光子学设计的启发式方法和性能界限
Heuristic Methods and Performance Bounds for Photonic Design
摘要：
在光子设计问题中，科学家或工程师选择器件的物理参数以最佳地匹配某些期望的器件行为。光子设计问题的许多实例可以自然地被描述为在计算上难以全局解决的数学优化问题。正因为如此，已经开发了几种启发式方法来近似解决这些问题。这些方法通常会产生非常好的设计，并且在许多实际应用中，很容易超过依赖人类直觉的“传统”设计。然而，由于这些启发式方法不能保证找到的近似解是全局最优的，问题仍然是设计者希望做得更好。这个问题通过性能界限或不可能性结果来解决，它确定了任何设计都无法达到的性能水平。我们专注于算法的性能界限，这涉及大量的计算来确定。我们说明了各种启发式方法和性能界限上的两个例子。在这些例子中（以及许多其他没有在这里报告）的性能界限表明，启发式设计是接近最优的，并在实践中可以被认为是全局最优的。这篇评论有助于清楚地建立光子设计问题，并统一现有的方法计算性能界限，同时也提供了一些自然的概括和属性。
英文摘要：
In the photonic design problem, a scientist or engineer chooses the physical parameters of a device to best match some desired device behavior. Many instances of the photonic design problem can be naturally stated as a mathematical optimization problem that is computationally difficult to solve globally. Because of this, several heuristic methods have been developed to approximately solve such problems. These methods often produce very good designs, and, in many practical applications, easily outperform 'traditional' designs that rely on human intuition. Yet, because these heuristic methods do not guarantee that the approximate solution found is globally optimal, the question remains of just how much better a designer might hope to do. This question is addressed by performance bounds or impossibility results, which determine a performance level that no design can achieve. We focus on algorithmic performance bounds, which involve substantial computation to determine. We illustrate a variety of both heuristic methods and performance bounds on two examples. In these examples (and many others not reported here) the performance bounds show that the heuristic designs are nearly optimal, and can considered globally optimal in practice. This review serves to clearly set up the photonic design problem and unify existing approaches for calculating performance bounds, while also providing some natural generalizations and properties.
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