Computational bounds to light-matter interactions via local conservation laws

Abstract

We develop a computational framework for identifying bounds to light-matter interactions, originating from polarization-current-based formulations of local conservation laws embedded in Maxwell's equations. We propose an iterative method for imposing only the maximally violated constraints, enabling rapid convergence to global bounds. Our framework can identify bounds to the minimum size of any scatterer that encodes a specific linear operator, given only its material properties, as we demonstrate for the optical computation of a discrete Fourier transform. It further resolves bounds on far-field scattering properties over any arbitrary bandwidth, where previous bounds diverge.

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

“…In summary, we have shown that recently developed methods for calculating limits on sesquilinear electromagnetic objectives [42,45,[51][52][53], can be applied to a wide variety of design problems, including spatial multiplexing [22][23][24], metaoptics [92][93][94][95], linear computation [25][26][27] and light extraction [96][97][98][99]. Employing the language of communication theory, this program stands as a significant extension of prior work on channel-based electromagnetic limits [8,30,[55][56][57][58][59][60].…”

“…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].…”

“…During this brief overview, two innovations necessary for handling generic input-output formulations are introduced: a further generalization on the variety of operator constraints that can be imposed based on the definition of the T operator, beyond the possibility of local clusters examined in Refs. [45,51,52], and a generalization of the type of vector image constraints that should be usually considered, as required to enforce that every transformation in an input-output set references the same underlying structure. Finally, Sec.…”

Quasinormal Coupled Mode Theory

“…There is an emerging interest in identifying fundamental limits to response in such structures [44,64], and the QCMT framework could be ideal for identifying new bounds via the convenient mode/channel structure of the underlying equations. The QCMT framework could be paired with known sum rules on modal densities [65,66], or used in tandem with energy-conservation constraints [67][68][69] to identify the extreme limits of what is possible.…”

Bounds on Efficiency Metrics in Photonics

“…To answer this question, we need to determine a design's suboptimality with respect to some performance metric. Recently, there has been a large amount of work in this area, attempting to find bounds of this form for a variety of metrics, including mode volume [9], free space concentration [10], integral overlap [11,12], among many others [13][14][15][16][17][18][19][20].…”