Electromagnetic response of a random half-space of Mie scatterers within the effective-field approximation and the determination of the effective optical coefficients

We calculate the coherent reflectance of light from a half-space with randomly located spherical particles using the effective field approximation to solve the integral equation obeyed by the scattered fields. We obtain the effective refractive index and the coherent reflection coefficient to first order in the density of particles. Then we use basic principles of continuum electrodynamics to derive expressions for the effective permittivity and permeability tensors of the half-space. The results are not restricted to particles of radius small compared to the wavelength of the incident radiation. It is shown that an effective magnetic permeability arises, even in the case when the particles are non-magnetic. The present work provides a standard framework to pursue higher order approximations for denser media.