The Mueller scattering matrix elements (Sij) and the cross sections for the scattering of an electromagnetic plane wave from two infinitely long, parallel, circular cylinders at oblique incidence are derived. Each cylinder can be of arbitrary materials (any refractive index). The incident wave can be in any polarization state. To find the scattering coefficients needed for calculating Sij and the cross sections, the multiple scatterings are taken into account for all orders. The formal solutions of the scalar wave equation are obtained for the three regions concerned (the region outside the two cylinders and the region inside each cylinder), and the scattering coefficients are found by satisfying the boundary conditions. The scattering coefficients for some special cases (normal incidence, small radii, perfectly conducting cylinders, and a single cylinder) are given and discussed. The results for these special cases are compared (numerically or analytically) with those obtained in other published works. To our knowledge, this is the first comprehensive study of the two-cylinder problem. Applications of this formalism, including calculations of Sij and the cross sections, will be presented in part II of this series [ J. Opt. Soc. Am. A 5, 1097 ( 1988)].
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