Computational methods and techniques for nonlinear optics

The nonlinear optical effects originating from the light-matter interaction under intense light excitations can produce many exotic optical phenomena and are the basis of many novel applications of modern optics, including optical communications systems, optical sensing, and materials research. In recent years, the development of metamaterials, photonic crystals, and topological optics allows unconventional enhanced nonlinear effects that may potentially exceed traditional nonlinear materials. With the spectacular experimental development of nonlinear optics, computational methods and techniques for nonlinear optics have obtained prominent progress. This chapter summarizes the computational methods of free-carrier nonlinearities via the hydrodynamic description in a nonperturbative regime and bound-state electron nonlinearities via the Maxwell-Bloch description in a simplified two-level quantum system. The full-wave consideration of nonlinear dynamics of plasmonics and bound-state electrons reveals key contributions to the emerging nonlinear optical applications and allows the design of high effective nonlinearities in a desired spectral range.