Single-Mode Limit and Bending Losses for Shallow Rib $\hbox{Si}_{3}\hbox{N}_{4}}$ Waveguides

The single-mode limit and bending losses for shallow rib waveguides are studied using the full vectorial film mode matching method. The maximum rib height for single-mode waveguides is found to be on the order of 10 nm for a rib width of 2 μm and a wavelength of 785 nm, with the exact value depending on the core thickness and the polarization. Bending losses are calculated as a function of several geometrical parameters, for both polarizations and for the fundamental and the first order modes. Bending losses decrease significantly with rib height for single-mode waveguides. For slightly larger rib heights, giving multimode waveguides, it is found that the bending losses for the first-order mode are several orders of magnitude larger than for the fundamental mode. Thus, a small bend can act as an excellent mode filter, making it possible to use higher ribs giving low bending losses for the fundamental mode, while maintaining the waveguide practically single-mode. For TM-polarization, leakage loss can be important and can cause bending losses to increase for larger rib heights (8-80 nm).