A method for fabricating three-dimensional optical waveguides is disclosed. In this method, a single crystal semiconductor layer is grown upon an insulator which has an index of refraction lower than the semiconductor. The semiconductor layer is deposited to a thickness which provides confinement of light propagating in the semiconductor layer in the vertical direction. An effective larger index of refraction over a cross-sectional region of the semiconductor layer is then formed to provide confinement of light in the lateral direction. In the preferred method, the growth of single crystal semiconductor upon the insulator is achieved by a vapor-phase lateral epitaxial overgrowth technique.Devices fabricated according to the method are also disclosed.