Fundamental bounds for scattering from absorptionless electromagnetic structures

Abstract

The ability to design the scattering properties of electromagnetic structures is of fundamental interest in optical science and engineering. While there has been great practical success applying local optimization methods to electromagnetic device design, it is unclear whether the performance of resulting designs is close to that of the best possible design. This question remains unsettled for absorptionless electromagnetic devices since the absence of material loss makes it difficult to provide provable bounds on their scattering properties. We resolve this problem by providing non-trivial lower bounds on performance metrics that are convex functions of the scattered fields. Our bounding procedure relies on accounting for a constraint on the electric fields inside the device, which can be provably constructed for devices with small footprints or low dielectric constrast. We illustrate our bounding procedure by studying limits on the scattering cross-sections of dielectric and metallic particles in the absence of material losses.

Trade-offs in absorption and scattering by nanophotonic structures

“…where W and W t are functionals associated with reactive (complex) power flow, see [6] for their explicit forms resembling (3), ( 4) and (7). Because the two constraints together enforce both real and imaginary components of the design region's material properties, we refer to this as the "prescribed materials" case and use a subscript Z to distinguish these results from the prescribed losses case.…”

“…To this end, bounds on single-frequency nanophotonic performance have been developed at varying levels of design constraint specificity, with more general bounds covering broader scenarios and more specific methods providing tighter physical limits for stricter design constraints. This categorization is not binary, and previous methods of deriving such bounds increase in specificity from shapeindependent bounds [4], shape-dependent bounds [5], and finally, shape-and material-dependent bounds [6][7][8][9][10]. Broadband performance bounds have also been established using sum rules [11] and assumptions regarding specific response profiles [12].…”

$\mathbb{T}$-Operator Limits on Optical Communication: Metaoptics, Computation, and Input-Output Transformations

“…Archi-tectures possessing impressive field-transformation capabilities have already been demonstrated, from free-space (grating) couplers [33,34] to beam steering [35,36] and polarization control [37,38], suggesting that large-scale optimization methods may allow scattering attributes to be tailored to a far greater degree than what has been seen in past intuition-based designs. Simultaneously, ramifying from the core ideas of Lagrange duality and interpreting physical relations as optimization constraints expounded below [39][40][41][42], a string of recent articles on improved bounds for scattering phenomena (including radiative heat transfer [32], absorbed power [43], scattered power [44], and Purcell enhancement [45]) have shown that, in some cases, only modest improvements over standard designs are even hypothetically attainable [44][45][46][47][48][49][50][51][52][53].…”

Computational bounds to light-matter interactions via local conservation laws

“…Underlying all of these results is one or two energy-conservation laws, arising in various formulations of Maxwell's equations. Additional bounds have been identified via Lagrangian duality [43,44] or physical ap-proximations [45][46][47]. Yet there are pivotal applications for which all of these approaches either do not apply or offer trivial bounds.…”