Microlasers as a platform to study fluctuations in non-Hermitian dynamical systems

材料研究部门和电气、通信和网络系统部门为该奖项提供资金，支持理论研究和教育，以推进对通信和传感系统关键组件新型激光系统的特性和设计的理解。纳米制造技术的巨大进步使得基于芯片的紧凑结构的制造成为可能，这种结构可以限制光和可调谐激光发射。然而，在允许设计具有改进功能的复杂激光系统的同时，对制造的高水平控制和许多可用的设计参数对激光理论提出了重大挑战。研究的目的是发展概念基础和计算工具，以研究复杂的片上激光系统的特性。本研究的概念、方法和计算工具将有助于设计新的应用，如用于光谱学和电控光开关的片上相干光源。除了指导和培训研究生关于激光物理的现代分析和计算技术，拟议的研究将建立工程师和物理学家之间的跨学科合作，并有可能加速基础科学向光谱学等应用的转化。材料研究部门和电气、通信和网络系统部门为该奖项提供资金，支持理论研究和教育，以推进对具有复杂谐振腔几何形状和空间调制增益和损耗的新型激光系统的动力学和噪声特性的理解。光学系统折射率实部的控制是现代光子学和量子光学的基础。复杂激光系统的选择性泵浦是这个项目的核心，它代表了一个新的设计空间，涉及到虚数和折射率实部的同时电调谐（非厄米工程），对激光物理学具有潜在的变革意义。这些激光系统的一个关键特性是它们的波动是由非厄米演化算符控制的，这是目前从数学到生物学、化学和物理学等多个领域感兴趣的问题。研究的一个目标是利用微激光作为一个物理系统，从理论上研究由非厄米算子控制的波动特性和动力学，其中这些算子的参数可以连续调谐。PI的早期工作已经证明，通过空间定制泵浦注入对增益和损耗进行明智的空间调制可以提供新的功能，并显着提高微激光器的外耦合光功率。在早期的工作中，PI开发了稳态从头算激光理论（SALT），以获取存在光泄漏和空间孔燃烧相互作用的激光特性。这些早期的研究专门针对稳态操作。提出的研究的主要目标之一是建立一个理论和计算框架来研究复杂激光系统稳态行为之外的非平衡动力学和噪声特性，这是SALT无法获得的。研究将集中在有趣的动力制度，其中波动动力学表现出谱退化或不稳定的自脉冲。拟议的研究将整合来自众多领域的最先进技术和概念，如量子光学的随机演化技术、非厄米算子的光谱理论和激光理论。将通过PI的现有合作保持与实验的密切联系。为研究开发的概念、方法和计算工具将有助于设计用于光学传感和基于频率梳的光谱学的新型相干光源。除了指导和培训研究生关于激光物理的现代分析和计算技术，拟议的研究将建立工程师和物理学家之间的跨学科合作，并有可能加速基础科学向光谱学等应用的转化。

NONTECHNICAL SUMMARYThe Division of Materials Research and the Division of Electrical, Communications, and Cyber Systems contribute funds to this award, which supports theoretical research and education towards advancing the understanding of the properties and the design of novel laser systems that are key components of communication and sensing systems. Enormous progress in nanofabrication technologies has allowed the fabrication of compact chip-based structures that enable confinement of light and tunable laser emission. However, and while allowing the design of complex laser systems with improved functionality, the high level of control over fabrication and the many available design parameters present a substantial challenge for laser theory. The objective of the research is to develop conceptual foundations and computational tools to investigate the properties of complex on-chip laser systems. The concepts, methods, and computational tools developed in the course of the proposed research will be instrumental in the design of novel applications such as on-chip coherent light sources for spectroscopy and electrically controllable optical switches. In addition to mentoring and training graduate students on modern analytical and computational techniques of laser physics, the proposed research will forge interdisciplinary collaborations between engineers and physicists, and has the potential to accelerate the translation of basic science to applications such as optical spectroscopy. TECHNICAL SUMMARYThe Division of Materials Research and the Division of Electrical, Communications, and Cyber Systems contribute funds to this award, which supports theoretical research and education towards advancing the understanding of the dynamics and noise properties of novel laser systems that feature complex resonator geometries and spatially modulated gain and loss. The manipulation of the real part of the index of refraction of optical systems is the cornerstone of modern photonics and quantum optics. Selective pumping of complex laser systems, which is at the core of this project, represents a new design space that relates to the simultaneous electrical tuning of the imaginary along with the real part of the index of refraction (non-Hermitian engineering), with potentially transformative implications for laser physics. A key property of these laser systems is that their fluctuations are governed by non-Hermitian evolution operators, which are of current interest across several fields ranging from mathematics to biology, chemistry, and physics. One objective of the research is to theoretically investigate fluctuation properties and dynamics governed by non-Hermitian operators using microlasers as a physical system, where the parameters of such operators can be continuously tuned. The PI's earlier work has demonstrated that judicious spatial modulation of gain and loss through spatially tailored pump injection can provide novel functionalities and significantly boost the out-coupled optical power of microlasers. Instrumental in that earlier work was the Steady-state Ab Initio Laser Theory (SALT) that the PI had developed to access laser characteristics in the presence of optical leakage and spatial hole-burning interactions. These earlier studies have exclusively addressed steady-state operation. One of the primary goals of the proposed research is to develop a theoretical and computational framework to study the nonequilibrium dynamics and noise properties of complex laser systems beyond their steady state behavior, which is not accessible by SALT. The research will focus on interesting dynamical regimes where the fluctuation dynamics display spectral degeneracies or instabilities towards self-pulsing. The proposed research will integrate state-of-the-art techniques and concepts from a multitude of fields, such as stochastic evolution techniques of quantum optics, spectral theory of non-Hermitian operators, and laser theory. Close contact to experiments will be maintained through existing collaborations of the PI. The concepts, methods, and computational tools developed for the research will be instrumental in the design of novel coherent light sources for optical sensing and frequency-comb-based spectroscopy. In addition to mentoring and training graduate students on modern analytical and computational techniques of laser physics, the proposed research will forge interdisciplinary collaborations between engineers and physicists, and has the potential to accelerate the translation of basic science to applications such as optical spectroscopy.