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A simple light-beam spot-size converter (SSC) using a microscale graded-index (GRIN)-slab tip with a hemicylindrical endface for efficient coupling between a single-mode fiber and a fine-core waveguide is reported. Numerical examples based on the finite-difference time-domain (FDTD) method have shown that the tip made of a-SiOx:H is capable of coupling a narrow field, 0.5 μm in radius at a wavelength of 1.55 μm, to a 5.3-μm radius standard single-mode fiber with a coupling loss as low as 0.07 dB. A micro GRIN slab with an index difference of as much as 34% was successfully fabricated. It has been confirmed experimentally that a GRIN slab with a hemicylindrical endface of 27-μm radii, a thickness of 33 μm, and a length of 35 μm, is capable of converting a spot radius of a single-mode fiber (5.3 μm) into a spot radius of 1.1 μm at a wavelength of 1.55 μm.