Structures including an edge coupler and methods of forming a structure including an edge coupler. The structure includes a waveguide core over a dielectric layer and a back-end-of-line stack over the dielectric layer and the waveguide core. The back-end-of-line stack includes a side edge and a truncated layer that is overlapped with a tapered section of the waveguide core. The truncated layer has a first end surface adjacent to the side edge and a second end surface above the tapered section of the waveguide core. The truncated layer is tapered from the first end surface to the second end surface.