A low loss coupling arrangement between a slab/strip waveguide and a rib waveguide in an optical waveguiding structure formed on a silicon-on-insulator (SOI) platform utilizes tapered sections at the input and/or output of the rib waveguide to reduce loss. Optical reflections are reduced by using silicon tapers (either vertical tapers, horizontal tapers, or two-dimensional tapers) that gradually transition the effective index seen by an optical signal propagating along the slab/strip waveguide and subsequently into and out of the rib waveguide. Loss can be further reduced by using adiabatically contoured silicon regions at the input and output of the rib waveguide to reduce mode mismatch between the slab/strip waveguide and rib waveguide. In a preferred embodiment, concatenated tapered and adiabatic sections can be used to provide for reduced optical reflection loss and reduced optical mode mismatch.