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Comprehensive design and analysis of optical coupling between silicon nanophotonic waveguide and standard single-mode fiber is presented. The coupling structure employs an integrated asymmetric graded refractive index (GRIN) lens deposited at the end of the tapered waveguide, and the GRIN lens has an optimized refractive index profile with a super high numerical aperture for aberration-free subwavelength focusing/collimating. The influence of end-facet reflection of the GRIN lens on the coupling efficiency is investigated. The optimized GRIN lens with a proper antireflection coating shows a coupling efficiency of ~90% between a 300-nm-thick silicon nanophotonic waveguide and a standard single-mode fiber. A 3-D modeling and simulation of the GRIN lens is carried out. The influences of fiber displacement and angular misalignment on the coupling efficiency are analyzed. The overall systematic design and analysis indicate that this integrated GRIN-lens-based optical coupler offers a compact and efficient solution for nanophotonic waveguide coupling with a good alignment tolerance.