光学超晶格是一种具有人工微结构的非线性光学材料。通过设计适当的超晶格结构，可以满足相应的准相位匹配(QPM)条件从而提升非线性光学过程的转换效率。传统的QPM理论主要基于倒格矢动量补偿原理，在推导相位匹配条件时通常未考虑基波衰减的影响，因此某种意义上可视作一种小信号近似下的相位匹配理论。本项目中，我们拟对光学超晶格中的相位匹配问题进行更为深入的研究。在考虑基波衰减的情况下，从基本方程出发研究相应的准相位匹配条件，将传统基于“小信号”的QPM理论发展为“大信号”下的严格准相位匹配(RQPM)理论，并通过将平面波角谱方法引入到非线性谐波转换过程，进一步完善RQPM理论并拓展其适用范围，探索可能出现的新物理效应。我们希望通过本项目的研究彻底解决光学超晶格结构设计的非线性“求逆”问题，实现针对复杂非线性光学过程的超晶格结构按需设计。

The optical superlattice (OSL) is a kind of nonlinear optical material with artificial microstructures. In optical superlattices, the nonlinear conversion efficiency can be greatly enhanced when the corresponding quasi-phase-matching (QPM) condition is satisfied. However, the pump-depletion effect of the fundamental wave is usually not counted in the traditional QPM theory, thus it can be considered as a theory under the so-called small-signal approximation. In this project, the phase-matching problem in optical superlattices will be treated more carefully. The rigorous QPM condition without small-signal approximation is deduced directly from the nonlinear coupled equations, and a rigorous quasi-phase-matching (RQPM) method can be developed accordingly. With the help of the angular spectrum theory, the RQPM method can be further improved to deal with complicated problems in different research fields. Finally, we hope the nonlinear "inverse problem" of OSL design can be solved with the RQPM method, and a general on-demand OSL designing theory for complicated nonlinear optical processes can be developed.