Upper Bounds on Scattering Processes and Metamaterial-Inspired Structures That Reach Them

Abstract

The physical limitations on time-harmonic scattering processes are investigated on the basis of the optical theorem. Previously derived least upper bounds on the total scattering and absorption cross-sections are obtained from it in a straightforward manner. In addition, it reveals a practical upper bound for the bistatic cross-section when evaluated in any direction. It is proved further that the maximum upper bound of the bistatic cross-section occurs in the forward scattering direction and that the corresponding upper bound for the backscattering direction is four times smaller than this maximum value. Metamaterialinspired electrically small antennas and scattering particles that approach these upper bounds are demonstrated. These examples numerically validate the derived upper bounds, as well as illustrate the important physical principles underlying them.

Maximum Gain, Effective Area, and Directivity

“…which is solved as a generalized eigenvalue problem analogously to Section II-A. The solution to this problem is greater or equal to (16) and taking its minimum value produces the dual problem [34] G ub,r ≈ 4π min…”

“…The trade-off between losses and directivity for a selfresonant antenna can be analyzed by separating the radiated power P r and losses P Ω in (16) giving the optimization problem maximize I H UI subject to I H XI = 0…”

“…Trade-off between maximum directivity and Q-factor for arbitrarily shaped antennas is presented in [15]. Upper bounds for scattering of metamaterialinspired structures are found in [16]. Recently, a composition of Huygens multipoles has been proposed [17] to increase the directivity.…”

Fundamental Limits to Near-Field Optical Response over Any Bandwidth

“…* hyungki.shim@yale.edu † owen.miller@yale.edu icant ongoing debate about whether a plasmonic or an all-dielectric approach is better, and in which scenarios 2D materials might be better than conventional bulk materials. Unlike all previous bounds and sum rules [24][25][26][27][28][29][30][31][32][33][34][35][36][37][38][39][40][41][42][43], the material figure of merit we derive here enables general quantitative answers to these questions. In a frequencybandwidth phase space, we map out which materials are optimal and where the critical thresholds, from dielectric to plasmonic and bulk to 2D, occur.…”

“…With suitable boundary conditions, a Hilbert transform (i.e., a Kramers-Kronig-like transform) then enables a sum rule, relating integrated response over all frequencies to that of a single frequency. Conversely, energy-conservation bounds-recognized primarily within the past decade [24,[36][37][38][39][40][41][42][43]60]-exploit the power-quantity-by-amplitude form in a different way. In writing a power quantity as the imaginary part of an amplitude, the amplitude itself is linear in the electromagnetic fields and/or currents (holding the incident field fixed).…”