Matrix analysis for back reflection and mode conversion in silicon waveguide bend structure

Abstract

Waveguide bend structure is a main building block in many silicon photonic devices such as in ring resonators, S-bend attenuators, arrayed waveguide filters and optical delay lines in addition to the use in routing the optical signal. The curvature structure of the bend may induce back reflection at the interfaces and mode conversion effects. In this work, a scattering-matrix model is suggested to account for these effects in the case of coexisting different polarizations (i.e., TE and TM modes) that is unavoidable when the TM mode is of interest due to the lower cut-off of the TE mode. The waveguide used in the analysis is an inverted ridge, where the silicon core is 500 nm in width and 220 nm in height. The silicon core is surrounded by silicon dioxide from all sides except being exposed to air at the top. The analysis is focused on the C-band but can be extended to other spectral regions. Finite difference time domain simulations are carried out showing back refection levels in the order of −50 dB and mode cross coupling in the order of −55 dB. The presented matrix model shows good agreement and can be used to analyze complex photonic circuits when numeral simulations is of a high computational burden.