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We propose a new method for mode conversion and coupling between an optical fiber and a sub-micrometer waveguide using a subwavelength grating (SWG) with a period less than the 1st order Bragg period. The coupler principle is based on gradual modification of the waveguide mode effective index by the SWG effect that at the same time frustrates diffraction and minimizes reflection loss. We demonstrate the proposed principle by two-dimensional Finite Difference Time Domain (FDTD) calculations of various SWG structures designed for the silicon-on-insulator (SOI) platform with a Si core thickness of 0.3 µm. We found a coupling loss as small as 0.9 dB for a 50 µm-long SWG device and low excess loss due to fiber misalignment, namely 0.07 dB for a transverse misalignment of ±1 µm, and 0.24 dB for an angular misalignment of ±2 degrees. Scaling of the SWG coupler length down to 10 µm is also reported on …