基于希尔伯特分形超晶格结构的准相位匹配研究  

Quasi-Phase-Matching Based on Hilbert Fractal Superlattice Structure

作　　者：吕家富 马博琴[1] 王雪颖 Lü Jiafu;Ma Boqin;Wang Xueying(School of Data Science and Intelligent Media,Communication University of China,Beijing 100024,China;School of Information and Communication Engineering,Communication University of China,Beijing 100024,China)

机构地区：[1]中国传媒大学数据科学与智能媒体学院,北京100024 [2]中国传媒大学信息与通信工程学院,北京100024

出　　处：《中国激光》2022年第6期100-107,共8页Chinese Journal of Lasers

摘　　要：准相位匹配技术是一种弥补相位失配的有效办法,在激光谐波产生和非线性光参量放大等方面备受关注。现有的准周期超晶格结构存在结构单一性问题,运用豪斯多夫维数计算方法,设计并制备出二维希尔伯特分形结构,将其应用到光学超晶格中。通过希尔伯特分形结构的衍射图与周期性结构的衍射图的对比,验证了希尔伯特分形结构可以提供丰富的倒易矢量,由此可产生波长为543,632,696,900nm的二次谐波,为超短脉冲激光等技术的发展提供了更多的选择。Objective The quasi-phase-matching theory was first proposed to compensate for the phase mismatching caused by different refractive indices of the fundamental and harmonic waves in nonlinear photonic crystals.The team from Nanjing University introduced the one-dimensional Fibonacci quasi-periodic domain structure into the optical superlattice.As the order of the quasi-periodic structure is weaker than that of the periodic structure,the quasi-periodic domain structure,especially that with the fractal structure,has richer Fourier components.Therefore,more extensive reciprocal vectors are in the reciprocal space.Recently,researchers have been exploring and designing more excellent optical superlattice structures to meet the increasing application requirements for superlattice materials.However,owing to its low Hausdorff dimension,the corresponding nonlinear frequency conversion efficiency is not attained in existing fractal superlattice structures,such as the Cantor set and Koch curve.In this paper,we propose the design and preparation of the Hilbert fractal superlattice structure,apply to the experiment of nonlinear optical high-order harmonic generation.Results from the novel fractal structure experimental methods and research findings can be helpful to the phase matching of multiple wavelengths and high-order harmonic output of quasi-continuous wavelengths.Methods Using the characteristics of a fractal,we illustrated that the fractal structure was obtained by broadening the fractal curve into a stripe structure.Further,we showed that the Hilbert fractal structure was a two-dimensional space-filling curve.Then,taking third-order Hilbert fractal structure as an example,we used an iterative method to deduce the design method of the n-order Hilbert fractal structure.Furthermore,the fractal dimension of the Hilbert fractal structure was obtained by calculating the Hausdorff dimension.Moreover,the derivation proves that the reciprocal space of the structure provides rich reciprocal vectors.Next,using the local layout a

关 键 词：非线性光学 倒易矢量 希尔伯特分形 准相位匹配 光学超晶格 

分 类 号：O734[理学—晶体学]