Optimized 3D simulation method for modeling of out-of-plane radiation in silicon photonic integrated circuits

We present an accurate and fast 3D simulation scheme for out-of-plane grating couplers, based on two dimensional rigorous (finite difference time domain) grating simulations, the effective index method (EIM), and the Rayleigh-Sommerfeld diffraction formula. In comparison with full 3D 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 example.