# Random Laser Action in Dye-Doped Polymer Media with Inhomogeneously Distributed Particles and Gain
## 4 Discussion  
As discussed in Section 3, the BS RLs show spectral peaks higher than conventional RLs with dye and TiO\({}_{2}\) particles for both incoherent and coherent random lasing. In this section, the implications of the obtained results are discussed.  
Figure 8: Ratio of the number of spectral spikes in different height ranges. The volume fraction of scattering particles is 10%. The pumping energy and energy density are 13 \(\upmu\)J and 22.8 \(\upmu\)J/mm\({}^{2}\), respectively.  
Figure 7: **(a)** Maximum peak intensity, **(b)** spike height, and **(c)** the number of spikes in the emission spectrum versus the TMFP. Each dashed ellipse represents a group of scattering particles having the same volume fraction. The different colors represent the different volume fractions of SPs. The pumping energy and the energy density are 13 \(\upmu\)J and 22.8 \(\upmu\)J/mm\({}^{2}\), respectively. The error bars represent the standard errors.  
In our experiments, transparent particles without gain were used for the SPs. Thus, the volume of the medium, including the laser dye, is lower than that for the gain medium without SPs. Despite this decrease in the gain region, we observed a higher spectral peak and greater slope efficiency. This can be attributed to the difference in the distributions of pump lights. As discussed in Reference [18], the pump light spreads wider and deeper in the BS medium than in the homogeneous medium. In addition, the amount of pump light escaping from the subsurface region can decrease owing to the SPs near the surface; thus, the pump light is carried deeper into the medium. The pump region can also be increased by only reducing the volume fraction of scattering particles; however, this results in a weaker scattering strength and RL emission. Thus, more efficient pumping and lasing can be achieved by employing an inhomogeneous distribution of scattering particles in the BS media.  
Subsequently, we observed that the spectral peak width decreased for the incoherent random lasing and that the number of spectral spikes decreased for the coherent random lasing. In a previous study [18], it was shown that the number of resonant wavelengths per mode decreased for the coherent lasing of BS RLs. Our new results for incoherent random lasing indicate that only light with wavelengths near the peak wavelength can remain. These results confirmed that the BS RLs exhibit stronger wavelength selectivity than the conventional RLs. One possible reason for this is the difference in the scattering free path and the path length distribution in the gain medium. Light exhibits normal diffusion in the homogeneous medium, whereas it undergoes a Levy-like flight [20] in the BS medium. This anomalous diffusion of light can affect the selection of the emitted wavelengths. Further studies should be performed to understand this phenomenon.  
Finally, we focus on the difference between the SPs used in this study and a previous study [18], where irregular-shaped and dye-doped particles with sizes in the range of 53-300 \(\upmu\)m were used. In this study, we used transparent spherical particles with diameters in the range of 30-100 \(\upmu\)m to determine whether the results obtained in the previous study were universal for BS gain media. According to the experimental results, the emission spectra exhibit the same characteristics, even if the SPs have no gain and have different shapes. The maximum peak intensity increased by \(\sim\)40% for SPs with irregular-shaped and dye-doped particles with sizes in the range of 53-100 \(\upmu\)m [18] (Figure 5). As shown in Figure 7a, the maximum peak intensity increased by \(\sim\)20% for transparent spherical particles. The effect of the difference in the particle shape of SPs needs to be small, because neither scattering nor reflection or refraction occurs at the surface boundary of the SPs. Therefore, this difference is most likely due to the difference in the size distribution and the gain ability of the SPs.