We derive upper bounds to free-space concentration of electromagnetic waves, mapping out the limits to the maximal intensity for any spot size and optical-beam-shaping device. For sub-diffraction-limited optical beams, our bounds suggest the possibility for orders-of-magnitude intensity enhancements compared with existing demonstrations, and we use inverse design to discover metasurfaces operating near these new limits. We also demonstrate that our bounds may surprisingly describe maximal concentration defined by a wide variety of metrics. Our bounds require no assumptions about symmetry, scalar waves, or weak scattering, instead relying primarily on the transformation of a quadratic program via orthogonal-projection methods. The bounds and inverse-designed structures presented here can be useful for applications from imaging to three-dimensional printing.

中文翻译：

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电磁波的最大自由空间浓度

我们推导了电磁波自由空间集中的上限，将任何光点大小和光束整形设备的最大强度的限制都标出。对于亚衍射极限光束，我们的边界表明与现有演示相比，可以增强数量级的强度，并且我们使用逆设计来发现在这些新极限附近工作的超颖表面。我们还证明了我们的界限可能令人惊讶地描述了由各种指标定义的最大浓度。我们的边界不需要关于对称性，标量波或弱散射的任何假设，而是主要依靠通过正交投影方法对二次程序进行转换。