Structures for an optical power modulator and methods of fabricating a structure for an optical power modulator. A waveguide core includes a longitudinal axis, a first section, and a second section spaced from the first section along the longitudinal axis. An active layer includes a portion positioned along the longitudinal axis between the first section and the second section of the waveguide core. The active layer contains a material configured to have a first state with a first refractive index in response to an applied stimulus and a second state with a second refractive index different from the first refractive index.