The structural property of the matter always play an important role in many physics processes, in other words, many physics phenomena can be realized and controlled by this kind of structure. Hence the structural property of different matter had been intensively investigated in the past, such as the diffraction phenomenon in grating structure, plasmons, photonic band gap in different structured photonic crystals, and so on. In the field of nonlinear optics, lots of studies have introduced these structures into nonlinear photonic crystals (NPCs). The disadvantages of this method are complex fabrication and unchangeable SH pattern. Hence, to solve these problems, in our previous research [Optics Express, 24(12), 15666-15671(2016)], the concept of structured FW, in which the wavefront phase of the FW is periodically modulated by a spatial light modulator (SLM) in real time, was introduced to the process of SHG.

In this paper, we numerically and experimentally investigated the nonlinear Raman-Nath second harmonic generation of hybrid structured fundamental wave whose phase modulation combined periodic and random structure. The second harmonic generation of both one- and two-dimensional hybrid structured fundamental wave were investigated. The results show that more diffraction spots can be obtained in these hybrid structures than the pure periodic modulation cases. Besides, the total intensity of the second harmonic not only can be dramatically enhanced without altering the diffraction angles, but also is increasing with the degree of randomness of the structure. This study enriches the family of second harmonic generation of structured fundamental wave and has potential application in dynamically controlling second harmonic wave in arbitrary directions.

Huaqing Zhou, Haigang Liu, Minghuang Sang, Jun Li, and Xianfeng Chen, Nonlinear Raman-Nath second harmonic generation of hybrid structured fundamental wave, Optics Express, 25(4), 3774-3779 (2017).