Ultra-Compact Waveguide-Integrated TE-Mode Converters With High Mode Purity by Designing Ge/Si Patterns

In this letter, we propose ultra-compact TE-polarized even-to-odd mode converter designs by introducing Ge/Si patterns into silicon waveguide-integrated functional region. The Ge areas with continuous boundaries are determined by topology optimization that combines finite element method, geometric projection method, and method of moving asymptotes. Both two-dimensional (2D) and quasi-3D designs are presented. Simultaneous beam splitting and phase shifting are achieved in the functional region with only $1.0 \times 1.55\;{\rm{\mu }}{{\rm{m}}^2}$ area. Based on the 3D finite-difference time-domain simulations, the quasi-3D designs possess satisfactory mode purity (>0.99) at center wavelength 1550 nm, and the mode purity keeps higher than 0.92 within the wavelength range from 1500 to 1600 nm. Meanwhile, the forward transmission efficiency is shown higher than 0.89 within the operational bandwidth. Moreover, the robustness is demonstrated by considering the loss of Ge material and the geometric deviations. The proposed mode-order converters bring together advantages including wavelength footprint, high mode purity, low insertion loss, and large operational bandwidth.