Tailoring photonic metamaterial resonances for thermal radiation
© Bermel et al; licensee Springer. 2011
Received: 23 May 2011
Accepted: 6 October 2011
Published: 6 October 2011
Selective solar absorbers generally have limited effectiveness in unconcentrated sunlight, because of reradiation losses over a broad range of wavelengths and angles. However, metamaterials offer the potential to limit radiation exchange to a proscribed range of angles and wavelengths, which has the potential to dramatically boost performance. After globally optimizing one particular class of such designs, we find thermal transfer efficiencies of 78% at temperatures over 1,000°C, with overall system energy conversion efficiencies of 37%, exceeding the Shockley-Quiesser efficiency limit of 31% for photovoltaic conversion under unconcentrated sunlight. This represents a 250% increase in efficiency and 94% decrease in selective emitter area compared to a standard, angular-insensitive selective absorber.
PACS: 42.70.Qs; 81.05.Xj; 78.67.Pt; 42.79.Ek
Solar thermophotovoltaic (TPV) systems offer a distinct approach for converting sunlight into electricity [1–6]. Compared to standard photovoltaics, sunlight is not absorbed directly by a photovoltaic material, but is instead absorbed by a selective absorber. That selective absorber is thermally coupled to a selective emitter, which then thermally radiates electromagnetic radiation. The key challenge to making such a system efficient is achieving a relatively high temperature. Generally, this implies high optical concentrations . However, one could consider whether there would be another way to concentrate heat in the selective absorber--without using optical concentrators at all. The key idea here is to replace the effect of optical concentration using a different method.
The most plausible approach to thermal concentration is angular selectivity--only allowing light to be absorbed within a small range of angles. The reason is that the apparent size of the sun is only a small fraction of the sky--approximately 1 part in 46,200 . Several researchers have considered this in the context of photovoltaics  and thermophotovoltaics [6, 10]. Metamaterials, such as photonic crystals, offer unprecedented control over wavelength- and angle-dependent absorptivity. In such systems, photon resonances can be tailored to target particular frequencies and conserved wavevectors to provide pinpoint control over thermal emission. Such an approach can be applied to create selective solar absorbing surfaces for applications such as solar thermal electricity, solar thermoelectrics, and solar thermophotovoltaics. The critical figure of merit is generally the fraction of incident solar radiation capable of being captured as heat. Typically, modest infrared emissivities put strict upper limits on the overall thermal transfer efficiency possible for the unconcentrated AM1.5 solar spectrum. However, carefully designed photonic metamaterials can strongly suppress thermal losses in the infrared.
where I m and V m are the current and voltage of the thermophotovoltaic diode at the maximum power point, C is the concentration in suns relative to the solar constant I s (usually taken to be 1 kW/m2), and A s is the surface area of the selective solar absorber. This system can conceptually be decomposed into two halves: the selective solar absorber front end and the selective emitter plus TPV diode back end. Each half can be assigned its own efficiency: η t and η p , respectively.
where B is the window transmissivity, is the spectrally averaged absorptivity, is the spectrally averaged emissivity, and σ is the Stefan-Boltzmann constant.
where and A E are the effective emissivity and area of the selective emitter, respectively.
2 Results and discussion
It was found that although in principle solar thermophotovoltaic systems in unconcentrated sunlight can exceed efficiencies of 42%, achieving such performance requires suppression of emissivities to unreasonably low levels. Conventional materials with undesired emissivities of 0.05 display much lower efficiencies of 10.5%. However, most of the theoretically allowed performance can be restored by introducing angular selectivity of the assumed form in Equation 5, with up to 37% overall system efficiency. The system also acts as a thermal concentrator, with receiver areas 20 times larger than the emitter areas. Finally, we considered 2D arrays of nanoscale cylindrical holes in single crystal tungsten as a candidate metamaterial for angle-selective operation, and found the optimal design parameters to be a period of 800 nm, a radius of 380 nm, and a depth of 3.04 μ m, with a thermal transfer efficiency of 75.0% in unconcentrated sunlight at 400 K.
Simulations of electromagnetic properties were conducted following the same methods as outlined in . We employ a finite difference time-domain (FDTD) simulation  implemented via a freely available software package developed at MIT, known as MEEP . A plane wave is sent from the normal direction and propagated through space. On each grid point of a flux plane defined at the front and back of the computational cell, the electric and magnetic fields are Fourier-transformed via integration with respect to preset frequencies at each time-step. At the end of the simulation, the Poynting vector is calculated for each frequency and integrated across each plane, which yields the total transmitted and reflected power at each frequency . The dispersion of tungsten is captured via a Lorentz-Drude model . Apart from the approximations of material dispersions and grid discretization, these calculation methods are exact.
The emissivity of each structure can be calculated from the absorptivity computed above via Kirchhoff's law of thermal radiation, which states that the two quantities must be equal at every wavelength for a body in thermal equilibrium .
The system efficiency is calculated from numerical integration (via the trapezoidal rule) of Eqs. 3 and 4, and taking their product as in Equation 2. It can then be globally optimized through the application of the multi-level single-linkage (MLSL), derivative-based algorithm using a low-discrepancy sequence (LDS) . This algorithm executes a quasi-random (LDS) sequence of local searches using constrained optimization by linear approximation (COBYLA) , with a clustering heuristic to avoid multiple local searches for the same local minimum. We verified that other global search algorithms, such as DIRECT-L , yield similar results. This ability to directly utilize and compare multiple optimization packages on the same problem is provided by the NLopt package, written by Prof. Steven G. Johnson and freely available at http://ab-initio.mit.edu/nlopt.
The authors thank Nenad Miljkovic, Youngsuk Nam, and Evelyn Wang. This work was supported by the MRSEC Program of the National Science Foundation under award number DMR-0819762 (MG), the MIT S3TEC Energy Research Frontier Center of the Department of Energy under Grant No. DE-SC0001299 (YY), and the Army Research Office through the Institute for Soldier Nanotechnologies under Contract Nos. DAAD-19-02-D0002 and W911NF-07-D0004 (PB, IC).
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