From Solar Cells to Ocean Buoys: Wide-Bandwidth Limits to Absorption by Metaparticle Arrays

Abstract

In this paper, we develop an approximate wide-bandwidth upper bound to the absorption enhancement in arrays of metaparticles, applicable to general wave-scattering problems and motivated here by ocean-buoy energy extraction. We show that general limits, including the well-known Yablonovitch result in solar cells, arise from reciprocity conditions. The use of reciprocity in the stochastic regime leads us to a corrected diffusion model from which we derive our main result: an analytical prediction of optimal array absorption that closely matches exact simulations for both random and optimized arrays under angle/frequency averaging. This result also enables us to propose and quantify approaches to increase performance through careful particle design and/or using external reflectors. We show in particular that the use of membranes on the water's surface allows substantial enhancement.

Limits to surface-enhanced Raman scattering near arbitrary-shape scatterers

“…Using the same method as in Ref. 28, we can relate the near field of the scattering problem E(x 0 ) to the far-field component T p 00 along −k 0 in the emission problem through [SI-2]:…”

“…Combined with the LDOS limit, we then obtain a bound on the Raman enhancement. We also obtain a second bound for the concentration problem using reciprocity in the case of a periodic structure (a similar approach was used to derive the Yablonovitch limit for solar cells from LDOS enhancement 28 ). By comparing the two concentration bounds as a function of period, we obtain a tighter bound for periodic structures.…”

Hydrodynamics of large wave energy converter arrays with random configuration variations

“…Theoretical bounds to extraction in large randomly spaced WEC arrays with multiple rows were studied by Benzaouia et al. (2019). Employing the radiative transfer equation and the diffusion assumption, they obtained theoretical expressions for the average gain from the isolated body performance and average spatial parameters of the array.…”

Maximal single-frequency electromagnetic response

“…[19], it may be possible to do so through generalized quadratic constraints based on causality. Finally, a key variable missing from conservation-law-based approaches to bounds is the refractive index of a transparent medium, which appears in bounds pertaining to the broadband absorption of sunlight [97][98][99][100], but otherwise do not appear in any of the bounds referenced here. Accounting for refractive index may require a unification of conservation-law approaches with, perhaps, those based on Lagrangian duality [101].…”