OP: High Order Perturbation of Surfaces Methods for Crossed Surface Plasmon Resonance Sensors: Simulation, Validation, and Design

表面等离子体共振（SPR）传感器是一种相对较新的测量生物和化学相互作用的普遍技术。这些装置对由于生物或化学反应的发生而引起的结构折射率的变化作出反应。这种变化改变了结构内金属-介电界面处的表面波的行为，然后对其进行测量，形成数千种高灵敏度和有效的测试的基础，不仅用于化学和生物物种检测，还用于医学诊断和环境测量。事实上，2008年的一篇调查文章（J. Homola），用于检测化学和生物物种的表面等离子体共振传感器。化学评论，108(2):462-493,2008)列出了用于食品质量和安全分析（62个）、医疗诊断（33个）和环境监测（21个）的SPR生物传感器。自该出版物问世以来的十年里，该榜单大幅增长。该项目将推动这些SPR传感器的数值模拟技术的发展。数值模拟将通过与实验人员的直接合作进行验证和验证。“表面高阶摄动”（HOPS）算法是模拟相关模型方程解的众多潜在格式中最优的。尽管对于手头的问题来说，HOPS方法具有优势，但为了工程师的使用，它们还需要进一步的改进。这个研究项目的目的是发展几项改进。首先，该项目将研究当前感兴趣的三维、矢量、多层结构的扩展。其次，本项目将探讨边界变形和波数的散射场联合扩展的可能性。这些后一种开发将要求新的严格的分析（这个项目将交付）来确定它们的适用领域。一旦这些补充已经实施和测试，这些算法将根据实验室实验结果进行验证。在此之后，该项目旨在创建一个优化框架，以设计具有增强传感能力的SPR传感器。这将涉及适当的目标函数的设计，其次是新的前向求解器与最先进的最小化库的有效接口。

Surface Plasmon Resonance (SPR) sensors are a relatively new yet pervasive technology for measuring biological and chemical interactions. These devices respond to the change in the refractive index of a structure due to the occurrence of a biological or chemical reaction. Such a change modifies the behavior of surface waves at metal-dielectric interfaces within the structure, which are then measured to form the basis for thousands of highly sensitive and effective tests for not only chemical and biological species detection, but also medical diagnosis and environmental measuring. Indeed, a 2008 survey article (J. Homola, Surface plasmon resonance sensors for detection of chemical and biological species. Chemical Reviews, 108(2):462­493, 2008) lists SPR biosensors for Food Quality and Safety Analysis (62 listed), Medical Diagnostics (33 listed), and Environmental Monitoring (21 listed). In the decade since the appearance of this publication the list has grown substantially. This project shall advance the state of the art in the numerical simulation of these SPR sensors. The numerical simulation will be validated and verified through direct collaboration with experimentalists.The algorithm of "High Order Perturbation of Surfaces" (HOPS) is optimal among the wide class of potential schemes for simulating solutions of the relevant model equations. Despite their advantageous properties for the problem at hand, the HOPS methods require further enhancements for their use by engineers. This research project aims to develop several improvements. First, the project will study extensions to the three dimensional, vectorial, multiply layered configurations of current interest. Second, the project will investigate the possibility of a joint expansion of the scattered fields in both boundary deformation and wavenumber. These latter developments will mandate new rigorous analysis (which this project will deliver) to determine their domain of applicability. Once these additions have been implemented and tested, these algorithms will be vaildated against the laboratory experimental results. After this, the project aims to create an optimization framework to design SPR sensors with enhanced sensing capabilities. This will involve the design of appropriate objective functions, followed by the efficient interfacing of the new forward solvers to state of the art minimization libraries.