Ideal near-field thermophotovoltaic cells

We ask the question, what are the ideal characteristics of a near-field thermophotovoltaic cell? Our search leads us to a reformulation of near-field radiative heat transfer in terms of the joint density of electronic states of the emitter-absorber pair in the thermophotovoltaic system. This form reveals that semiconducting materials with narrowband absorption spectra are critical to the energy conversion efficiency. This essential feature is unavailable in conventional bulk semiconductor cells but can be obtained using low dimensional materials. Our results show that the presence of matched van Hove singularities resulting from quantum-confinement in the emitter and absorber of a thermophotovoltaic cell boosts both the magnitude and spectral selectivity of radiative heat transfer; dramatically improving energy conversion efficiency. We provide a model near-field thermophotovoltaic system design making use of this idea by employing the van Hove singularities present in carbon nanotubes. Shockley-Queisser analysis shows that the predicted heat transfer characteristics of this model device are fundamentally better than existing thermophotovoltaic designs. Our work paves the way for the use of quantum dots, quantum wells, two-dimensional semiconductors, semiconductor nanowires and carbon nanotubes as future materials for thermophotovoltaic cells.Comment: 9 pages, 5 figure

High temperature epsilon-near-zero and epsilon-near-pole metamaterial emitters for thermophotovoltaics

We propose a method for engineering thermally excited far field electromagnetic radiation using epsilon-near-zero metamaterials and introduce a new class of artificial media: epsilon-near-pole metamaterials. We also introduce the concept of high temperature plasmonics as conventional metamaterial building blocks have relatively poor thermal stability. Using our approach, the angular nature, spectral position, and width of the thermal emission and optical absorption can be finely tuned for a variety of applications. In particular, we show that these metamaterial emitters near 1500 K can be used as part of thermophotovoltaic devices to surpass the full concentration Shockley-Queisser limit of 41%. Our work paves the way for high temperature thermal engineering applications of metamaterials.Comment: 15 pages, 8 figure

Broadband super-Planckian thermal emission from hyperbolic metamaterials

We develop the fluctuational electrodynamics of metamaterials with hyperbolic dispersion and show the existence of broadband thermal emission beyond the black body limit in the near field. This arises due to the thermal excitation of unique bulk metamaterial modes, which do not occur in conventional media. We consider a practical realization of the hyperbolic metamaterial and estimate that the effect will be observable using the characteristic dispersion (topological transitions) of the metamaterial states. Our work paves the way for engineering the near-field thermal emission using metamaterials

Hierarchical Mean-Field T\mathbb{T} Operator Bounds on Electromagnetic Scattering: Upper Bounds on Near-Field Radiative Purcell Enhancement

We show how the central equality of scattering theory, the definition of the $\mathbb{T}$ operator, can be used to generate hierarchies of mean-field constraints that act as natural complements to the standard electromagnetic design problem of optimizing some objective with respect to structural degrees of freedom. Proof-of-concept application to the problem of maximizing radiative Purcell enhancement for a dipolar current source in the vicinity of a structured medium, an effect central to many sensing and quantum technologies, yields performance bounds that are frequently more than an order of magnitude tighter than all current frameworks, highlighting the irreality of these models in the presence of differing domain and field-localization length scales. Closely related to domain decomposition and multi-grid methods, similar constructions are possible in any branch of wave physics, paving the way for systematic evaluations of fundamental limits beyond electromagnetism

Material Scaling and Frequency-Selective Enhancement of Near-Field Radiative Heat Transfer for Lossy Metals in Two Dimensions via Inverse Design

The super-Planckian features of radiative heat transfer in the near-field are known to depend strongly on both material and geometric design properties. However, the relative importance and interplay of these two facets, and the degree to which they can be used to ultimately control energy flow, remains an open question. Recently derived bounds suggest that enhancements as large as $|\chi|^4 \lambda^{2} / \left(\left(4\pi\right)^{2} \Im\left[\chi\right]^{2} d^{2}\right)$ are possible between extended structures (compared to blackbody); but neither geometries reaching this bound, nor designs revealing the predicted material ($\chi$) scaling, have been previously reported. Here, exploiting inverse techniques, in combination with fast computational approaches enabled by the low-rank properties of elliptic operators for disjoint bodies, we investigate this relation between material and geometry on an enlarged space structures. Crucially, we find that the material proportionality given above does indeed emerge in realistic structures. In reaching this result, we also show that (in two dimensions) lossy metals such as tungsten, typically considered to be poor candidate materials for strongly enhancing heat transfer in the near infrared, can be structured to selectively realize flux rates that come within $50\%$ of those exhibited by an ideal pair of resonant lossless metals for separations as small as $2\%$ of a tunable design wavelength.Comment: 6 pages, 2 figure

