Maximal single-frequency electromagnetic response

Abstract

Modern nanophotonic and meta-optical devices utilize a tremendous number of structural degrees of freedom to enhance light–matter interactions. A fundamental question is how large such enhancements can be. We develop an analytical framework to derive upper bounds to single-frequency electromagnetic response, across near- and far-field regimes, for any materials, naturally incorporating the tandem effects of material- and radiation-induced losses. Our framework relies on a power-conservation law for the polarization fields induced in any scatterer. It unifies previous theories on optical scattering bounds and reveals new insight for optimal nanophotonic design, with applications including far-field scattering, near-field local-density-of-states engineering, optimal wavefront shaping, and the design of perfect absorbers. Our bounds predict strikingly large minimal thicknesses for arbitrarily patterned perfect absorbers, ranging from 50–100 nm for typical materials at visible wavelengths to micrometer-scale thicknesses for polar dielectrics at infrared wavelengths. We use inverse design to discover metasurface structures approaching the minimum-thickness perfect-absorber bounds.

Physical limits on electromagnetic response

“…When P is set to the domain identity I Ω , the first relation of Eq. ( 10) is a statement of the conservation of real power within the domain [40]: the power drawn by the polarization current from the field, the inner product Im E i T , must equal the sum of the power lost by the polarization current to material extinction [135],…”

“…[39-44, 111, 150, 151]. As highlighted by the expositive examples below, the extent to which these limits incorporate various physical phenomena may be tuned by selecting, either by intuition or algorithm [40], the collection of constraints (P k projections) that are concurrently imposed, and, in contrast to many traditional approaches to limits, where individual components of an expression are bounded and then subsequently summed or composed to form a global bound, the optimization framework of Eq. ( 13) properly describes interactions between constraints.…”

“…We then focus our discussion on an emerging general methodology for evaluating photonic design bounds based on optimization theory and conservation principles that follow either directly from Maxwell's equations or the identities of scattering theory. Originally developed as an instrument for investigating maximal scattering cross section limits [38][39][40], the framework is applicable to a broad range of design problems where the objective can be expressed as a quadratic function of the fields [41][42][43]. The constraints have clear physical meaning, limiting both the amplitude of the polarization response, important to power transfer, and the extent that the phase of the polarization response can be modified, with consequences on the engineering of resonances.…”

A place for two-dimensional plasmonics in electromagnetic wave detection

“…Interplay of Ohmic and radiative damping was recently studied for 2d plasmons in discs [45], but practically important absorption cross section were not analysed. General constraints on extinction and absorption were recently derived in [46], but applications were demonstrated only for bulk plasmonic structures. The absorption cross sections limited by material loss in 2DES were analysed in [47], but developed quasistatic theory did not reproduce the dipole cross-section limit.…”

Gradient descent globally solves average-case non-resonant physical design problems

“…One prominent approach to answering this question has been to provide lower bounds on the cost function that captures the device performance and is being optimized -while the optimization problem itself is non-convex and hard to solve globally, such bounds can often be computed efficiently by solving a convex problem. Several approaches to setting up this convex problem and calculating these lower bounds using physically motivated convex relaxations [22][23][24][25][26] or by an application of Lagrange duality [27][28][29][30] have been recently pursued. In many problems of interest, these lower bounds, computed numerically, are reasonably close to the locally optimized results and thus indicate that the design is near globallyoptimal [31,32].…”