GlobalToperator bounds on electromagnetic scattering: Upper bounds on far-field cross sections

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 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 (Re [χ ] 0) exhibits a diluted (homogenized) effective medium scaling ∝|χ |/ Im [χ ]; 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 [χ ] > 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.

Universal Theory of Light Scattering of Randomly Oriented Particles: A Fluctuational-Electrodynamics Approach for Modeling of Light Transport in Disordered Nanostructures

“…The abstract format of these formulas provides a convenient landscape to explore the fundamental limits of scattering in random systems, as demonstrated in other studies of bounds in scattering and absorption. 24,32 In this context, for example, the formula of asymmetry parameter [Eq. (4c)] can be used to evaluate the limits for maximum forward or backward scattering under a set of particular constrains.…”

“…Under the Lippmann-Schwinger approach, the formulas of C abs and C sca for an incident field E i are given by (details in Supporting Information, Section S1.1): 24,32 C abs = 1…”

Inverse design in photonics by topology optimization: tutorial

“…When the performance of the structure is discussed, the authors propose using the word optimized, as well as providing a measure of the structure performance relative to theoretical limits or relative to references from the literature, cf. [34][35][36].…”

Fundamental Bounds to Time-Harmonic Quadratic Metrics in Electromagnetism: Overview and Implementation

“…Considerable computational resources are often spent in the topological optimization of electromagnetic structures [1], such as radiators [2], waveguide components [3], or cavities [4]. Nevertheless, the resulting designs are rarely compared to their physical bounds, i.e., those bounds which provide the best possible metric realization of a given problem [5,6,7,8,9,10,11,12,13] and which could be used to judge the performance of the optimizer.…”

“…This allows us to use the tools of convex optimization [14], a special class of mathematical optimization problems considered to be one of the most employable theories in computational mathematics [14]. Notable examples in this area of study are fundamental bounds to Q-factor [15], radiation efficiency [16,17,18], antenna gain [19,20,16], thermal radiation [11,21] scattering cross-sections [22,10,23] and their tradeoffs [24].…”