Optimized 3-D Simulation Method for Modeling Out-of-Plane Radiation in Silicon Photonic Integrated Circuits

We present an accurate and fast 3-D simulation scheme for out-of-plane grating couplers, based on 2-D rigorous [finite difference time domain (FDTD)] grating simulations, the effective index method, and the Rayleigh-Sommerfeld diffraction formula. In comparison with full 3-D FDTD simulations, the rms difference in electric field is below 5% and the difference in power flux is below 3%. A grating coupler for coupling from a silicon-on-insulator photonic integrated circuit to an optical fiber positioned 0.1 mm above the circuit is designed as an example.