Abstract

Using a selective emitter with high emissivity in the visible wavelength region and low emissivity in the infrared wavelength region, we reduced the infrared contribution to the blackbody radiation spectrum and shifted the peak emission to shorter wavelengths. We made precise measurements of thermal radiation loss. The conversion efficiency from input electric power to visible light radiation was quantitatively evaluated with high accuracy. Using the proposed selective emitter, the conversion efficiencies in excess of 95% could be produced. Our conclusions pave the way for the design of incandescent lamps with luminous efficiencies exceeding 400 lm/W.

©2010 Optical Society of America

1. Introduction

Incandescent lamps based on the principle of blackbody radiation have many advantages compared with other types of modern electric light sources: they require no external regulating equipment, are inexpensive to manufacture, and work well on either alternating current or direct current over a wide range of applied voltages. As a result, the incandescent lamp has been used worldwide for room lighting and car headlights for more than 100 years. However, the luminous efficiency of the incandescent lamp is low, on the order of 15-20 lm/W, which means that only 2–5% of the total electric power is converted to visible light [1,2]. Therefore, the incandescent lamp is gradually being replaced by other types of electric light sources such as fluorescent lamps, high-intensity discharge lamps, and light-emitting diodes. These newer technologies seem to provide more visible light and less heat for a given electrical energy input; thus, some jurisdictions are in the process of eliminating incandescent light bulbs in favor of more energy-efficient lighting.

Instead of turning to new light-source technologies, an incandescent lamp of higher luminous efficiency could be obtained by modifying the blackbody radiation of the incandescent bulb itself, that is, by reducing the infrared radiation contribution to the blackbody spectrum without reducing the visible wavelength radiation. Many studies have reported the modification of blackbody radiation using one- [39], two- [1016], or three-dimensional [1723] tailored structures. All of these studies were based on sophisticated and time-consuming technologies, such as electron beam lithography and a repetitive etching and deposition process. In addition, these studies have not provided clear evidence for the modification of the blackbody radiation spectrum. Furthermore, in order to increase the luminous efficiency of incandescence, it is important to evaluate the thermal losses due to conduction and radiation versus input electric power as well as confirming the shift in peak wavelength of the radiation spectrum. Detailed quantitative evaluations of the thermal losses are still lacking.

Here we demonstrate that using a selective emitter with high emissivity in the visible wavelength region and low emissivity in the infrared wavelength region, we obtained the modification of the blackbody radiation spectrum whose visible radiation output was enhanced and whose infrared contribution was reduced. Precise measurements of the emitter’s radiation spectrum at several temperatures and the conversion efficiencies from input electric power to visible light radiation were quantitatively evaluated with high accuracy. We found that the efficiency of the selective emitter exceeded 95%. Our conclusion paves the way for the design of incandescent lamps with luminous efficiencies beyond 400 lm/W.

2. Modification of the blackbody radiation; theory and experiment

The thermal equilibrium state in a vacuum can be written as

Pin = Pcond+Prad,
where Pin is the total input electric power, Pcond is the thermal loss due to conduction from the lead wires, and Prad is the dissipation due to thermal radiation. At high temperatures (e.g., 2500 K), the energy dissipation due to thermal radiation becomes much larger than the energy dissipation due to conduction; energy dissipation ratios of 9:1 are typical. Therefore, input power can be efficiently converted into thermal radiation in the incandescent bulb. However, the energy radiated at visible wavelengths is about 10% of the total radiated energy; the remaining 90% is radiated in the infrared. Therefore, it would be advantageous to reduce the infrared thermal radiation without reducing the visible wavelength radiation. Given an emissivity in the visible range as large as 1 and an emissivity in the infrared nearly equal to 0, the following radiation process will occur: at lower temperatures, input power will be efficiently converted into a temperature increase of the system (filament) due to the inhibition of the thermal radiation (low emissivity in the infrared region). At higher temperatures, when the peak of the blackbody radiation spectrum enters the large emissivity region, the input power will suddenly convert into visible radiation. Thus, we can concentrate input electric energy into the visible wavelength region.

