Repeatable optical waveguide interconnection including an index matching elastomeric solid layer providing core and cladding index of refraction matching and related methods

A repeatable optical waveguide interconnection may include first and second optical waveguides having respective first and second end faces. Each of the first and second optical waveguides may include a core having a core index of refraction, and a cladding surrounding the core and having a cladding index of refraction different than the core index of refraction. The interconnection may further include a first index matching elastomeric solid layer having a proximal face coupled to the first end face, and a distal face opposite the proximal face to be repeatably optically coupled to the second end face. The first index matching elastomeric solid layer may have an index of refraction profile matching an index of refraction of the core and the cladding.