Numerical Simulation of Compact Photonic Structures using Time Domain Volterra Integral Equation Algorithms

电磁仿真是许多科学和技术分支中的一项常见活动，多年来已经提出并开发了许多技术来达到这一目的。特别是，随着所审议问题的规模和几何复杂性的增加，通用数值技术的使用已经变得广泛，因为它们具有灵活性和相对易用性。各种应用对宽带响应的需求以及以直截了当的方式处理非线性和频率色散材料的需要也进一步推动了时间域方法的发展。典型的例子在通信技术、光子学、EMC和信号完整性应用中广泛存在。不幸的是，数值模拟工具的灵活性往往是以牺牲计算效率为代价的，无论是在运行时间方面还是在巨大的内存消耗方面。因此，必须在问题的复杂性和规模与产生的模拟的准确性之间进行权衡，这严重阻碍了许多技术领域的系统进步，并迫使行业进行不受欢迎的高水平昂贵和耗时的试验和错误试验。越来越明显的是，依靠快速增长的计算机能力不是克服当前模拟包局限性的可持续战略。因此，重要的是以尽可能有效的方式使用可用的计算资源，并不断开发新的和改进的算法。紧凑型光子器件处于广泛集成光电子应用的许多最先进研究的前沿。例如，制造技术的进步使得微腔和相关结构得以可靠地实现，这些结构正被积极地探索用于许多重要目的。任何数值模拟算法都必须解决三个基本问题：(1)适当的物理机制的封装；(2)问题几何的表示；(3)高效的计算机实现，并且有经验的实践者认识到这些问题彼此之间以及与所研究的问题的类别都是高度耦合的。然而，近年来，出于简单性和可用性的原因，出现了使用通用数字代码的趋势，尽管这种方法很有吸引力，但并不是一种可持续的方法。这个项目建议为上面介绍的高度专题性的问题开发和应用有选择地定制的数值算法，并寻求结合申请者已经进行的大量工作，以找到与计算高效的几何描述和计算机实现所涉及的物理的有效表示。这将提供强大的模拟能力，这将大大有助于未来的科学进步以及利用新技术设计实用的商业产品

Electromagnetic simulation is a common activity in many branches of science and technology and over the years many techniques have been proposed and exploited for this purpose. In particular, as the scale and geometric complexity of the problems under consideration has increased, the use of general purpose numerical techniques has become widespread, due to their flexibility and relative ease of use. The development of time domain approaches has also received further impetus from the demand for wide band responses for a variety of applications as well by the need to deal with non-linear and frequency dispersive materials in a straightforward manner. Typical examples are widespread throughout communications technologies, photonics, EMC and signal integrity applications. Unfortunately, the flexibility of numerical simulation tools is often bought at the expense of computational efficiency, both in terms of run times and voracious memory consumption. Consequently, both the complexity and scale of the problems are having to be balanced against the accuracy of the simulations produced, which is severely hampering systematic progress in many technological areas as well as necessitating that industry undertakes undesirably high levels of expensive and time consuming trial and error experimentation. It is becoming ever more apparent that relying on rapidly increasing computer power is not a sustainable strategy for overcoming the limitations of present day simulation packages. Therefore it is important that the computational resources available are used in the most effective manner possible and that new and improved algorithms are constantly under development.Compact photonic devices are at the forefront of much of the state-of-the-art research for a wide range of integrated optoelectronic applications. For example, advances in fabrication technologies have allowed reliable realisation of micro-cavity and related structures that are being actively explored for a number of important purposes.The are three fundamental issues that any numerical simulation algorithm must address: (1) encapsulation of the appropriate physical mechanisms; (2) representation of the problem geometry; (3) efficient computer implementation, and experienced practitioners recognise that these issues are both highly coupled to each other as well as to the class of problem under investigation. However, in recent years there has been a move toward the use of universal numerical codes for reasons of simplicity and availability, which although attractive is not a sustainable approach. This project proposes to develop and apply numerical algorithms selectively customised for the highly topical class of problems introduced above and seeks to couple a significant body of work already undertaken by the applicants to find an effective representation of the physics involved with computationally efficient geometric descriptions and computer implementations. This will provide a powerful simulation capability that will significantly aid future scientific progress as well as the design of practical commercial products exploiting the new technologies