Second harmonic generation of narrow beams in subdiffractive photonic crystals

The aim of the present work is to convert radiation from a very narrow beam at the fundamental frequency in a very narrow beam at the second harmonic (SH) frequency. Therefore, it is needed the subdiffractive propagation condition for both fundamental and second harmonic waves. However, for an efficient second harmonic generation (SHG) there are two other conditions to be fulfilled: the phase matching and a sufficiently strong nonlinear coupling between the Bloch modes of the two waves. Finally, using the numerical finite-difference time domain (FDTD) technique we demonstrate SHG of narrow beams and evaluate the efficiency of the process, which is increasing with respect to the efficiency in the homogeneous case due to the decreasing of the group velocity in PC.