We will show how to extract information from the Mie coefficients to properly design dual systems combined with chiral
elements for having optically active structures. Such optically active elements will scatter the light omnidirectionally,
where the amount of rotation of light is fixed in any given direction independently of the incident polarization. The key
elements are the preservation of helicity by equaling the electric and magnetic responses from the material, and by the
proper manipulation of the angular momentum.
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.