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 be 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.

中文翻译：

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光子设计的启发式方法和性能界限

在光子设计问题中，科学家或工程师选择设备的物理参数以最好地匹配某些所需的设备行为。光子设计问题的许多实例可以自然地表述为数学上最优化的问题，该问题在计算上难以整体解决。因此，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，其性能很容易超过依靠人类直觉的“传统”设计。但是，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，因此问题仍然是设计师可能希望做得更好。性能限制或不可能结果可解决此问题，它决定了任何设计都无法达到的性能水平。我们专注于算法性能范围，这涉及确定的大量计算。我们在两个示例中说明了各种启发式方法和性能界限。在这些示例（以及此处未报告的其他示例）中，性能界限表明，启发式设计几乎是最佳的，在实践中可以认为是全局最佳的。这篇综述旨在清楚地设置光子设计问题，并统一现有的计算性能范围的方法，同时还提供了一些自然的概括和特性。在这些示例（以及此处未报告的其他示例）中，性能界限表明，启发式设计几乎是最佳的，在实践中可以认为是全局最佳的。这篇综述旨在清楚地设置光子设计问题，并统一现有的计算性能范围的方法，同时还提供了一些自然的概括和特性。在这些示例（以及此处未报告的其他示例）中，性能界限表明，启发式设计几乎是最佳的，在实践中可以认为是全局最佳的。这篇综述旨在清楚地设置光子设计问题，并统一现有的计算性能范围的方法，同时还提供了一些自然的概括和特性。