Maximum Electromagnetic Local Density of States via Material Structuring

The electromagnetic local density of states (LDOS) is crucial to many aspects of photonics engineering, from enhancing emission of photon sources to radiative heat transfer and photovoltaics. We present a framework for evaluating upper bounds on LDOS in structured media that can handle arbitrary bandwidths and accounts for critical wave scattering effects with no heuristic approximations. The bounds are solely determined by the bandwidth, material susceptibility, and device footprint, with no assumptions on geometry. We derive an analytical expression for the maximum LDOS consistent with the conservation of energy across the entire design domain, which upon benchmarking with topology-optimized structures is shown to be nearly tight for large devices. Novel scaling laws for maximum LDOS enhancement are found: the bounds saturate to a finite value with increasing susceptibility and scale as the quartic root of the bandwidth for semi-infinite structures made of lossy materials, with direct implications on material selection and design applications.Comment: Corrected minor typos throughout paper; corrected mislabel of inverse designs in Figure 1; added full Supplementary Information; added acknowledgment

T\mathbb{T}-operator bounds on angle-integrated absorption and thermal radiation for arbitrary objects

We derive fundamental per-channel bounds on angle-integrated absorption and thermal radiation for arbitrary bodies---for any given material susceptibility and bounding region---that simultaneously encode both the per-volume limit on polarization set by passivity and geometric constraints on radiative efficiencies set by finite object sizes through the scattering $\mathbb{T}$-operator. We then analyze these bounds in two practical settings, comparing against prior limits as well as near optimal structures discovered through topology optimization. Principally, we show that the bounds properly capture the physically observed transition from the volume scaling of absorptivity seen in deeply subwavelength objects (nanoparticle radius or thin film thickness) to the area scaling of absorptivity seen in ray optics (blackbody limits).Comment: 9 pages including appendices, 2 figures, 1 tabl

Fundamental limits to attractive and repulsive Casimir--Polder forces

We derive upper and lower bounds on the Casimir--Polder force between an anisotropic dipolar body and a macroscopic body separated by vacuum via algebraic properties of Maxwell's equations. These bounds require only a coarse characterization of the system---the material composition of the macroscopic object, the polarizability of the dipole, and any convenient partition between the two objects---to encompass all structuring possibilities. We find that the attractive Casimir--Polder force between a polarizable dipole and a uniform planar semi-infinite bulk medium always comes within 10% of the lower bound, implying that nanostructuring is of limited use for increasing attraction. In contrast, the possibility of repulsion is observed even for isotropic dipoles, and is routinely found to be several orders of magnitude larger than any known design, including recently predicted geometries involving conductors with sharp edges. Our results have ramifications for the design of surfaces to trap, suspend, or adsorb ultracold gases.Comment: 6 pages, 3 figure

Fundamental limits to radiative heat transfer: theory

Near-field radiative heat transfer between bodies at the nanoscale can surpass blackbody limits on thermal radiation by orders of magnitude due to contributions from evanescent electromagnetic fields, which carry no energy to the far-field. Thus far, principles guiding explorations of larger heat transfer beyond planar structures have assumed utility in surface nanostructuring, which can enhance the density of states, and further assumed that such design paradigms can approach Landauer limits, in analogy to conduction. We derive fundamental shape-independent limits to radiative heat transfer, applicable in near- through far-field regimes, that incorporate material and geometric constraints such as intrinsic dissipation and finite object sizes, and show that these preclude reaching the Landauer limits in all but a few restrictive scenarios. Additionally, we show that the interplay of material response and electromagnetic scattering among proximate bodies means that bodies which maximize radiative heat transfer actually maximize scattering rather than absorption. Finally, we compare our new bounds to existing Landauer limits, as well as limits involving bodies maximizing far-field absorption, and show that these lead to overly optimistic predictions. Our results have ramifications for the ultimate performance of thermophotovoltaics and nanoscale cooling, as well as related incandescent and luminescent devices.Comment: 12 pages including appendices, 1 figure; SM and PSV contributed equall

Fundamental Limits on Second Harmonic Generation

Recent advances in fundamental performance limits for power quantities are proving to provide a powerful theoretical tool for understanding the optimization of wave phenomena. To date, however, in any approach allowing power conservation to be enforced locally, the linearity of the wave equation plays a critical role. In this manuscript, we generalize the current quadratically constrained quadratic program framework for evaluating linear photonics limits to incorporate nonlinear processes under the undepleted pump approximation. Via the exemplary objective of enhancing second harmonic generation in a (free-form) wavelength-scale structure, we illustrate a model constraint scheme that can be used in conjunction with standard convex relaxations to bound performance in the presence of nonlinear dynamics. Representative bounds are found to anticipate features observed in optimized structures discovered via computational inverse design. Extensions of our results to other frequency-conversion processes, including Raman scattering and four-wave mixing, are straightforward.Comment: 10 pages, 4 figure