Abstract: In one embodiment, a coupler includes a glass tube having a refractive index n3 and a passageway, a first optical waveguide and a second optical waveguide positioned within the passageway, each of the first optical waveguide and the second optical waveguide comprising a core surrounded by a cladding. The glass tube further includes a tapered region having a taper length. A coupling region is present between the first optical waveguide and the second optical waveguide within the tapered region. A refractive index of the cladding is less than a refractive index of the core, and a lowest refractive index of the cladding of the first optical waveguide and the second optical waveguide is n2. Additionally, n3 is lower than n2 such that a value of ?2-3 is 0.07%??2-3?0.125, where ?2-3 equals (n22?n32)/2n22.