Lossless backward second-harmonic generation of extremely narrow subdiffractive beams in two-dimensional photonic crystals

We report efficient second harmonic generation using extremely narrow beams (with diameter of the order of the wavelength) that propagate in the self-collimation (or nondiffractive) regime in a two-dimensional photonic crystal. We design and numerically test an AlGaAs photonic crystal membrane, where both fundamental and generated second harmonic beams propagate without diffraction and without out-of-plane losses. The characteristics of the generated second harmonic that is mainly propagating in the backward direction and the conversion efficiency of the proposed scheme are obtained by nonlinear finite-difference time-domain numerical simulations.