Global T operator bounds on electromagnetic scattering: Upper bounds on far-field cross sections

Sean Molesky, Pengning Chao, Weiliang Jin, Alejandro W. Rodriguez

Research output: Contribution to journalArticlepeer-review

27 Scopus citations


We present a method based on the scattering 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 plane-wave scattering from an arbitrarily shaped, compact body of homogeneous electric susceptibility χ 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 (Reχâ‰0) exhibits a diluted (homogenized) effective medium scaling âχ/Imχ; 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 (Reχ>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.

Original languageEnglish (US)
Article number033172
JournalPhysical Review Research
Issue number3
StatePublished - Jul 2020

All Science Journal Classification (ASJC) codes

  • General Physics and Astronomy


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