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A novel constant-width variable-index transition has been developed that allows for both low-loss fiber-waveguide coupling and efficient device operation on the same lithium niobate chip. A thick titanium film (750 Å) is utilized at the input end of the transition, resulting in large and tight mode confinement. At the output of the transition, the waveguide is designed to be close to cutoff by decreasing the Ti thickness to 375 Å. This causes the mode size to increase so that mode coupling loss between a small mode-size waveguide ( intensity full width of 4.25 μm by full depth of 2.80 μm) and a single-mode fiber ( intensity full width of 7 μm) is reduced by approximately 1.4 dB per interface at 1.3-μm wavelength.