The upper inset of Fig. 1 displays the quantitative model that explains this modification of the blackbody radiation. Based on Kirchhoff’s law for a system in thermal equilibrium in which transmittance is negligibly small, the emissivity ε(λ) can be related to the reflectance R(λ) in the following equation,

 figure: Fig. 1

Fig. 1 Emitter reflectance spectrum. The reflectance spectrum is a step-function-like structure designed to shift the resulting radiation toward the visible. The lower inset shows the optical thin-film structure observed by a transmission electron microscope (TEM). The upper inset presents the quantitative model for the modification of the blackbody radiation. The black line represents the reflectance spectrum, the blue line is the emissivity spectrum described by ε(λ) = 1 - R(λ), the green line is the blackbody radiation spectrum, and the red line is the modulated thermal radiation created by the product of the blackbody radiation spectrum and the emissivity ε(λ).

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ε  ​ ​(λ)  ​ ​ =1R​ ​ ​(λ).

Therefore, a material with high reflectance in the infrared wavelength region and low reflectance in the visible wavelength region (the brown line) will display a reverse trend in emissivity (the blue line). The thermal radiation spectrum Φ(λ) becomes the product of the blackbody radiation spectrum Β(λ) (green line) and the emissivity ε(λ),

Φ  ​ ​(λ)  ​ ​ =ε  ​ ​(λ)B  ​ ​(λ),
as shown in red. Thus, we can reduce infrared radiation by imposing a step-function-like reflectivity onto the surface of the heating material.

The lower inset of Fig. 1 shows an optical thin-film structure that exhibits a step-function-like reflectance, observed with a transmission electron microscope (TEM). This thin film deposition was performed by co-sputtering Cr metal and Cr2O3 oxide onto a copper substrate [2427]. The thickness of the Cr and Cr2O3 co-deposited film was 100 nm. After deposition, a SnO2 layer with a thickness on the order of 50 nm was deposited onto the CrO layer as an anti-reflection coating. Figure 1 provides the reflectance spectrum of the film, measured by a spectrophotometer from 0.3 μm to 1.5 μm and by a standard Fourier-transform infrared spectrometer from 1.5 μm to 20 μm. This film reduced infrared radiation below 5.5 μm, corresponding to radiation at 550 K, estimated by Wien’s displacement law. We note here that the optical reflectance shown in Fig. 1 can be obtained by various methods; however, thin film deposition provides many advantages: well-established optical design, control of optical properties (film thickness), material availability, and a cost-competitive manufacturing process.

Figure 2 shows the thermal radiation spectrum of the emissivity-modulated layer (hereafter called an ‘emitter’) obtained using a Fourier transform infrared spectrometer at 580 K (red circles), 670 K (yellow circles), 785 K (green circles), and 870 K (blue circles). For comparison, the thermal radiation spectrum from a copper plate was included (open squares). To protect the sample from oxidation and energy losses due to natural air convection, the sample was placed in a vacuum chamber that was evacuated to about 10−3 Pa. The temperatures of the sample and the chamber were measured using type-K thermocouples (0.1Φ). The thermal radiation spectrum of the copper plate clearly obeys Planck’s law of blackbody radiation and is fit by

B(λ)=αλ−5exp(β/λT)1,
where α = 3.743 × 108 Wμm4/m2, β = 1.438 × 104 μmK, and T is the absolute temperature of the system (K). The solid lines were fit with a wavelength-independent constant emissivity, ε0 = 0.13.

 figure: Fig. 2

Fig. 2 Thermal radiation spectrum from the emitter obtained by a FTIR spectrometer at 580 K (red circles), 670 K (yellow circles), 785 K (green circles), and 870 K (blue circles). For comparison, the thermal radiation spectrum from a copper plate (emissivity ε0 = 0.13) is shown (open squares). The thermal radiation spectrum of the plate obeys Planck’s law, and the results are fit by solid curves. The arrows mark the peak positions of the thermal radiation spectrum for the emitter and the plate for each temperature. The inset shows the 580 K thermal radiation spectrum from the emitter (solid circles) and the plate (open squares). The radiation spectrum of the emitter was fit using the product of the wavelength-dependent emissivity and Planck’s law, and the results were fit with theoretical curves obtained using Eq. (5).

