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.
For what applications are plasmonic materials better than all-dielectric materials, and vice versa? Or 2D materials versus their bulk counterparts? How does the requisite bandwidth affect materials selection? Here, we use the complex-analytic properties of certain optical-response functions in conjunction with novel energy-conservation constraints to derive fundamental limits to near-field optical response for any material, over any bandwidth. We show that certain canonical geometries can approach the bounds at specific frequencies, while at many others there is significant opportunity for structured materials to surpass them by orders of magnitude. We map out a frequency-bandwidth phase space in which we identify optimal materials among plasmonic, all-dielectric, and 2D-material candidates, and we put forward a quantitative material figure of merit to stimulate new-materials discovery.
KEYWORDS: Near field, Near field optics, Nanophotonics, Photonic crystals, Metamaterials, Antennas, Optical testing, Biomedical optics, Thermography, Medical imaging
Near-field nanophotonics offers the promise of orders-of-magnitude enhancements for phenomena ranging from spontaneous-emission engineering to Casimir forces via zero-point quantum fluctuations. An increasing variety of approaches — photonic crystals, metamaterials, metasurfaces, antennas, and more — has underscored our lack of understanding as to how large these effects can be. We provide a general answer to this question, deriving the first sum rule for near-field optical response as well as general upper bounds for any bandwidth, i.e. power–bandwidth limits. Within such a unified framework valid for structures of arbitrary shape and size, we approach single-frequency limits as bandwidth goes to zero and the sum rule as bandwidth goes to infinity. Power–bandwidth limits are derived from energy-conservation principles and depend on the susceptibility at the frequency of interest, and the sum rule arises from the requirement of causality and only depends on susceptibility at zero frequency. We explore to what extent power–bandwidth bounds can be attained for real materials and how the sum rule can be realized for canonical geometries. We further prove a "monotonicity" theorem that enables us to bound the integrated frequency response of any complicated structure in terms of the response of simple geometries. Our framework provides a universal measure of intrinsic optical-response characteristics that helps identify optimal nanophotonic materials for any combination of frequency and bandwidth, leading to wide-ranging applications in medical imaging and thermophotovoltaics.
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