Influence of positional correlations on the propagation of waves in a complex medium with polydisperse resonant scatterers

We present experimental results on a model system for studying wave propagation in a complex medium exhibiting low frequency resonances. These experiments enable us to investigate a fundamental question that is relevant for many materials, such as metamaterials, where low-frequency scattering resonances strongly influence the effective medium properties. This question concerns the effect of correlations in the positions of the scatterers on the coupling between their resonances, and hence on wave transport through the medium. To examine this question experimentally, we measure the effective medium wave number of acoustic waves in a sample made of bubbles embedded in an elastic matrix over a frequency range that includes the resonance frequency of the bubbles. The effective medium is highly dispersive, showing peaks in the attenuation and the phase velocity as functions of the frequency, which cannot be accurately described using the Independent Scattering Approximation (ISA). This discrepancy may be explained by the effects of the positional correlations of the scatterers, which we show to be dependent on the size of the scatterers. We propose a self-consistent approach for taking this "polydisperse correlation" into account and show that our model better describes the experimental results than the ISA

On the Derivation of Vector Radiative Transfer Equation for Polarized Radiative Transport in Graded Index Media

Light transport in graded index media follows a curved trajectory determined by the Fermat's principle. Besides the effect of variation of the refractive index on the transport of radiative intensity, the curved ray trajectory will induce geometrical effects on the transport of polarization ellipse. This paper presents a complete derivation of vector radiative transfer equation for polarized radiation transport in absorption, emission and scattering graded index media. The derivation is based on the analysis of the conserved quantities for polarized light transport along curved trajectory and a novel approach. The obtained transfer equation can be considered as a generalization of the classic vector radiative transfer equation that is only valid for uniform refractive index media. Several variant forms of the transport equation are also presented, which include the form for Stokes parameters defined with a fixed reference and the Eulerian forms in the ray coordinate and in several common orthogonal coordinate systems.Comment: This paper has been submitted to JQSR

Single-Scattering Optical Tomography

We consider the problem of optical tomographic imaging in the mesoscopic regime where the photon mean free path is of order of the system size. Within the accuracy of the single-scattering approximation to the radiative transport equation, we show that it is possible to recover the extinction coefficient of an inhomogeneous medium from angularly-resolved measurements. Applications to biomedical imaging are described and illustrated with numerical simulations.Comment: Finalized and submitted to PR