Generation of light from a 1-D random sequence of nonlinear domains

In dielectric structures such as photonic crystals that combine two types of materials it is likely that one may find a large degree of disorder. This is also true for nonlinear photonic crystals that combine two different orientations of the same material or a nonlinear with a linear material. Such a disorder may not always be detrimental for the propagation or generation of light. In the present work, we consider second harmonic generation in one-dimensional disordered nonlinear structures. When considering a random sequence of two different orientations of the same material, we show that second harmonic generation does not vanish but instead it exhibits a linear grow with respect to the number of domains considered. In structures that combine a nonlinear with a linear material, even when a large degree of disorder is introduced by allowing an extremely large dispersion in the size of the domains, the coherence of such second order nonlinear process is shown to survive.