Global $\mathbb{T}$ operator bounds on electromagnetic scattering: Upper bounds on far-field cross sections

Abstract

We present a method based on the scattering $\mathbb{T}$ operator, and conservation of net real and reactive power, to provide physical bounds on any electromagnetic design objective that can be framed as a net radiative emission, scattering or absorption process. Application of this approach to planewave scattering from an arbitrarily shaped, compact body of homogeneous electric susceptibility $\chi$ is found to predictively quantify and differentiate the relative performance of dielectric and metallic materials across all optical length scales. When the size of a device is restricted to be much smaller than the wavelength (a subwavelength cavity, antenna, nanoparticle, etc.), the maximum cross section enhancement that may be achieved via material structuring is found to be much weaker than prior predictions: the response of strong metals ($\mathrm{Re}[\chi ]<0$) exhibits a diluted (homogenized) effective medium scaling $\propto |\chi |/\mathrm{Im}[\chi ]$; below a threshold size inversely proportional to the index of refraction (consistent with the half-wavelength resonance condition), the maximum cross section enhancement possible with dielectrics ($\mathrm{Re}[\chi ]>0$) shows the same material dependence as Rayleigh scattering. In the limit of a bounding volume much larger than the wavelength in all dimensions, achievable scattering interactions asymptote to the geometric area, as predicted by ray optics. For representative metal and dielectric materials, geometries capable of scattering power from an incident plane wave within an order of magnitude (typically a factor of two) of the bound are discovered by inverse design. The basis of the method rests entirely on scattering theory, and can thus likely be applied to acoustics, quantum mechanics, and other wave physics.

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• Heuristic Methods and Performance Bounds for Photonic Design
• Hierarchical Mean-Field $\mathbb{T}$ Operator Bounds on Electromagnetic Scattering: Upper Bounds on Near-Field Radiative Purcell Enhancement
• Trace Expressions and Associated Limits for Non-Equilibrium Casimir Torque
• Maximum Radiation Efficiency of Arbitrarily-Shaped Implantable Antennas
• Trade-offs in absorption and scattering by nanophotonic structures
• Conservation-law-based global bounds to quantum optimal control
• Towards Maximum Optical Efficiency of Ensembles of Colloidal Nanorods
• Tight Bounds on the Effective Complex Permittivity of Isotropic Composites and Related Problems
• Fundamental Bounds on the Performance of Monochromatic Passive Cloaks
• Can photonic heterostructures provably outperform single-material geometries?