In this paper we extend the Fourier decomposition method to compute both propagation constants and the corresponding electromagnetic field distributions of guided waves in millimeter-wave and integrated optical structures. Our approach is based on field Fourier expansions of a pair of wave equations which have been derived to handle inhomogeneous mediums with diagonalized permittivity and permeability tensors. The tensors are represented either by a grid of homogeneous rectangles or by distribution functions defined over rectangular domains. Using the Fourier expansion, partial differential equations are converted to a matrix eigenvalue problem that correctly models this class of dielectric structures. Finally numerical results are presented for various channel waveguides and are compared with those of other literatures to validate our formulation.