In an example, a coupled system includes a first waveguide, at least one second waveguide, and an interposer. The first waveguide has a first refractive index n1 and a tapered end. The at least one second waveguide each has a second refractive index n2. The interposer includes a third waveguide having a third refractive index n3 and a coupler portion, where n1>n2>n3. The tapered end of the first waveguide is adiabatically coupled to a coupler portion of one of the at least one second waveguide. A tapered end of one of the at least one second waveguide is adiabatically coupled to the coupler portion of the third waveguide of the interposer. The coupled system is configured to adiabatically couple light between the first waveguide and the at least one second waveguide and between the at least one second waveguide and the third waveguide.