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 num...

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实现超振动：数学工具及其应用综述

随着早期的理论分析已发展为广泛的实验实现，超级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：这是第一个广泛使用超振荡的应用领域，并且最近有了很大的增长。这篇综述为计划扩大已经使用了超级振荡的应用程序中的边界或将超级振荡应用于新应用程序的任何人提供了一种工具。通过回顾构造超级振荡的数学方法，包括它们的考虑和功能，我们为想要构造使用超级振荡的器件的任何人提供了选择。超级振荡具有内在的取舍：随着光斑尺寸的减小，它的相对强度随着高能边带的出现而降低。不同的方法提供了优化这些折衷方案的不同方面的解决方案，以适应不同的目的。尽管有...