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A subwavelength gratings (SWG) assisted directional coupler (DC) is proposed to work as beam splitter (BS) for 850 nm chip-based optical coherence tomography (OCT). The bandwidth of the SWG assisted DC is maximized to 110 nm by selecting appropriate SWG geometries including its duty cycle and period. The axial point spread functions (PSFs) derived from the BS transmittances proves the optimized bandwidth is broad enough to support axial resolution higher than $4 \;\mu m$. Meanwhile, the SWG period can be manipulated to match the center wavelength between BS and light source so that the wavelength mismatching induced resolution degradation is effectively mitigated. Furthermore, a statistical analysis is performed to demonstrate the SWG assisted DC is a high fabrication-tolerant device in terms of axial resolution, even the SWG geometries suffer from a fabrication jitter in 20 nm variance.