随着高次谐波的发展，需对其进行系统研究。本文总结了高次谐波的主 要进展，包括气体和固体介质高次谐波的发现，气体高次谐波的经典解释和量子解释，固体高次谐波基于布洛赫(Bloch)和瓦尼埃(Wannier)函数的 不同模型解释，以及阿秒脉冲串和孤立阿秒脉冲的实现。基于单电子近似和强场近似，通过量子理论模拟计算了高次谐波的产生，得到了高次谐波能谱图，展示了能谱图中的平台区和截止区。通过与经典模型的对比描绘了量子与经典模型下产生谐波的长短量子轨道，两种模型下的量子轨道在能谱平台区基本重合，并展现了两种模型电子电离和复合时刻与辐射的谐波能量关系，最后展示了宏观传播对谐波的影响。本文有利于认识高次谐波的产生，并对高次谐波的设计提供理论依据。

With the development of high harmonics, a systematic study is needed. This paper summarizes the main advances in high harmonics, including the discovery of high harmonics in gaseous and solid media, the classical and quantum interpretations of high harmonics in gases, different model interpretations of high harmonics in solids based on Bloch and Wannier functions, and the realization of attosecond bursts and isolated attosecond pulses. Based on the single-electron approximation and the strong-field approximation, the generation of high harmonics is computed by quantum theoretical simulations, and high harmonic energy spectra are obtained, showing the plateau and cutoff regions in the energy spectra. The long and short paths of harmonic generation under the quantum and classical models are shown by comparison with the classical model, and the paths under the two models are basically overlapped in the platform region of the energy spectrum. And the harmonic energy relationship between the electron ionization and recombination moments and radiation of the two models are shown, and finally, the effect of propagation on the harmonics is shown. This work is carried out to facilitate the understanding of high harmonic generation and to provide a theoretical basis for high harmonic design.