A single-mode optical waveguide with a core, surrounded by a cladding consisting of an inner soft layer and an outer harder layer is described. The outer layer has a grating structure on its inner surface, whose spatial frequency is the same as that of the guided mode. The thickness of the inner cladding is sufficient to keep the grating outside the mode field in undeformed regions of the waveguide, so that normally no out-coupling of the light results. Connections are made by crossing two such waveguides at an angle and pressing them together. This results in deformation of the two waveguides such that the gratings are brought into proximity with the cores. Light is coupled out of one waveguide and into the other in the deformed region, resulting in a self-aligning optical connection. The out-coupled light propagates normal to the waveguide axis, so errors in the crossing angle cause little change in efficiency. Because the cladding system is sufficiently resilient to recover after deformation, the connection is remakeable.