Many integrated optical-based subsystems incorporate optical guided-wave devices and connecting optical waveguides with two-dimensional confinement and a high index contrast. The modes present in such waveguides and devices are not purely of the TE or TM type but hybrid in nature, with all the six components of the electric and magnetic fields being present. Over the last three decades, many semi-analytical and numerical approaches have been developed to study the modes in optical waveguide structures: however, to characterize polarization issues in such systems, a fully vectorial approach is necessary. In that respect the fully vectorial H-field based finite element method (FEM)  is one of the most rigorous and versatile of the approaches. The main advantage of the FEM over many other methods is its more accurate representation of the waveguide cross-section. In an optoelectronic system, when modes are hybrid in nature, polarization conversion can take place in the optical system, either unintentionally or deliberately at different waveguide junctions. The least squares boundary residual method , which is a fully vectorial and rigorously convergent method, is also used here to characterize optoelectronic systems. The beam propagation method (BPM) is field evolutionary in its approach and a versatile method for the characterization of a z-dependent guided-wave structure. A numerically efficient full-vectorial FEM-based BPM  has been developed to characterize z-dependent guided-wave devices. Results for the polarization cross-talk in such systems will be presented, along with their various minimization approaches. Results will also be presented for the design optimization of various compact polarization rotators using cascaded sections with or without a slanted side wall and also with curved waveguide sections.