Second order nonlinear interactions in periodic waveguides

We illustrate the results of an investigation of second harmonic generation (SHG) in planar nonlinear waveguides assisted by a Bragg grating, along the propagation direction, reproducing a photonic-bandgap (PBG) structure. The analysis is performed in the time domain using a home-made finite difference time domain (FDTD) computer code that exploits the auxiliary differential equations (ADE) scheme, in order to take into account the dispersion effect. By tuning the signal at the fundamental wavelength at the band edge, the density of optical modes is enhanced, allowing a group velocity decrease and a strong localization of the energy inside the nonlinear structure, the conversion efficiency of the SHG process being drastically increased.