Nonlinear optics in waveguide arrays and photonic nanowires

In this paper we review our works in the field of nonlinear optics in waveguide arrays (WAs) and photonic nanowires. We first focus on the new equation governing light propagation in optical fibers with sub-wavelength cores which simultaneously takes into account (i) the vector nature of the electromagnetic modes inside fibers, (ii) the strong dispersion of the nonlinearity inside the spectral body of the pulse, (iii) and the full variations of the vector mode profiles with frequency.