We report optical second harmonic generation (OSHG) in a two dimension photonic crystal of centro-symmetric dielectric based on finite difference time domain (FDTD) algorithm. The electromagnetic field distribution in the structure and the intensity of second harmonic (SH) from electric quadrupole polarization along the waveguide are analyzed. The results show that the acute spatial variation of electromagnetic field results in the radiation of SH, and the intensity is proportional to the square of waveguide length. When the beam intensity of the pumping wave is 1.3 MW/mm2, which has wavelength of 10.6 μm, the conversion efficiency of power is 0.307% for a photonic crystal of Silicon with a length of 40 μm.
Second harmonic generation in photonic crystal cavities in (111)-oriented GaAs