Structures for a polarizer and methods of forming a structure for a polarizer. A polarizer includes a first waveguide core and a layer that is positioned adjacent to a side surface of the first waveguide core. The layer is composed of a first material having a permittivity with an imaginary part that ranges from 0 to about 15. A second waveguide core is positioned over the first waveguide core. The second waveguide core is composed of a second material that is different in composition from the first material.