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The peak position (indicated by arrows) of the thermal radiation spectrum of the emitter (solid circles) is shifted toward shorter wavelengths, the longer-wavelength emission is reduced, and the shorter-wavelength emission is enhanced compared to the thermal radiation spectrum of the copper plate. This behavior is clearly visible at lower temperatures, and the 580 K-thermal radiation spectrum from the emitter (solid circles) and the plate (open squares) are depicted in the inset. The reductions in longer-wavelength emission, along with the enhancements of shorter-wavelength emission at each temperature, clearly demonstrate the wavelength dependence of the emissivity. The emissivity is small at longer wavelengths (5–20 μm), and large at shorter wavelength (1–5 μm). Quantitatively, the modulated spectrum at each temperature (Φ(λ)) was fit by the product of the wavelength-dependent emissivity and Planck’s law of blackbody radiation,

Φ(λ)=ε(λ)αλ5exp(β/λT)1.

The solid line is a theoretical curve obtained from Eq. (5), where the experimentally measured emissivity ε(λ) was used for the fit. An almost perfect fit was obtained for the blackbody radiation spectrum of the copper plate and the shifted radiation spectrum of the emitters. From the physics point of view, this finding provides a robust experimental demonstration of the fundamental Kirchhoff’s law, which states that the absorption and emission of a body must be equal and that the radiation intensity of an emitter can never exceed that of an ideal blackbody.

Figure 3 shows the total radiation intensity (the integration of the thermal radiation spectrum in Fig. 2) as a function of temperature (T4) for the copper plates (blue circles) and for the emitters (red circles). It is generally known that the total radiation intensity, I, obeys the Stefan-Boltzmann law, I∝T4. This behavior is clearly shown by the linear dependence of the T4 line for the copper plate. The superlinear behavior of the total radiation intensity from the emitter (red circles) cannot be explained by the simple Stefan-Boltzmann law. It requires the integration of the convolution of the wavelength-dependent emissivity and Planck’s law,

Iemit(T)=ε00(λλ0)αλ5exp(β/λT)1dλ,
where we postulate that ε(λ) is the wavelength-dependent emissivity with a step-function form described by ε(λ) = ε0θ(λ − λ0) (λ0 = cutoff wavelength). To integrate this function analytically, we assumed that exp(β/λΤ) >> 1, leading to Wien’s radiation formula, which is a good approximation for the present experiment. From the emissivity spectrum, we chose a cutoff wavelength λ0 = 5.5 μm and a constant ε0 = 0.9. The red line is the theoretical fit determined by Eq. (6), which well reproduces the superlinear behavior of the total radiation intensity of the emitter.

 figure: Fig. 3

Fig. 3 The total radiation intensity as a function of temperature (T4) for the copper plates (blue circles) and the emitters (red circles). The Stefan–Boltzmann law, I∝T4, is clearly shown for the plate. The red line is the theoretical fit determined by Eq. (6). The inset shows the change in temperature as a function of input power for the plates (blue circles) and for the emitters (red circles) to estimate the ratio of the energy dissipation between the thermal radiation and the conduction. The solid blue line is the curve obtained using Eq. (7), given the linear dependence of conduction loss on temperature, denoted by the solid black line. The solid red line is the theoretical fit to the power dissipation curve of the emitters obtained by Eq. (8). This leads to the conclusion that almost 80% of the input power can be converted into thermal radiation at shorter wavelengths using the emitter.

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The Fig. 3 inset shows the magnitude of the change in temperature as a function of input power for the copper plates (blue circles) and for the emitters (red circles) to estimate the energy dissipation ratio of thermal radiation to conduction.

