Collaborative Research: Engineering fractional photon transport for random laser devices

小型化激光器的快速发展使光学技术的消费应用从根本上改变了我们的信息社会，从高速通信系统到集成光学传感器，扫描仪和高分辨率成像设备。此外，量子信息技术的新兴范式要求我们有能力提高微型激光设备中光发射过程的速率，这些激光设备可以在多个频带上有效运行，并“按需释放光子”。为了应对这些挑战，该研究项目推进了对依赖于结构无序介质中工程波传输和局部化效应的新型激光器件的理解。该研究小组利用新型计算方法与纳米纤维和器件表征合作，设计和开发了一类具有宽带行为的新型激光结构，用于下一代节能纳米光子器件中的小型化光源，如片上小型化光谱仪，光学传感器，成像系统和更强大的量子源。该项目支持波士顿大学和犹他州大学的一名研究生，并鼓励本科生通过这两个机构充满活力的外展计划参与研究。PI开发的计算和实验框架将通过波士顿大学和犹他州大学的课程项目进行传播。这一外联计划的一个重要组成部分是通过参与该项目吸引代表性不足的少数群体从事计算科学和光学工程职业。该项目通过提出一种基于非规则三维域中分数阶微分算子的有效数值解的理论和实验相结合的方法，来应对具有定制光子输运特性的随机激光器件的多尺度建模所带来的令人信服的挑战。分数阶微积分算子在空间上表现出非局部特性，在时间上表现出历史效应，自然地描述了非均匀非周期介质中波输运的相关效应。这些效应通常提供显著的离散化和计算挑战。然而，建立在分数波扩散方程模型的初步成功异常波传输，该项目开发了一种新的方法，有效地耦合分数输运方程的电动力学描述的有源光子器件具有复杂的非周期性的几何形状。为了完成这一任务，我们建立在开源的光谱/HP元素库Nektar++框架的成功，旨在支持使用光谱/HP元素方法开发偏微分方程的高性能可扩展求解器。该项目使用新的分数运算符的数学技术，与从亚波长光子膜实现的随机激光器件的制造和实验表征相一致。基于这个高效的平台，该项目展示了定制的随机结构和非周期性介质中的激光行为，这些结构和介质通过设计表现出超慢光子亚扩散现象。该项目的主要智力价值是开发一种新型的具有成本效益的小型化无序工程随机激光器，具有定制的光子扩散特性，可以作为经典和量子光学信息处理的更强大的光子源。该项目通过为下一代随机激光设备提供基础，用于光学成像、传感和光谱学，并为在计算光子模型中更广泛地采用分数算子奠定基础，从而实现了更广泛的影响。该奖项反映了NSF的法定使命，并通过使用基金会的智力价值和更广泛的影响评审标准进行评估，被认为值得支持。

The rapid development of miniaturized lasers enabled consumer applications of optical technology that have radically transformed our information society ranging from high-speed communication systems to integrated optical sensors, scanners, and high-resolution imaging devices. Moreover, the emerging paradigm of quantum information technology requires our ability to enhance the rate of optical emission processes in miniaturized laser devices that can operate efficiently over multiple frequency bands and release “photons on demand”. Responding to these challenges, this research project advances the understanding of novel laser devices that rely on engineered wave transport and localization effects in structurally disordered media. The research team utilizes novel computational methods in partnership with nanofabrication and device characterization to design and develop a new class of laser structures with broadband behavior for use as miniaturized light sources in the next generation of power-efficient nanophotonics devices, such as on-chip miniaturized spectrometers, optical sensors, imaging systems, and more robust quantum sources. The project supports one graduate student at Boston University and at the University of Utah and encourages the involvement of undergraduate students in the research through a vibrant outreach program at both institutions. The computational and experimental frameworks developed by the PIs will be disseminated through course projects at both Boston University and the University of Utah. An important component of this outreach plan is to attract underrepresented minorities to a career in computational science and optical engineering through participation in the project. This project responds to the compelling challenges posed by the multi-scale modeling of random laser devices with tailored photon transport properties by proposing a combined theoretical and experimental approach based on the efficient numerical solution of fractional differential operators in non-regular three-dimensional domains. Fractional calculus operators exhibit non-local characteristics in space and history-effects in time that naturally describe correlation effects in the wave transport across non-homogenous, aperiodic media. These effects typically provide significant discretization and computational challenges. However, building on the initial success of fractional wave-diffusion equation models for anomalous wave transport, this project develops a new methodology to efficiently couple fractional transport equations to the electrodynamics description of active photonic devices with complex non-periodic geometries. To accomplish this task, we build on the success of the open-source spectral/hp element library Nektar++ framework designed to support the development of high-performance scalable solvers for partial differential equations using the spectral/hp element method. The project uses novel mathematical techniques of fractional operators in concert with the fabrication and experimental characterization of random laser devices realized from sub-wavelength photonic membranes. Based on this efficient platform, the project demonstrates lasing behavior in tailored random structures and aperiodic media that exhibit ultra-slow photon sub-diffusion phenomena by design. The primary intellectual merit of the project is the development of a novel class of cost-effective, miniaturized, disorder-engineered random lasers with tailored photon diffusion properties that can find applications as more robust photon sources for classical and quantum optical information processing. This project enables a substantial broader impact by providing the foundation for the next generation of random laser devices for optical imaging, sensing, and spectroscopy, and laying the foundation for broader adoption of fractional operators in computational photonic models.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.