Refractive index profile renormalization for a silicon waveguide bend

An index profile renormalization method is proposed to study the effective refraction index increase in a high-index contrast waveguide bend such as a silicon waveguide bend. This method transforms a waveguide bend to an equivalent straight waveguide (ESW). The simulation results show that the ESW method can calculate the effective refraction index increase in a three-dimensional (3D) bend, costing much less time than the traditional finite difference time domain method and the index profile renormalization (IPR) method developed for small radius cases. In addition, the field center shift is studied. The relationships are established between the effective refraction index increase and field center shift from the bend axis along the radial direction for estimations based on the approximated IPR method. These results can lead to great convenience in estimating the effective refraction index increase in 3D bend, which could be used in conditions requiring critical phase control.