Investigation On Characteristics Of Second Harmonic Generation In One-dimensional Quasi-periodic Photonic Crystals

As a new artificial material photonic crystal has attracted widespread attention,because of its characteristics of photonic band-gap and photonic localization,particularly in the field of nonlinear optics, it can be used in improving optical frequency conversion, therefore further research on second harmonic generation character in nonlinear photonic crystals has significant application value.In order to analyze second harmonic generation process in one-dimensional nonlinear photonic crystals, firstly, this dissertation briefly summarizes the basic background and the present progress of domestic and international research theories of photonic crystals, and then several general theoretical methods are compared,afterwards advantages and disadvantage are introduced. A detailed analysis of Transfer matrix method and Shooting method has been made, and researches on transmittance and effective refractive index of periodic and quasi periodic onedimensional photonic crystals have been made. Secondly, based on the classical electromagnetic theory, in the view of the second-order wave equation, the first-order complete coupled-wave equations are deduced. Using transfer matrix method, the exact analysis expressions of fundamental frequency field and second harmonic field under the pump undepletion are obtained, and by combining with Shooting method,the calculation model for second harmonic generation process is established with the pump depletion. Second harmonic generation with the pump depletion and undepletion is simulated in periodic one-dimensional photonic crystals and the conversion efficiency is significantly higher than that in massive crystals. The average computation speed taken by this model is faster than that of traditional calculation model. Thirdly, by modifying the periodic structure introduced by a replacing defect of photonic crystal, second harmonic generation results are obtained in quasi periodic one-dimensional photonic crystal under the pump depletion and undepletion. Its conversion efficiency is much higher than that of periodic onedimensional photonic crystal and the iterative convergence problem in periodic onedimensional photonic crystal is optimized. Finally, by solving phase matching andgroup velocity matching equations, the restriction curves satisfying both equations are obtained. It is found that the equations have multiple solutions of layer thicknesses and refractive index ratio can compensate for the mismatching refractive index quantity between fundamental frequency wave and second harmonic wave.Based on the restrictive condition, the processes of transmission and second harmonic generation of ultra-short pulse through the quasi-periodic one-dimensional photonic crystal are simulated and analyzed by applying the frequency discretization,and the output pulse has been obtained.