  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.
