## 3 Results and Discussion
In detail, the crystalline orientations identified using PP configuration in Figures 6-9 are -75.2\({}^{\circ}\), -9.1\({}^{\circ}\), -43.6\({}^{\circ}\), and 96.5\({}^{\circ}\). If using the average values of A\({}_{\rm g}\)\({}^{1}\) and A\({}_{\rm g}\)\({}^{2}\) at NA, the crystalline orientations identified using NA configuration in Figures 6-9 are -66.9\({}^{\circ}\), -3.7\({}^{\circ}\), -40.7\({}^{\circ}\), and 97.1\({}^{\circ}\). The largest difference between the results of PP and those of NA is 8.3\({}^{\circ}\), less than the rotating step (10\({}^{\circ}\)) of polarized direction during the Raman experiments. There results verified the validity and effectiveness of proposed method. In either the Figure 7b or the Figure 9b, the experimental data of A\({}_{\rm g}\)\({}^{2}\) showed a secondary maximum at the direction vertical to that of the primary maximum. Moreover, the primary maximum was much larger than the secondary one. Quite a few existing experiments, not only in this work but also some by other groups, detected such a phenomenon similar to that in the Figure 7b or the Figure 9b, which showed this phenomenon of A\({}_{\rm g}\)\({}^{2}\) might, probably but not inevitably, appear under PP configuration only [17; 22]. [PERSON] et al. believed that it was induced by the birefringence relatively obvious under the PP configuration and could be well described by using the Equation (4) [17]. While under the NA configuration, according to the Equation (6) the polarization-intensity curve seemed to be a peanut-like shape with only one maximum direction. In this work, the layer numbers of all the samples were identified by using the method similar to that in [20] The B\({}_{\rm 2g}\) - A\({}_{\rm g}\)\({}^{2}\) wavenumber difference, \(\Delta\omega\), under NA configuration was used to conclude the layer number by using the following identifying criterion: 1 layer if \(\Delta\omega\geq\) 30.3 cm\({}^{-1}\), 2 layers if 30.3 cm\({}^{-1}\)\(>\Delta\omega\geq\) 29.3 cm\({}^{-1}\), 3 layers if 29.3 cm\({}^{-1}\)\(>\Delta\omega\geq\) 28.4 cm\({}^{-1}\), 4 layers if 28.4 cm\({}^{-1}\)\(>\Delta\omega\geq\) 27.8 cm\({}^{-1}\), and \(>\) 4 layers if 27.8 cm\({}^{-1}\)\(>\Delta\omega\), where each \(\Delta\omega\) was the average value of all the 37 data at polarization direction from 0\({}^{\circ}\) to 360\({}^{\circ}\) with 10\({}^{\circ}\) rotating step. As for the samples corresponding to Figures 5-9, the \(\Delta\omega\) were 28.83 cm\({}^{-1}\), 29.22 cm\({}^{-1}\), 30.09 cm\({}^{-1}\), 28.29 cm\({}^{-1}\), and 27.59 cm\({}^{-1}\), respectively. Hence the layer numbers were regarded as 3, 3, 2, 4, and \(>\)4 layers. Figure 7: Normalized intensities of (**a**) A\({}_{\rm g}\)\({}^{1}\) at PP, (**b**) A\({}_{\rm g}\)\({}^{2}\) at PP, (**c**) A\({}_{\rm g}\)\({}^{1}\) at NA, and (**d**) A\({}_{\rm g}\)\({}^{2}\) at NA of a 2-layer phosphorene specimen. In fact, the wavenumber difference \(\Delta\omega\) used for identifying the layer number clearly depended on whether the PP or NA Raman configurations were used. If using the same identifying criterion on the data under different polarized Raman configurations, the results may be inconsistent. Hencethe accurate identification of layer number requires an in-situ measurement combining polarized micro-Raman with AFM. Besides, the method in this work is more flexible to apply than the traditional one. In detail, as a necessary for PP configuration, the 360\({}^{\circ}\) continuously adjustable analyzer is not a standard, but a customized accessory for most of the Raman system and microscope. And it is located inside the cabinet of the spectrograph, which is far from practically for angular-resolution polarized Raman measurement like the identification of the crystalline orientation. The NA configuration, by contrast, is only based on a standard Raman system and only a continuously adjustable polarizer is required.