Global<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi mathvariant="double-struck">T</mml:mi></mml:math>operator bounds on electromagnetic scattering: Upper bounds on far-field cross sections
Sean Molesky, Pengning Chao, Weiliang Jin, Alejandro W. Rodriguez
Abstract
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 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 (Re [ ] 0) exhibits a diluted (homogenized) effective medium scaling | |/ Im [ ]; 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 (Re [ ] > 0) shows the same material dependence as Rayleigh scattering.