Vector solution for the mean electromagnetic fields in a layer of random particles

The mean electromagnetic fields are found in a layer of randomly oriented particles lying over a half space. A matrix-dyadic formulation of Maxwell's equations is employed in conjunction with the Foldy-Lax approximation to obtain equations for the mean fields. A two variable perturbation procedure, valid in the limit of small fractional volume, is then used to derive uncoupled equations for the slowly varying amplitudes of the mean wave. These equations are solved to obtain explicit expressions for the mean electromagnetic fields in the slab region in the general case of arbitrarily oriented particles and arbitrary polarization of the incident radiation. Numerical examples are given for the application to remote sensing of vegetation.