Chen Yuyao, Fiorentino Alfredo, Dal Negro Luca
Boston University, Department of Electrical and Computer Engineering and Photonics Center, 8 Saint Mary's Street, Boston, Massachusetts, 02215, USA.
Università di Catania, Dipartimento di Fisica e Astronomia "Ettore Majorana", via S. Sofia, 64, 95123, Catania, Italy.
Sci Rep. 2019 Jun 18;9(1):8686. doi: 10.1038/s41598-019-44774-3.
The goal of this letter is to introduce the concept of a non-resonant fractional random laser. This is achieved by extending the classical Letokhov model of photon diffusion through disordered gain media to fractional differential operators in space and time. Fractional transport equations effectively describe anomalous photon sub-diffusion phenomena in non-uniform random scattering media with memory and long-range spatial correlation effects. In particular, by analytically solving fractional transport equations in the one-dimensional slab geometry we obtain simple closed-form expressions for the critical amplification volumes required to initiate the laser action in both fractional-order (FO) and distributed-order (DO) space-time fractional reaction-diffusion equations. Our findings demonstrate the benefits of anomalous sub-diffusive photon transport in active media with correlated disorder and stimulate the engineering of novel non-resonant random lasers with significantly reduced footprint and amplification volumes beyond the limitations of uniform disorder and Markovian diffusion processes.
这封信的目的是介绍非共振分数阶随机激光器的概念。这是通过将经典的列托霍夫光子在无序增益介质中扩散的模型扩展到空间和时间上的分数阶微分算子来实现的。分数阶输运方程有效地描述了具有记忆和长程空间相关效应的非均匀随机散射介质中的反常光子次扩散现象。特别是，通过解析求解一维平板几何结构中的分数阶输运方程，我们得到了分数阶（FO）和分布阶（DO）时空分数阶反应扩散方程中启动激光作用所需的临界放大体积的简单闭式表达式。我们的研究结果证明了反常次扩散光子输运在具有相关无序的有源介质中的优势，并激发了新型非共振随机激光器的工程设计，其占地面积和放大体积显著减小，超越了均匀无序和马尔可夫扩散过程的限制。
