Effective Propagation Constant of Fibrous Media Containing Parallel Fibers in the Dependent Scattering Regime

The radiative properties of a particulate medium are strongly influenced by the particle concentration and wavelength of the incident radiation. Independent scattering prevails at very low particle concentration, such that the spacing between the particles is much larger than the particle size and incident wavelength. As the particle spacing decreases, near-field multiple scattering and far-field interference of the scattered waves become increasingly pronounced. These dependent scattering effects cause the extinction efficiency and the phase velocity of electromagnetic waves, which are related to the effective propagation constant of the medium, to deviate from those in the independent scattering regime. This paper presents the theoretical formulation of the effective propagation constant of a nondissipative medium containing closely spaced parallel fibers. The dispersion relations for oblique incidence are derived for a transverse magnetic and a transverse electric mode incident wave. Numerical results for Rayleigh limit fibers are presented to illustrate the effect of fiber volume fraction on the propagation constant and extinction efficiency of the medium.