Structures including an edge coupler and methods of fabricating a structure including an edge coupler. The structure includes a waveguide core region on a first dielectric layer, and a second dielectric layer on the waveguide core region and the first dielectric layer. The waveguide core region has a tapered section with an end surface that terminates adjacent to an edge of the first dielectric layer. The second dielectric layer includes a first trench and a second trench that are each positioned adjacent to the tapered section of the waveguide core region.