DIAGRAMMATIC TREATMENT OF LIGHT-SCATTERING BY A COLLECTION OF KERR PARTICLES

The standard diagram technique for impurity scattering is extended to the case in which the impurity potential linearly depends on the inten sity of the local field. A Bethe-Salpeter equation is derived which de scribes diffusion of light in a nonlinear random medium. In order to c ope diagrammatically with the nonlinear behavior of the impurities, on e has to introduce vertices at which four propagators meet. As for the case of linear impurities, configurational averages can be taken at t he diagrammatic level. However, the resulting dressed diagrams are of a much more complicated structure than usual. Furthermore, two diagram s that are topologically different from each other may represent the s ame expression. In decomposing the dressed diagrams, certain cuts can be performed only if other cuts are carried out first. This implies th at the Bethe-Salpeter equation cannot be derived by simply cutting all dressed diagrams into irreducible pieces. Instead, a more sophisticat ed procedure has to be followed. It is developed by performing a topol ogical classification of the dressed diagrams. In calculating the diag rams of the Bethe-Salpeter equation those with more than two vertices are discarded. This leads to three coupled nonlinear integral equation s which describe radiative transport in a dilute suspension of weakly nonlinear Kerr particles. The dimension of the particles is small as c ompared to the wavelength of the light. The solution of the integral e quations must satisfy a constraint that follows from energy conservati on. Analytical work and predictions on experiments will be presented i n a forthcoming paper.