A new concatenated configuration of optical fibers is proposed to improve misalignment tolerance and working distance in a free-space optical interconnection. The structure is composed of three segments: a thermally expanded core fiber, a coreless silica fiber, and a claddingless graded-index fiber. A numerical analysis for the design of each fiber segment is performed completely, and the device characteristics are experimentally evaluated in terms of the tolerances for a 1-dB coupling-loss increment against longitudinal, transverse, and angular misalignments.