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但普遍的技术，用于测量生物和化学相互作用。这些器件响应于由于生物或化学反应的发生而引起的结构的折射率的变化。这种变化改变了结构内金属-电介质界面处表面波的行为，然后对其进行测量，以形成数千种高灵敏度和有效测试的基础，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年的调查文章（J. Homola，Surface plasmon resonance sensors for detection of chemical and biological species. Chemical Reviews，108（2）：462 - 493，2008）列出了用于食品质量和安全分析（列出的62种）、医疗诊断（列出的33种）和环境监测（列出的21种）的SPR生物传感器。在这份出版物问世后的十年里，这份名单有了很大的增长。该项目将推进这些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核实。在用于模拟相关模型方程解的广泛类别的潜在方案中，“高阶曲面扰动”（HOPS）算法是最佳的。尽管HOPS方法对于手头的问题具有有利的特性，但对于工程师的使用，HOPS方法需要进一步增强。该研究项目旨在开发几项改进措施。 首先，该项目将研究扩展到三维，矢量，多层结构的当前利益。第二，该项目将调查在边界变形和波数方面联合扩展散射场的可能性。这些最后的发展将要求进行新的严格分析（本项目将提供），以确定其适用范围。一旦这些补充已经实施和测试，这些算法将验证对实验室的实验结果。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的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.