Extraordinary enhancement of second harmonic generation in a periodically patterned distributed Bragg reflector

Extraordinary enhancement of second harmonic generation is engineered in a three-dimensional air-bridge photonic crystal slab with a multiple-layer dielectric structure by the spectral element method. By exploiting the symmetry of the multiple-layer system, the large matrix equation arising in the spectral element method can be solved by using the block Thomas algorithm to significantly improve the efficiency of the solver. A 63-layer structure with a total thickness less than 8 μm is designed to achieve large enhancement of the second harmonic generation effect by almost 10 orders of magnitude, with an output second harmonic field power rate of more than 0.1% under a typical laser incident field of 0.5 MV/m. In addition, the sensitivity of the transmittance to the thickness of each layer is investigated. The sensitivity result shows that at the resonant frequency with large second harmonic generation, the sensitivity to the thickness is large, so the thickness precision is important to obtain large enhancement for the second harmonic generation. The application of this system to highly monochromatic light sources is discussed.