The saturable Lorentz model for ab initio nonlinear optics

The finite-difference time-domain (FDTD) method is one of the most powerful methods available for solving Maxwell equations rigorously for light propagation in complex settings, such as for self-focusing and four-wave mixing in photonic devices. However, there are still open fundamental questions and technical challenges associated with the inclusion of atomic-level contributions to that framework. These questions and challenges are particularly relevant to modeling sub-wavelength nanophotonic devices that can have only a small number of atoms in one (e.g., nanofilms) or more dimensions (e.g., nanorods or nanoparticles) and where continuum-optics theory fails to describe light-matter interaction accurately.