The differential theory of diffraction by arbitrary cross-section cylindrical objects is developed for the most general case of an incident field with a wave vector outside the cross-section plane of the object. The fast Fourier factorization technique recently developed for studying gratings is generalized to anisotropic and/or inhomogeneous media described in cylindrical coordinates; thus the Maxwell equations are reduced to a first-order differential set well suited for numerical computation. The resolution of the boundary-value problem, including an adapted S-matrix propagation algorithm, is explained in detail for the case of an isotropic medium. Numerical applications show the capabilities of the method for resolving complex diffraction problems. The method and its numerical implementation are validated through comparisons with the well-established multipole method.
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