No abstract

We present an exact and compact solution to plane-wave scattering from a dielectric cylinder enclosing N parallel eccentric dielectric. cylinders. The host cylinder and the cylindrical inclusions may be lossy and they are all considered infinitely long with circular cross sections. Free space is assumed for the exterior and harmonic time dependence is used throughout the analysis. The direction of incidence is normal to the axis of the host cylinder. The cases of TE and TM polarization are treated through use of scalar potentials which obey the homogeneous Helmholtz equation.The electromagnetic field of the incident and scattered waves as well as within the inhomogeneous cylindrical structure is expressed by infinite sums of scalar cylindrical wavefunctions. The unknown wave amplitudes (Le., the coefficients) of the multipolar expansions in the various regions of space are determined by application of the indirect mode-matching technique, which is based on the scalar Green theorem of the second kind and the translational addition theorem of scalar cylindrical wavefunctions. The orthogonality of the latter and the continuity of the fields across the cylindrical interfaces are inherent characteristics of the indirect mode-matching formulation. The analysis results in a set of infinite coupled linear equations for the unknown wave amplitudes, which is solved by truncation and matrix-inversion. Expressions for the backscattering and extinction cross sections per unit length are finally given. Noninvasive diagnostics of human limbs and quality control of multifiber cables could be considered as potential applications of this theory. The numerical investigation of this paper first deals with the problem of finding the appropriate truncation number. We provide specific information about the dependence of the truncation number on the size (i.e., the radius) and structure (i.e., number, radius and location of inclusions) of the composite scatterer, obtained through convergence checks of the backscattering cross section per unit length. Energy conservation and reciprocity checks are also done.Having a concise general theory and the associated computer code, allowed us to focus on the practical problem of detecting eventual geometrical asymmetries in a batch of glass fibers embedded into a' common cylindrical glass cladding. We therefore present numerical results to expose the effect of radial and azimuthal asymmetries on backscattering from single-core, double-core and triple-core fiber optic cables. The primary conclusion is that, in several cases, it is possible to detect geometrical imperfections of the cable through the effect on the transverse Sensing electromagnetic wave. TM polarization is more sensitive; the effect of asymmetries on backscattering is more pronounced for strongly guiding step-index fibers.