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A new approach of the sinusoidal bend Y-junction optical waveguides analysis using the method of lines (MOL) has been developed. In this paper, the shape of the Y-junction is approximated by cascading straight waveguide structure or segment. The segment may have different width and length depending on the refractive index profile of the Y-junction. The loss of the Y-junction is calculated by overlapping the propagated field with the fundamental mode of the structure. The result was compared with commercial software and it was found that the two results give similar answer.