ABSTRACT
The use of periodic structures in nonlinear optics has many interesting aspects. This chapter discusses the problem of factorization of truncated Fourier expansions of fields put in nonlinear Maxwell equations, in view of the numerical modeling of the diffraction by periodic structures in nonlinear optics. Due to the boundary conditions, modeling of periodic media in linear and nonlinear optics requires integrating boundary-value differential equations. The unknown field components at a given boundary are expressed as a linear combination of the unknown components on another interface. Numerical integration of the Fourier transformed linearized Maxwell equations in nonlinear optics has been done successfully using different techniques. They all present the same numerical difficulties, as in linear optics, enhanced by the requirement to correctly represent the electric field inside the optically-nonlinear region. The chapter also presents some closing thoughts on the key concepts discussed in the preceding chapters of this book.
