通过扩散光子注量率的几何分布概率加权获得球形随机激光阈值尺寸的新的近解析途径
New near-analytical path to the threshold size of spherical random lasing via geometric-distribution-probability weighting of the diffusive photon fluence rate
摘要：
我们证明了一个新的近解析路径的阈值大小的随机激光的情况下，均匀和各向同性散射球。我们评估了一个几何分布概率（GDP）加权积分的扩散方程导出的时间依赖性光子注量率在一个球形边界，在响应均匀的，同步的，和三角洲功能的光子代内的球体。GDP基于建模光子源与相同场点之间的视线距离来加权建模Delta函数光子源对球形边界域处的光子注量率的时间行为的贡献。积分表现出一个双相模式与时间的全球最小值，然后是指数增长。对应于全局最小值的时间的视线长度随着球的大小的增加而单调减小。假设该视线长度等于球体半径的条件指示阈值，由此介质可以维持边界处的光子注量率随时间的增长。这个阈值的视线长度进行评估超过增益/散射比[0.001，10000]覆盖扩散准弹道制度。与辐射转移方法相比，应用一个简单的经验增益/散射比的阈值视线长度预测的阈值大小在扩散区域和优于阈值大小的本征模式分解在半弹道区域。该方法为研究增益散射介质中的放大扩散过程提供了新的思路。
英文摘要：
We demonstrate a new near-analytical path to the threshold-size of random-lasing for the case of a uniform and isotropic-scattering sphere. We assess a geometric-distribution-probability (GDP) weighted integration of the diffusion-equation derived time-dependent photon fluence-rate at a spherical boundary, in response to uniform, synchronous, and Delta-functional photon generations within the sphere. The GDP weights the contribution of the modeled Delta-functional photon sources to the temporal behavior of the photon fluence rate at the spherical boundary-domain based on the line-of-sight distance between the modeled-photon source and the same field point. The integral manifests a bi-phasic pattern versus time with a global minimum followed by an exponential growth. The line-of-sight length that corresponds to the time of global minimum decreases monotonically as the size of the sphere increases. The condition that this line-of-sight length equaling the radius of the sphere is hypothesized to indicate a threshold whereby the medium can sustain the growth of the photon fluence-rate at the boundary over time. This threshold line-of-sight length is assessed over a gain/scattering ratio of [0.001, 10000] covering the diffusive to quasi-ballistic regimes. The threshold line-of-sight length applied with a simple empirical gain/scattering ratio predicts the threshold size over the diffusive region and outperforms the threshold size given by the eigen-mode-decomposition in the semi-ballistic region, when compared to the radiative transfer approach. The method sheds new insights to amplified diffusion process in a scattering medium with gain.
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