## 3 Results  
Figure 2a shows the evolution of the emission spectrum of the NPDDNLC sample as the pump energy density increases from 0.135 mJ/cm\({}^{2}\) to 0.39 mJ/cm\({}^{2}\). The pump energy density is defined as the ratio of the pump energy to the pump area. When the pump energy density is low, the emission spectrum is a broad spontaneous emission with the full width at half maximum (FWHM) of about 35 nm. As the pump energy increases, some discrete sharp peaks suddenly emerge on the top of the spontaneous emission spectrum. The FWHM of the discrete sharp peaks is about 0.3 nm, which is more than 100 times smaller than the FWHM of the spontaneous emission. This indicates the occurrence of coherent random lasers. When the pump energy density further increases, more discrete sharp peaks appear on the top of the spontaneous emission spectrum, and the peak intensity of the sharp peaks increases sharply. The peak intensity and FWHM of the emission spectrum of the NPDDNLC sample as a function of the pump energy density are shown in Figure 2b. The peak intensity of the emission spectrum increases slowly as the pump energy density increases to 0.2 mJ/cm\({}^{2}\). However, when the pump energy density is larger than 0.2 mJ/cm\({}^{2}\), the peak intensity of the emission spectrum increases dramatically. The FWHM of the emission spectrum narrows slowly as the pump energy density increases to 0.2 mJ/cm\({}^{2}\). However, when the pump energy density exceeds 0.2 mJ/cm\({}^{2}\), the FWHM of the emission spectrum narrows sharply to about 0.3 nm. Therefore, we obtain that the pump threshold, defined by the sharp narrowing of the emission spectrum and the slope changing of the peak intensity as the pump energy density increases, is about 0.2 mJ/cm\({}^{2}\), which is much lower than that in the references [10; 34; 35; 36]. Figure 1: The schematic diagram of the experimental setup. The inset is the optical photograph of the sample. \(\lambda/2\), P, NBS, CL, EM, and FS express the half-wave plate, polarizer, neutral beam splitter, cylindrical lens (focal length of 10 cm), energy meter, and fiber spectrometer, respectively. Figure 2: (**a**) Evolution of the emission spectrum of the NPDDNLC sample as a function of the pump energy density. (**b**) The peak intensity and FWHM of the emission spectrum of the NPDDNLC sample as a function of the pump energy density. For investigating the influence of the TiN nanoparticles on the performance of random lasers of the NPDDNLC sample, we also studied the emission spectrum of the dye-doped nematic liquid crystal (DDNLC) sample at different pump energy densities as shown in Figure 3a. Similar to Figure 2a, some discrete sharp peaks can be observed on the top of the spontaneous emission spectrum. However, it is worth noting that the emission spectrum of the DDNLC sample as a function of the pump energy density has some different characteristics compared to that of the NPDDNLC sample shown in Figure 2a. Although, the pump energy density in the DDNLC sample is much larger than that in the NPDDNLC sample, the number of the discrete sharp peaks of the emission spectrum of the DDNLC sample is much less than that of the NPDDNLC sample. The discrete sharp peaks of the emission spectrum of the DDNLC sample is weaker and the amplitude of the spontaneous emission is larger than that of the NPDDNLC sample. Figure 3b shows the peak intensity and FWHM of the emission spectrum of the DDNLC sample as a function of the pump energy density. Similar to Figure 2b, the peak intensity of the emission spectrum increases distinctly and FWHM of the emission spectrum narrows sharply when the pump energy density exceeds a given value. However, the pump threshold of the DDNLC sample is about 2.0 mJ/cm\({}^{2}\), which is 10 times larger than the pump threshold of the NPDDNLC sample.