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This paper presents a powerful technique to treat the problem of wave propagation along weakly guiding single-mode optical waveguides. The shape as well as the 3-D index variation of the guide may be quite arbitrary as along as the weakly guiding character is preserved. The technique is based on the solution of a scalar-wave equation by the forward-marching fast Fourier transform (FFT) method. Excellent agreements were obtained, with known solutions, for various optical guiding structures. We have also demonstrated the capability of this technique to treat other exotic single-mode structures.