Enhanced Cerenkov SHG in planar nonlinear waveguide reproducing a 1-D PBG

Summary form only given. Guided infrared modes can be coupled with a radiation mode according to the Cerenkov configuration. The guided infrared modes creates a nonlinear polarization which has a faster phase velocity than that of a free wave at the harmonic frequency in the material, the usual case with normally dispersive materials. In this case, the harmonic radiation created by the nonlinear polarization radiates into the substrate at an angle that assures conservation of the k-vector component parallel to the interface, automatically providing phase-matching. Enhancement in the nonlinear conversion efficiency can be increased if a "longitudinal" field confinement is achieved. This can be obtained by a suitable grating design on a waveguide which "simulates" a 1-D photonic band gap structure (PBG). The advantages that can derive from the use of a medium with periodic linear properties have been recently considered in the study of the photonic band gap (PBG) structures. Not only is exact phase-matching achievable, but a further enhancement of the conversion efficiency is possible by tuning the fundamental field near the photonic band edge, at a transmission resonance. There, the waves experience confinement, which translates into a large density of modes (DOM), and the field is enhanced inside the PBG structure leading to enhanced available nonlinear gain. In the present work, the Cerenkov SHG process enhanced by a PBG waveguide is investigated through a coupled mode theory, which permits both linear and nonlinear mode coupling. Our theory shows how the band edge tuning conditions and the phase-matching requirements can be satisfied at the same time.