There has been substantial interest in miniaturizing optical systems by flat optics. However, one essential optical component, free space, fundamentally cannot be substituted with conventional local flat optics with space-dependent transfer functions, since the transfer function of free space is momentum-dependent instead. Overcoming this difficulty is important to achieve the utmost miniaturization of optical systems. In this work, we show that free space can be substituted with nonlocal flat optics operating directly in the momentum domain. We derive the general criteria for an optical device to replace free space and provide two concrete designs of photonic crystal slab devices. Such devices can substitute much thicker free space. Our work paves the way for the utmost miniaturization of optical systems using a combination of local and nonlocal flat optics.

中文翻译：

---

利用非本地平面光学器件挤压自由空间

人们非常关注通过平面光学器件使光学系统小型化。然而，一种基本的光学组件，自由空间，基本上不能用具有依赖于空间的传递函数的常规局部平面光学器件来代替，因为自由空间的传递函数是与动量相关的。克服这一困难对于实现光学系统的最大程度的小型化很重要。在这项工作中，我们证明了可用直接在动量域中运行的非局部平面光学器件代替自由空间。我们推导了光学器件替代自由空间的一般标准，并提供了光子晶体平板器件的两种具体设计。这样的设备可以替代更厚的自由空间。