The energy dissipation for the copper plates, PCu, is described by

PCu(T)=εσS(T4T04)+ξ(TT0),
where ε is the emissivity, σ is the Stefan–Boltzmann constant (5.67 × 10−8 W/m2K4), S is the radiation area, and ξ is the overall heat transfer coefficient through the lead wires (0.5 ϕ). By fitting the change in temperature (ΔT) versus input power, we can precisely determine the ratio between the thermal radiation [Eq. (7), first term] and the heat transfer from the electric wires [Eq. (7), second term] at thermal equilibrium. The solid blue line is the fit obtained by Eq. (7) for ε = 0.13, S = 250 mm2, ξ = 5.625 × 10−4 W/K. On the basis of this high-accuracy fit, we determined the heat dissipation term due to conduction, which has a linear dependence on temperature, as denoted by the solid black line. We used the same experimental conditions to measure the energy dissipation of the emitters. Therefore, the heat dissipation due to conduction can be considered to have the same magnitude. For the emitters, using Eq. (6), we determined the ratio of energy dissipation of thermal radiation to conduction as follows:

Pemit  ​ ​(T)​ ​ =  ​{Iemit  ​ ​(T)Iemit  ​ ​(T0)}S+ξ  ​(TT0).

The solid red line shows the theoretical fit to the power dissipation curve (Pemit(T)) obtained by Eq. (8) using the same parameters (λ0, ε0, and ξ) as were used in fitting the relationship between the total radiation intensity and temperature of the emitter. When the emitter is heated to 700 K, almost 80% of the input power can be converted into thermal radiation at shorter wavelengths.

3. Discussion

If we can construct an emitter with a reflectance cutoff wavelength in the visible region, and the emitter does not degrade at high temperatures, the radiation spectrum of the incandescent light source will have no infrared component. This complete reduction of the infrared radiation will ensure a highly efficient incandescent light source. The blue line in Fig. 4 represents the theoretical change in temperature as a function of input power using Eq. (8) for a cutoff wavelength of λ0 = 0.7 μm. The black line is the heat dissipation term due to conduction from the electric wires using the same heat transfer rate as discussed in Fig. 3. At low temperatures, from 300 K to 1800 K, the material is efficiently heated without radiation loss due to the low emissivity in this temperature region (thermal radiation inhibition). However, at temperatures beyond 2000 K, the material starts to radiate in the visible wavelengths. The broken red line shows the extracted radiation power from the emitter, given the step-function reflectance spectrum displayed in the upper inset of Fig. 4. By reading off the ratio between the radiative power (dotted red line) and the total input power (solid blue line), we can estimate the conversion efficiency from electric power into visible radiation. This efficiency will exceed 90% at 2800 K. The red curve in the upper inset of Fig. 4 shows a theoretically-derived radiation spectrum. The concentration of radiative energy in the spectral luminous efficiency curves shown in the green line provides large luminous efficiencies, exceeding 400 lm/W. It is interesting to note that the incandescent lamp theoretically modeled here emits not white, but greenish light whose chromaticity centers on the solid red circle of the CIE (Commission Internationale de l’Eclairage) color space chromaticity diagram [28], as shown in the lower inset of Fig. 4, and its correlated color temperature is beyond 9000 K.

 figure: Fig. 4

Fig. 4 The blue line represents the theoretical temperature change as a function of input power generated from Eq. (8), given an emitter with a cutoff wavelength of λ0 = 0.7 μm. The black line is the heat dissipation term due to conduction from electric wires. The broken red line is the extracted radiative power from the emitter given the step-function reflectance spectrum described in the upper inset. The red curve in the upper inset is a theoretically derived radiation spectrum, and the green line is the spectral luminous efficiency curve. The chromaticity of the incandescent lamp investigated here centers on the red circle of the inset CIE chromaticity diagram, and its correlated color temperature is beyond 9000 K.

