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

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Abstract

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.

© 2012 Optical Society of America

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Figures (8)

Fig. 1. :
Fig. 1. : (A) Polarization averaged emissivity of a 100 nm thick film of ENZ material, following a Drude model, on a perfectly reflecting backing. The spectrally narrow peak is the ENZ resonance. The broad blur at shorter wavelengths is the onset of impedance matching in the Re(ε) ≈ 1 range. As loss is increased, these regions blend together and the magnitude of the emissivity tends towards unity in a broad spectral range. The inset shows the relative dielectric constant used. (B) Polarization averaged emissivity of a 100 nm thick material film in the ENP regime, based on a Lorentz model, on a perfectly reflecting backing. The component loss considered is identical to that used in (a): γA = γB. Again, the inset shows the relative dielectric constants used to calculate the polarization averaged emissivity. The spectrally sharp behavior shown here makes ENP type resonances a promising candidate for TPV applications.
Fig. 2. :
Fig. 2. : (A) Schematic of a multilayer metamaterial created by interlacing layers of optical metal and dielectric. (B) Schematic of a nanowire metamaterial created by embedding metallic nanowires in a host dielectric matrix. Both structures can be created with current fabrication techniques [26, 31].
Fig. 3
Fig. 3 Multilayer ENZ emitter: (A) Effective medium theory calculation of the emissivity of a planar multilayer structure. The metamaterial is composed of twenty unit cells of 5 nm thick tantalum (modeled by a Drude relation) and 45 nm of titanium dioxide (ε = 7.5) on optically thick tantalum. Both materials can be deposited by atomic layer deposition [29]. The inset shows the effective medium parameters as functions of wavelength. The ENP resonance is located outside of the plotted area and has little effect due to the spectral power distribution of a blackbody. (B) Transfer matrix calculation of the multilayer structure which shows excellent agreement with EMT. The inset shows the relative emission strength of an ideal blackbody as function of wavelength. The arrows denote the cutoffs of the emissivity plots.
Fig. 4
Fig. 4 Nanowire ENP emitter: (A) Comparison of the polarization averaged emissivity of a 280 nm thick metamaterial emitter making use of a host matrix of silicon (assumed to be a constant dielectric) and 20 nm diameter titanium nitride nanowires in a 120 nm square unit cell on an optically thick tantalum backing. The two curves compare emissivity as calculated by effective medium theory and finite difference time domain simulation (Lumerical) at normal incidence. The insets show the same comparison for s- and p-polarized emissivity over a compressed wavelength range of 1.5 to 2.1 μm at a polar angle of 50 degrees. Note the excellent agreement between EMT and the full numerical simulation. (B) Polarization averaged emissivity of the nanowire system described in (A) calculated using EMT. Emission peaks occurring below the designed emission are known to be part of the Bragg scattering regime [33]. These peaks have little effect in application due to low emitted power at wavelengths shorter than 800 nm for bodies cooler than 3000 K. The inset shows the effective medium parameters as functions of wavelength. The spectrally narrow, omnidirectional nature of the ENP emissivity peak is nearly ideal for use as an emitter in a TPV device.
Fig. 5
Fig. 5 Cross-sectional view of the narrow isofrequency surfaces of the metamaterial in the ENZ regime. The spherical isofrequency surface corresponds to vacuum. (A) As the perpendicular permittivity nears zero from the negative side, the dispersion relation inside the metamaterial becomes a narrow hyperboloid. (B) Ellipsoidal isofrequency surface as the perpendicular effective medium constant approaches ENZ from the positive side. Note that only waves at near-normal incidence from vacuum penetrate the metamaterial which are immediately absorbed due to the ENZ resonance. Furthermore, the large impedance mismatch at higher angles leads to high reflections. This results in highly directional emissivity patterns. (C) P-polarized emissivity plot for a 450 nm thick metamaterial emitter consisting of a host matrix of aluminum oxide (Al2O3) embedded with 15 nm diameter silver nanowires in a 115 nm square unit cell using the effective medium approach. The angularly sharp emission near normal incidence around 1.075 μm is usable for applications requiring coherent thermal radiation. The inset shows a polar plot of the emissivity along the 1.075 μm line. The secondary bands of high emissivity around the ENZ region is due to the impedance matching behavior in the ellispoidal/hyperboloidal isofrequency regime which moves to higher angles as the |Re(ε) → 0| condition is relaxed.
Fig. 6
Fig. 6 (A) Drude models of the optical properties of TiN and AZO based on the data presented in [38, 40]. (B) Fine-tuning of the ENP metamaterial resonance by altering the fill fraction of metal in the unit cell. In this plot the titanium nitride/silicon metamaterial system described in Fig. 4 is used. Both AZO and TiN achieve thermally stable plasmonic behavior in the near infrared (Table Sec.4).
Fig. 7
Fig. 7 (A) Comparison of the ultimate efficiency of a titanium nitride metamaterial emitter (Fig. 4) to that of a blackbody for a 0.71 eV material bandgap, corresponding to GaSb. Based on bulk material parameters, the metamaterial emitter will be thermally stable up to 1650 K. (B) Comparison of the angularly averaged spectral emission characteristics between the titanium nitride metamaterial design, an ideal blackbody, and an emitter which maximizes the efficiency of energy conversion at 1500 K. The large lobe of the metamaterial ENP resonance closely matches the position and magnitude of the emitter producing the highest TPV device efficiency.
Fig. 8
Fig. 8 (A) Theoretical efficiency of three TPV devices taking into account all discussed effects. The cell parameters of the Ta/TiO2 multilayer and TiN/Si nanowire systems are the same as in Fig. 3 and Fig. 4. The third system utilizes 250 nm long, 20 nm diameter AZO rods in a 125 nm square Al2O3 matrix, set on an optically thick tantalum backing, and an InGaAs photovoltaic cell with bandgap set at 2100 nm. In these plots the efficiency of heating the source is not included. However, due to the tantalum backing included in all designs, the performance of these devices should not be greatly altered by the characteristics of the heat source. (B) Final output power density showing the potential for TPV. Due to the lower energy bandgap of the InGaAs photovoltaic cell, the AZO based metamaterial system produces relatively higher power density at lower temperatures. The opposite is seen at higher temperatures. (inset) Schematic of a multilayer metamaterial near the TPV cell.

