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The evanescent coupling from a photonic crystal resonator to a micron-thick optical fiber is investigated in detail by using a three-dimensional finite-difference time-domain (3D-FDTD) method. Properly designed photonic crystal cavity and taper structures are proposed, and optimal operating conditions are found to enhance the coupling strength while suppressing other cavity losses including the coupling to the slab propagating mode and to the higher-order fiber mode. In simulation, the coupling into the fundamental fiber mode is discriminated from other cavity losses by spatial and parity filtering of the FDTD results. The coupling efficiency of more than 80% into the fundamental fiber mode together with a total Q factor of 5200 is achieved for the fiber diameter of 1.0 μm and the air gap of 200 nm between the fiber and the cavity.