Features in the speckle correlations of light scattered from volume-disordered dielectric media

A diagrammatic perturbation theory approach, based on a scalar wave treatment, is used to study the scattering of light of frequency \ensuremath{\omega} from a volume disordered dielectric medium. The dielectric medium is described by a position-dependent dielectric constant of the form $\ensuremath{\epsilon}(\stackrel{\ensuremath{\rightarrow}}{r})=\ensuremath{\epsilon}(\ensuremath{\omega})+\ensuremath{\delta}\ensuremath{\epsilon}(\stackrel{\ensuremath{\rightarrow}}{r}),$ where $\ensuremath{\epsilon}(\ensuremath{\omega})$ does not depend on $\stackrel{\ensuremath{\rightarrow}}{r},$ and $\ensuremath{\delta}\ensuremath{\epsilon}(\stackrel{\ensuremath{\rightarrow}}{r})$ is a zero-mean Gaussian random process defined by $〈\ensuremath{\delta}\ensuremath{\epsilon}(\stackrel{\ensuremath{\rightarrow}}{r})\ensuremath{\delta}\ensuremath{\epsilon}({r}^{\ensuremath{'}})〉={\ensuremath{\sigma}}^{2}\mathrm{exp}(\ensuremath{-}|\stackrel{\ensuremath{\rightarrow}}{r}\ensuremath{-}{r}^{\ensuremath{'}}{|}^{2}{/a}^{2}),$ where the angle brackets denote an average over the ensemble of realizations of $\ensuremath{\delta}\ensuremath{\epsilon}(\stackrel{\ensuremath{\rightarrow}}{r}),$ a is the correlation length of the disorder, and $\ensuremath{\sigma}$ is the root mean square deviation of the dielectric constant from its average value $\ensuremath{\epsilon}(\ensuremath{\omega}).$ The speckle correlation function $C(\stackrel{\ensuremath{\rightarrow}}{q},\stackrel{\ensuremath{\rightarrow}}{k}|{q}^{\ensuremath{'}},{k}^{\ensuremath{'}})=〈[I(\stackrel{\ensuremath{\rightarrow}}{q}|\stackrel{\ensuremath{\rightarrow}}{k})\ensuremath{-}〈I(\stackrel{\ensuremath{\rightarrow}}{q}|\stackrel{\ensuremath{\rightarrow}}{k})〉][I({q}^{\ensuremath{'}}|{k}^{\ensuremath{'}})\ensuremath{-}〈I({q}^{\ensuremath{'}}|{k}^{\ensuremath{'}})]〉$ where $I(\stackrel{\ensuremath{\rightarrow}}{q}|\stackrel{\ensuremath{\rightarrow}}{k})$ is proportional to the differential-scattering coefficient for the scattering of light of incident wave vector $\stackrel{\ensuremath{\rightarrow}}{k}$ into light of wave vector $\stackrel{\ensuremath{\rightarrow}}{q}$ is computed. In these calculations the contributions associated with both ladder and maximally crossed diagrams are summed in a Feynman diagram treatment of the speckle correlator, in the approximation that only s-wave-scattering terms are retained. Results are presented for the differential-scattering coefficient of light scattered from the disordered medium, which displays the phenomenon of enhanced backscattering, and for the correlator C in the approximation where ${C=C}^{(1)}{+C}^{(10)}{+C}^{(1.5)}.$ The contribution ${C}^{(1)}$ is proportional to $\ensuremath{\delta}(\stackrel{\ensuremath{\rightarrow}}{q}\ensuremath{-}\stackrel{\ensuremath{\rightarrow}}{k}\ensuremath{-}{q}^{\ensuremath{'}}+{k}^{\ensuremath{'}})$ and describes the memory and time-reversed memory effects. ${C}^{(10)}$ is proportional to $\ensuremath{\delta}(\stackrel{\ensuremath{\rightarrow}}{q}\ensuremath{-}\stackrel{\ensuremath{\rightarrow}}{k}+{q}^{\ensuremath{'}}\ensuremath{-}{k}^{\ensuremath{'}}),$ while ${C}^{(1.5)}$ is unrestricted in its dependence on $\stackrel{\ensuremath{\rightarrow}}{q},\stackrel{\ensuremath{\rightarrow}}{k},{q}^{\ensuremath{'}},{k}^{\ensuremath{'}}.$ The latter two contributions have recently been treated in the scattering of light from randomly rough surfaces, but have not been previously treated in the scattering of light by volume disordered media. A number of peaks associated with resonant processes are observed in ${C}^{(1.5)}$ considered as a function of the wave vectors of the incident and scattered light.