We derive upper bounds to free-space concentration of electromagnetic waves, mapping out the limits to maximum 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 to existing demonstrations, and we use inverse design to discover metasurfaces operating near these new limits. We also demonstrate that our bounds may surprisingly describe maximum 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 3D printing.
Electrically tunable optical metasurfaces based on Liquid Crystal (LC) offer fast switching speed, low cost, and mature technological development, making it highly desirable for these applications. However, to date, all electrically tunable metasurfaces are designed at a single phase using physical intuition, without controlling the alternate phase and thus leading to limited switching efficiencies (~30 %) and small angular steering (15 degrees). Here, we use adjoint-based “inverse design” (equivalent to “backpropagation” in deep learning) to discover tunable metasurfaces with state-of-the-art efficiency (>80 %) and wide-angle steering (144 degrees). Inverse design can efficiently compute sensitivities with respect to arbitrarily many geometrical degrees of freedom, and thus is very effective for optimizing complicated photonic devices.
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