as the dislocation and width parameters are increased. Finally it is shown that higher levels of turbulence and partial coherence will lead to more spreading and shift the beam peak more toward the on-axis position.     

Imaging through turbid media by polarized light

A theoretical approach to the calculation of the image of an inhomogeneity in transillumination of tissue-like media using polarized radiation is developed in the approximation of the basic polarization modes. The method is based on the solution of the nonstationary transfer equation in the Fokker-Planck approximation. An expression for the edge spread function of the image of a totally absorbing half-plane is derived. A generalization to the image profile of inhomogeneity that represents a finite-width stripe is presented. The spatial resolution (sharpness) and contrast of image are analyzed at various time intervals of detection. The image parameters are compared for the polarization-difference technique and imaging in unpolarized light. It is demonstrated that the imaging using the difference of linear polarizations is similar to the imaging using the pulsed unpolarized radiation with a detection interval of about z/2c (z is the thickness of the sample and c is the velocity of light). The results are in agreement with the experimental data on the differential polarization transillumination of tissue-like media.