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4. Conclusion

Generally, to obtain high luminous efficiencies from an incandescent light source, the filament must be heated to temperatures beyond 3000 K. This restricts the filament forms to materials with high melting points, such as tungsten. Furthermore, the lifetime of the filament shortens to around 1000 hours when the filament is operated near the melting point. However, an incandescent lamp with this selective emitter does not require such high temperatures to be efficient; therefore, we can reduce the operational voltage (we can obtain enough luminous flux using a large emitter). This reduction in applied voltage will effectively extend the lifetime of the filament (emitters), as the lifetime is approximately proportional to V−16 [29]. We believe that using this proposed emitter, we can obtain a 21st-century incandescent lamp with a luminous efficiency exceeding 400 lm/W and a lifetime longer than the 106 hour-lifetime of the bulb burning in the fire station in Livermore, California [30].

Acknowledgement

The authors acknowledge fruitful discussion with Makoto Yoshida and Yoshiaki Yasuda.

References and links

1. T. J. Keefe, (2007). The nature of light. (see also http://www.ccri.edu/physics/keefe/light.htm).

2. D. L. Klipstein, (1996). The great internet light bulb book, part 1. (see also http://freespace. virgin.net/tom. baldwin/bulbguide.html).

3. J. J. Greffet, R. Carminati, K. Joulain, J. P. Mulet, S. Mainguy, and Y. Chen, “Coherent emission of light by thermal sources,” Nature 416(6876), 61–64 (2002). [CrossRef]   [PubMed]  

4. P. J. Hesketh, J. N. Zemel, and B. Gebhart, “Organ pipe radiant modes of periodic micromachined silicon surfaces,” Nature 324(6097), 549–551 (1986). [CrossRef]  

5. P. J. Hesketh, J. N. Zemel, and B. Gebhart, “Polarized spectral emittance from periodic micromachined surface. I. Doped silicon: The normal direction,” Phys. Rev. B 37(18), 10795–10802 (1988). [CrossRef]  

6. P. J. Hesketh, J. N. Zemel, and B. Gebhart, “Polarized spectral emittance from periodic micromachined surface. II. Doped silicon: angular variation,” Phys. Rev. B 37(18), 10803–10813 (1988). [CrossRef]  

7. J. A. Schuller, T. Taubner, and M. L. Brongersma, “Optical antenna thermal emitters,” Nat. Photonics 3(11), 658–661 (2009). [CrossRef]  

8. J. Le Gall, M. Olivier, and J.-J. Greffet, “Experimental and theoretical study of reflection and coherence thermal emission by a SiC grating supporting a surface-phonon polariton,” Phys. Rev. B 55(15), 10105–10114 (1997). [CrossRef]  

9. S. Ingvarsson, L. Klein, Y. Y. Au, J. A. Lacey, and H. F. Hamann, “Enhanced thermal emission from individual antenna-like nanoheaters,” Opt. Express 15(18), 11249–11254 (2007). [CrossRef]   [PubMed]  

10. F. Kusunoki, T. Kohama, T. Hiroshima, S. Fukumoto, J. Takahara, and T. Kobayashi, “Narrow-band thermal radiation with low directivity by resonant modes inside tungsten microcavity,” Jpn. J. Appl. Phys. 43(No. 8A), 5253–5258 (2004). [CrossRef]  

11. S. Tay, A. Kropachev, I. E. Araci, T. Skotheim, R. A. Norwood, and N. Peyghambarian, “Plasmonic thermal IR emitters based on nanoamorphous carbon,” Appl. Phys. Lett. 94(7), 071113 (2009). [CrossRef]  

12. H. Sai, Y. Kanamori, and H. Yugami, “High temperature resistive surface grating for spectral control of thermal radiation,” Appl. Phys. Lett. 82(11), 1685–1687 (2003). [CrossRef]  

13. Y. C. Chang, C. M. Wang, M. N. Abbas, M. H. Shih, and D. P. Tsai, “T-shaped plasmonic array as a narrow-band thermal emitter or biosensor,” Opt. Express 17(16), 13526–13531 (2009). [CrossRef]   [PubMed]  

14. S. Maruyama, T. Kashiwa, H. Yugami, and M. Esashi, “Thermal radiation from two dimensionally confined mode in microcavities,” Appl. Phys. Lett. 79(9), 1393–1395 (2001). [CrossRef]  

