In general, the nonlinear behavior is due to the dependence of the polarization P(t) on
the applied electric field, E(t). Assuming an isotropic dispersive material, Maxwell’s
equations are:

FDTD - equations 28 -30

FDTD - equation 31

where PL represents the linear polarization, in general FDTD - equation is the dispersive polarization which is controlled by Lorentz model in Equation 20 and
denotes the nonlinear polarization.

The nonlinear polarization FDTD - equation may come from various model sources that produce the different nonlinear phenomenon. Currently OptiFDTD can handle four kinds of nonlinearity:

  • Dispersive second-order nonlinear material
  • Dispersive third-order nonlinear material
  • Dispersive Kerr effect
  • Dispersive Raman effect