LiNbO3 waveguides with Si overlays are emerging as a basic building block for a variety of integrated-optic components, including modulators, high-efficiency gratings, and narrowband WDM filters. However, the development and optimization of these devices are, in large part, hindered by the lack of understanding of the specifics of the Si-on-LiNbO3 structure which appear to differ dramatically from those of the Si and LiNbO3 waveguides, considered separately. In this work, we provide a specific insight into the waveguiding properties of vertically stacked Si-on-LiNbO3 waveguides. In particular, we present a detailed theoretical analysis of the effect of the Si film on the modal characteristics (propagation constant and field distribution) of the structure. The vectorial finite element method (VFEM) is used to numerically investigate a step-index and graded-index single-mode channel waveguide in LiNbO3, with a Si or Si/SiO2 multimode overlay. We show that for {\sim}70% of all Si thicknesses, in the range from 0 to 1.6 \mum, the highest order normal mode of the entire structure has more than 99.9% of the total energy confined in the LiNbO3 region, i.e., beneath the Si overlay. This fact is quite intriguing given the fact a planar Si layer of submicron thickness on bulk LiNbO3 is already multimoded. Furthermore, we show that the effective mode index of the structure is considerably modified compared to that of the LiNbO3 waveguide while the propagation loss is, on the other hand, practically unaffected ({\sim}0.3 dB/cm) even in the presence of the lossy Si film, as confirmed by our previous experimental results. Evidently, large modulation of the effective index and low-loss propagation provide an ideal combination of properties suitable for the fabrication of high-reflectance corrugated waveguide gratings, essential for a number of practical devices, in particular, WDM filters.


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