An apparatus for converting fiber mode to waveguide mode. The apparatus includes a silicon substrate member and a dielectric member having an elongated body. Part of the elongated body from a back end overlies the silicon substrate member and remaining part of the elongated body up to a front end is separated from the silicon substrate member by a second dielectric material at an under region. The apparatus also includes a waveguide including a segment from the back end to a tail end formed on the dielectric member at least partially overlying the remaining part of the elongated body. The segment is buried in a cladding overlying entirely the dielectric member. The cladding has a refractive index that is less than the waveguide but includes an index-graded section with decreasing index that is formed at least over the segment from the tail end toward the back end.