Tables (1)

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Table 1: Melting temperature and plasmonic figure of merit for near-IR metals.

Equations (15)

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ζ ( λ , θ , ϕ ) = α ( λ , θ , ϕ ) ,
ε | | = ε M ρ + ε D ( 1 ρ ) ε = ε M ε D ε M ( 1 ρ ) + ε D ρ ,
ε | | = ε D [ ε M ( 1 + ρ ) + ε D ( 1 ρ ) ε M ( 1 ρ ) + ε D ( 1 + ρ ) ] ε = ρ ε M + ( 1 ρ ) ε D ,
k 2 ε | | + k | | 2 ε = ω 2 c 2 .
η ult ( λ gap , T ) = 0 π / 2 cos ( θ ) sin ( θ ) d θ 0 λ g λ λ g ζ E ( λ , θ ) I B B ( λ , T ) d λ 0 π / 2 cos ( θ ) sin ( θ ) d θ 0 ζ E ( λ , θ ) I B B ( λ , T ) d λ
I B B ( λ ) = 8 π h c λ 5 ( e h c λ k B T 1 ) ,
Q B B ( λ g , T C ) R rad ( T C ) + G other ( T C ) R other ( T C ) = 0 ,
Q B B ( λ g , T C ) = 2 0 2 π d ϕ 0 π / 2 cos ( θ ) sin ( θ ) d θ 0 λ g λ λ g I B B ( λ , T C ) d λ ,
R rad ( T C ) = Q B B ( λ g , T C ) R other ( T C ) = G other ( T C ) .
Q E ( λ g , T E ) Q B B ( λ g , T C ) e V V C + G other ( T C ) G other ( T C ) e V V C I q = 0 ,
Q E ( λ g , T E ) = 0 2 π d ϕ 0 π / 2 cos ( θ ) sin ( θ ) d θ 0 λ g λ λ g ζ E ( λ , θ ) I B B ( λ , T E ) d λ ,
V O C = V C ln ( f rec 2 Q E ( λ g , T E ) Q B B ( λ g , T C ) f rec + 1 ) ,
η rec ( λ g , T E , T C ) = V O C V g .
η pow = V P I ( V P ) V O C I S C = v p p 2 ( v p p + ln ( 1 + v p p ) ) ( 1 + v p p e v p p ) ,
V O C = V P + V C ln ( 1 + V P V C ) .
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