Realising superoscillations: A review of mathematical tools and their application
Realising superoscillations: A review of mathematical tools and their application
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DOI：
10.1088/2515-7647/aba5a7
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发表时间：
2020-08
期刊：
影响因子：
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通讯作者：
Katrine S. Rogers;E. Rogers
中科院分区：
文献类型：
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作者：
Katrine S. Rogers;E. Rogers
随着早期的理论分析演变为广泛的实验实现，超振荡对越来越多的实际应用产生了越来越大的影响。在光学领域尤其如此：这是第一个广泛接受超振荡的应用领域，最近也有了很大的发展。这篇综述为任何计划在已经使用超振荡的应用程序中扩展边界或将超振荡应用于新应用程序的人提供了一个工具。通过回顾构建超振荡的数学方法，包括它们的考虑因素和功能，我们为任何想要构建使用超振荡的设备的人提供了选择。超振荡具有内在的权衡：随着光斑尺寸的减小，其相对强度会随着高能边带的出现而降低。不同的方法为优化这些权衡的不同方面提供了解决方案，以适应不同的目的。尽管有许多实现超振荡的技术方法，但数学方法可以分为三种方法：直接设计超振荡函数、设计瞳孔滤光片和设计超振荡透镜。这种基于数学方法的分类用于强调应用程序之间方法的可移植性。它还强调了未来理论发展的领域，使科学和技术的界限在现实世界的应用中得到进一步的推动。
Superoscillations are making a growing impact on an ever-increasing number of real-world applications, as early theoretical analysis has evolved into wide experimental realisation. This is particularly true in optics: the first application area to have extensively embraced superoscillations, with much recent growth. This review provides a tool for anyone planning to expand the boundaries in an application where superoscillations have already been used, or to apply superoscillations to a new application. By reviewing the mathematical methods for constructing superoscillations, including their considerations and capabilities, we lay out the options for anyone wanting to construct a device that uses superoscillations. Superoscillations have inherent trade-offs: as the size of spot reduces, its relative intensity decreases as high-energy sidebands appear. Different methods provide solutions for optimising different aspects of these trade-offs, to suit different purposes. Despite numerous technological ways of realising superoscillations, the mathematical methods can be categorised into three approaches: direct design of superoscillatory functions, design of pupil filters and design of superoscillatory lenses. This categorisation, based on mathematical methods, is used to highlight the transferability of methods between applications. It also highlights areas for future theoretical development to enable the scientific and technological boundaries to be pushed even further in real-world applications.