Structures including an edge coupler and methods of fabricating a structure including an edge coupler. The structure includes a dielectric layer including an edge, a waveguide core region on the dielectric layer, and multiple segments on the dielectric layer. The waveguide core region has an end surface, and the waveguide core region is lengthwise tapered toward the end surface. The segments are positioned between the waveguide core region and the edge of the dielectric layer. A waveguide core has a section positioned over the waveguide core region in an overlapping arrangement. The waveguide core has an end surface, and the section of the waveguide core is lengthwise tapered toward the end surface.