We report on several new types of sub-wavelength grating (SWG) gradient index structures for efficient mode coupling in high index contrast slab waveguides. Using a SWG, an adiabatic transition is achieved at the interface between silicon-on-insulator waveguides of different geometries. The SWG transition region minimizes both fundamental mode mismatch loss and coupling to higher order modes. By creating the gradient effective index region in the direction of propagation, we demonstrate that efficient vertical mode transformation can be achieved between slab waveguides of different core thickness. The structures which we propose can be fabricated by a single etch step. Using 3D finite-difference time-domain simulations we study the loss, polarization dependence and the higher order mode excitation for two types (triangular and triangular-transverse) of SWG transition regions between silicon-on-insulator slab waveguides of different core thicknesses. We demonstrate two solutions to reduce the polarization dependent loss of these structures. Finally, we propose an implementation of SWG structures to reduce loss and higher order mode excitation between a slab waveguide and a phase array of an array waveguide grating (AWG). Compared to a conventional AWG, the loss is reduced from -1.4 dB to < -0.2 dB at the slab-array interface.