Electromagnetic scattering interaction between leaves and thin branches

Recently the effect of multiple-scattering among vegetation particles has been found important for accurately predicting the scattering behavior. Although volume fraction of vegetation particles is very low, smaller vegetation particles generally tend to accumulate around bigger ones. Therefore a single vegetation structure should often be considered as a locally dense medium where multiple scattering could be significant. Characterization of the exact solution including all high-order multiple scattering for a vegetation medium is nearly impossible. Approximate analytical solutions capable of accounting for near-field interactions and computational efficient are extremely useful for developing accurate scattering models vegetation. In this paper, simple formulations which include scattering interaction up to the second order are developed for thin dielectric disks and thin dielectric cylinders representing´ vegetation leaves and stems. In this iterative approach, Rayleigh-Gans approximation is used to calculate the internal electric field, or equivalently the induced polarization current, of the particles. The Rayleigh-Gans approximation has been proved to be a valid approach for scatterers having at least one dimension which is much smaller than a wavelength and having a lossy permittivity. First the polarization current induced by the incident wave at each point within a particle is expressed in terms of the incident wave and the polarizability tensor of the thin dielectric disk or cylinder having the same thickness or diameter as that of the particle. To calculate the second-order scatter field, the exact near fields from all nearby particles are calculated numerically and used as the excitation for the second-order induced polarization current