Multiple light scattering by polydispersions of randomly distributed, perfectly-aligned, infinite mie cylinders illuminated perpendicularly to their axes

Radiative Transfer in Half Spaces of Arbitrary Dimension

“…The new analytic form of H also permits additional exact simplified benchmark values involving Catalan's constant C = 0.9159655942.... To add to the previously reported result [24,49] H 2D (1, c = 1) = √ 2e While the same kernel can describe two different scattering processes in half spaces of differing dimensionalities, the solutions of the respective albedo problems are different because the rate density of initial collisions C 0 (z) is nonexponential in the case of correlation, and the relationship between the scalar collision rate and emerging distribution is less directly expressed via Laplace transforms. Complete details of solving half space albedo problems with correlation will be considered in a future paper [99].…”

“…Also, planar waveguides comprised of dielectric plates with controlled or random patterns of holes lead to 2D transport and have proven useful for studying engineered disorder [21]. Similarly, bundles of aligned dielectric fibers, such as clumps of hair or fur, can also be treated with a Flatland approach [22,23,24,25], where it is common to employ an approximate separable product of 1D and 2D solutions [26]. Reactor design also makes use of such 2D/1D decompositions [27].…”

“…Under the conditions of weak localization, the reflectance will be amplified in the backward direction by an enhancement factor η that reaches a maximum for normal incidence and c = 1. The maximal enhancement factors for 2D and 3D half spaces are [22,24]…”

Light propagation in a two-dimensional medium with large inhomogeneities

“…The medium can be thought as being composed of parallel fiberlike inhomogeneities [8,11]. A transverse size of the scatterers is supposed to be much greater than the light wavelength.…”

“…Of particular interest is the multiple light scattering in various lowdimensional disordered systems [8][9][10][11][12][13][14][15][16][17][18][19], including artificial two-dimensional media [20], nematic liquid crystals [21], and biological tissues [7,22].…”