Grating coupler with high efficiency

An optical coupling device includes a first waveguide layer, including a first semiconductor material, which is disposed over a dielectric substrate layer. A dielectric intermediate layer overlies the first waveguide layer. A second waveguide layer, which includes a different, second semiconductor material, is disposed over the dielectric intermediate layer and is patterned to define a waveguide. A first grating in the second waveguide layer diffracts light of a given wavelength from the waveguide into a specified diffraction order at a given coupling angle, whereby a first fraction of the light propagates out of the device while a second fraction of the light is diffracted into the intermediate dielectric layer in a conjugate diffraction order. A second grating in the first waveguide layer diffracts the second fraction of the light into a second diffraction order, propagating out of the device at the given coupling angle.