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常见活动，并且多年来已经为此目的提出和开发了许多技术。特别是，随着所考虑的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普遍，由于它们的灵活性和相对容易使用。时域方法的发展也受到了各种应用对宽带响应的需求以及以直接方式处理非线性和频散材料的需求的进一步推动。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，无论是在运行时间和贪婪的内存消耗方面。因此，问题的复杂性和规模都必须与所产生的模拟的准确性相平衡，这严重阻碍了许多技术领域的系统进步，并迫使工业界进行不期望的高水平的昂贵和耗时的试错实验。越来越明显的是，依靠快速增长的计算机能力是克服当今模拟软件包的局限性的不可持续的战略。因此，以最有效的方式利用现有的计算资源，不断开发新的和改进的算法是非常重要的。紧凑型光子器件是当今最先进的研究的前沿，广泛应用于集成光电子领域。例如，制造技术的进步已经允许可靠地实现微腔和相关的结构，这些结构正被积极地探索用于许多重要的目的，这是任何数值模拟算法必须解决的三个基本问题：（1）适当的物理机制的封装;（2）问题几何的表示;（3）高效率的电脑执行，以及有经验的从业员认识到这些问题彼此之间以及与正在调查的问题类别之间都有高度的联系。然而，近年来，由于简单和可用性的原因，出现了使用通用数字代码的趋势，这虽然有吸引力，但不是一种可持续的方法。该项目建议开发和应用数值算法，选择性地定制为上述高度热门的一类问题，并寻求耦合的申请人已经进行了大量的工作，以找到一个有效的表示与计算效率的几何描述和计算机实现所涉及的物理。这将提供一个强大的模拟能力，这将大大有助于未来的科学进步，以及利用新技术的实际商业产品的设计

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