Fundamental limits to radiative heat transfer: Theory

Abstract

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.The concept of a blackbody, derived from electromagnetic reciprocity (or detailed balance), has provided a benchmark of the largest emission rates that can be achieved by a heated object: through nanoscale texturing, gray objects can be designed in myriad ways to mimic the response of a blackbody at selective wavelengths [1-3], with implications for a variety of technologies, including high-efficiency solar cells, selective emitters, and thermal sensors [4]. Over the past few decades, much effort has gone toward understanding analogous limits to enhancements of near-field radiative heat transfer (RHT) [5][6][7][8], supported by a rich and growing number of experimental [9-12] and theoretical [13][14][15][16][17] investigations, and motivated by potential applications to thermophotovoltaics [18,19], nanoscale cooling [20], and thermal microscopy [21,22]. A key principle underlying further near-field RHT enhancements is the use of materials supporting bound (plasmon and phonon) polaritons in the infrared, where the Planck distribution peaks at typical temperatures probed in experiments. This leads to strong subwavelength responses tied to corresponding enhancements in the density of states [23][24][25][26]; consequently, the amplified near-field RHT spectrum exhibits a narrow lineshape, justifying focus on selective wavelengths. However, while the properties of such polaritons, particularly their resonance frequencies, associated densities of states, and scattering characteristics can be modified through nanoscale texturing, only recently have computational methods [14][15][16]27] arisen to model RHT between bodi...

Upper bounds on absorption and scattering

“…τ,l = R (1) τ,l (ka) radial functions [56,34], and υ = (τ, s, m, l) a multi-index with s, l ∈ {1, 2}, m ∈ {0, . .…”

“…As the field of nanophotonics becomes more mature, interest is shifting away from the analysis of simple systems (uniform waveguides, spheres, rods, etc.) and toward the synthesis of structures with engineered electromagnetic behavior, e.g., maximal absorption [1], directional emission [2,3], directed scattering [4,5], fluorescence diplexing [6], waveguide power division [7], field confinement [8], and waveguide diplexing (wavelength splitters) [9]. In order to generate novel geometries optimized for these particular design objectives, computational inverse design is often employed, see, e.g., [10,11] and the references therein.…”

“…In the interest of driving optimal design, there is a need to tighten this class of bounds by making them dependent on both material and the shape of the allocated design region. Shape dependent bounds adapted in this way for maximum radiative heat transfer are given in [1,19]. Shape dependent bounds for maximum absorption are given in [20] and for photonic design in [21].…”

Fundamental Limits to Radiative Heat Transfer: The Limited Role of Nanostructuring in the Near-Field

“…In a complementary article [1], we exploited algebraic properties of Maxwell's equations and fundamental principles such as electromagnetic reciprocity and passivity, to derive fundamental limits to radiative heat transfer applicable in near-through far-field regimes. The limits depend on the choice of material susceptibilities and bounding surfaces enclosing arbitrarily shaped objects.…”

“…In a complementary article [1], we derived new bounds that simultaneously account for material and geometric constraints as well as multiple scattering effects. These bounds, valid from the near-through far-field regimes, incorporate the dependence of the optimal modal response of each object on the other while simultaneously being constrained by passivity considerations in isolation.…”