Effective optical response of silicon to sunlight in the finite-difference time-domain method

The frequency dependent dielectric permittivity of dispersive materials is commonly modeled as a rational polynomial based on multiple Debye, Drude, or Lorentz terms in the finite-difference time-domain (FDTD) method. We identify a simple effective model in which dielectric polarization depends both on the electric field and its first time derivative. This enables nearly exact FDTD simulation of light propagation and absorption in silicon in the spectral range of 300-1000 nm. Numerical precision of our model is demonstrated for Mie scattering from a silicon sphere and solar absorption in a silicon nanowire photonic crystal.