# Efficient Enhancement of Second Harmonic Generation via Noninvasive Modulation
## 1 Introduction  
Since the optical second harmonic generation (SHG) was discovered in 1961 [1], this nonlinear effect has been widely applied in imaging microscopy [2; 3; 4], laser frequency conversion [5; 6], optical detection and sensing [7; 8; 9; 10], etc. SHG is a parametric process without electron transitions, while two-photon fluorescence is a nonparametric process with electron transitions [11]. Due to lossless nonradiative energy, the signal and background of SHG are better than that of the two-photon fluorescence. Hence, instead of fluorescence markers, the SHG becomes the preference of biomedical imaging. The intensity of SHG has a significant influence on the applications, like that the stronger intensity of SHG can be sensitive to the variation of signal of optical detection and sensing. Conversion efficiency of SHG is an important parameter. For all these years, enhancing the conversion efficiency of SHG has always been the focus of researchers [12; 13; 14]. From various perspectives, researchers have proposed many factors to affect the conversion efficiency of the second harmonic, such as crystal material [15; 16], interaction length [17], crystal structure [18], and pump light intensity [19]. However, it is not always applicable to improve the signal quality of SHG via increasing the pump light intensity in bioimaging because of the phototoxicity that can damage the tissue and cells. In addition, most of above methods are related to the external crystal, which cannot be available to be applied in bioimaging applications where the second harmonic is generated by the protein molecule itself. Accordingly, a control and external method that is independent of the character of the medium is required in enhancing the second harmonic efficiency of biological tissue imaging. Previous research has demonstrated that conversion efficiency of SHG is affected by phase and intensity of fundamental frequency light [13]. Therefore, modulating the wavefront of fundamental frequency light in front of the crystal can change the intensity distribution and conversion efficiency of the SHG signal. Further, we can improve the conversion efficiency of the SHG through a structured light field with spatial distribution: for example, wavefront shaping technique [13], facet functionalization of nonlinear crystals [20, 21], and construction of structured light (i.e., vortex light) [22, 23, 24, 25], etc. Furthermore, if multiple degrees of freedom are modulated simultaneously, such as wavefront phase and amplitude, higher conversion efficiency can be obtained. When a coherent light beam transmits the scattering medium, a speckle pattern with multiple random degrees of freedom is formed. Introducing a scattering process can simultaneously generate structured beams with specific phase and amplitude [26]. It has been demonstrated that the wavefront shaping technique is a noninvasive method to modulate the spatial distribution of a scattering light field in previous studies. Accordingly, we can control the scattering field to achieve high conversion efficiency enhancement of SHG based on wavefront shaping technique. In this paper, we demonstrated experimentally that placing a scattering medium in front of the nonlinear crystal can greatly enhance the conversion efficiency of SHG using wavefront shaping technique. In the experiment, placing an appropriate scattering medium does not change the light intensity of fundamental frequency light, but changes the phase gradient and phase information of fundamental frequency light, which affect the intensity of SH. This method can be available in the applications for avoiding the phototoxicity. Meanwhile, we compared the impact of wavefront shaping on conversion efficiency of SHG with different scattering mediums (ground glass and zinc oxide film) mounted in front of nonlinear crystal. The results indicate that the enhancement effect of conversion efficiency is directly related to the character of the scattering medium.