A method to obtain the electromagnetic scattering properties of step discontinuities between integrated optical waveguides is presented. The method involves a new generalized scattering-matrix concept, together with the generalized telegraph-equation formalism and the modal matching technique. Our model encloses the optical waveguides with perfectly conducting walls. Reflection, transmission, and radiation coefficients can be obtained for step discontinuities in monomode or multimode optical waveguides with arbitrary refractive index profile functions. Furthermore, the method can be applied to any cascaded set of multiple discontinuities between planar or channel optical waveguides. In this way, segmented optical waveguides, optical waveguide gratings, transitions, and tapers can be analyzed by modelization as multiple abrupt discontinuities. Excellent convergence and accuracy were observed finding the optical waveguide modes. Results on convergence and accuracy for effective indices, as well as for radiation losses for step discontinuities, are given and compared with those presented by other authors.