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Different material platforms, each offering a set of unique advantages, have been introduced for photonic integrated circuits. These platforms may be used in the same photonic chip to explore their advantages. Consequently, the in-plane crossing of dissimilar waveguides may be inevitable. In this paper, we investigate, for the first time to our knowledge, the crossing of silicon nitride (Si_3N_4) and silicon (Si) strip waveguides. Recently, the imaging property of the Maxwell’s fisheye lens has been exploited to design waveguide crossings. However, the refractive indices of Si_3N_4 and Si are different by about 1.45, so the crossing medium should have different refractive indices at its edges to minimize reflection from the interface of the waveguide and the crossing medium. We utilize quasi-conformal transformation optics to design a rectangular Maxwell’s fisheye lens as a crossing medium of Si_3N_4 and Si strip …