15. I. Puscasu and W. L. Schaich, “Narrow-band tunable infrared emission from arrays of microstrip patches,” Appl. Phys. Lett. 92(23), 233102 (2008). [CrossRef]  

16. H. T. Miyazaki, K. Ikeda, T. Kasaya, K. Yamamoto, Y. Inoue, K. Fujimura, T. Kanakugi, M. Okada, K. Hatade, and S. Kitagawa, “Thermal emission of two-color polarized infrared waves from integrated plasmon cavities,” Appl. Phys. Lett. 92(14), 141114 (2008). [CrossRef]  

17. M. U. Pralle, N. Moelders, M. P. McNeal, I. Puscasu, A. C. Greenwald, J. T. Daly, E. A. Johnson, T. George, D. S. Choi, I. El-Kady, and R. Biswas, “Photonic crystal enhanced narrow-band infrared emitters,” Appl. Phys. Lett. 81(25), 4685–4687 (2002). [CrossRef]  

18. S. Y. Lin, J. G. Fleming, E. Chow, J. Bur, K. K. Choi, and A. Goldberg, “Enhancement and supression of thermal emission by a three-dimensional photonic crystal,” Phys. Rev. B 62(4), R2243–R2246 (2000). [CrossRef]  

19. F. Kusunoki, H. Kawabata, T. Hiroshima, J. Takahara, T. Kobayashi, T. Sumida, and S. Yanagida, “Suppression of total radiant flux by three-dimensional photonic crystal coatings,” Electron. Lett. 39(7), 622–623 (2003). [CrossRef]  

20. J. G. Fleming, S. Y. Lin, I. El-Kady, R. Biswas, and K. M. Ho, “All-metallic three-dimensional photonic crystals with a large infrared bandgap,” Nature 417(6884), 52–55 (2002). [CrossRef]   [PubMed]  

21. J. H. Lee, W. Leung, T. G. Kim, K. Constant, and K. M. Ho, “Polarized thermal radiation by layer-by-layer metallic emitters with sub-wavelength grating,” Opt. Express 16(12), 8742–8747 (2008). [CrossRef]   [PubMed]  

22. S. Y. Lin, J. G. Fleming, and I. El-Kady, “Three-dimensional photonic-crystal emission through thermal excitation,” Opt. Lett. 28(20), 1909–1911 (2003). [CrossRef]   [PubMed]  

23. S. Y. Lin, J. G. Fleming, and I. El-Kady, “Highly efficient light emission at λ = 1.5 microm by a three-dimensional tungsten photonic crystal,” Opt. Lett. 28(18), 1683–1685 (2003). [CrossRef]   [PubMed]  

24. J. C. C. Fan and P. M. Zavracky, “Selective black absorbers using MgO/Au cermet films,” Appl. Phys. Lett. 29(8), 478–480 (1976). [CrossRef]  

25. J. C. C. Fan and S. A. Spura, “Selective black absorbers using rf-sputtered Cr2O3/Cr cermet films,” Appl. Phys. Lett. 30(10), 511–513 (1977). [CrossRef]  

26. G. Zajac, G. B. Smith, and A. Ignatiev, “Refinement of solar absorbing black chrome microstructure and its relationship to optical degradation mechanism,” J. Appl. Phys. 51(10), 5544–5554 (1980). [CrossRef]  

27. A. Ignatiev, P. O’Neill, C. Doland, and G. Zajac, “Microstructure dependence of the optical properties of solar absorbing black chrome,” Appl. Phys. Lett. 34(1), 42–44 (1979). [CrossRef]  

28. T. Smith and J. Guild, “The C. I. E. colorimetric standards and their use,” Trans. Opt. Soc. 33(3), 73–134 (1932). [CrossRef]  

29. D. G. Fink, and H. W. Beaty, Standard Handbook for Electric Engineers, 11th Edition, McGraw-Hill, New York, 1978, p. 22.

30. Magazine Online, (see also http://www.homelighting.com/article.cfm?intarticleID=880).

References

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  • |

  1. T. J. Keefe, (2007). The nature of light. (see also http://www.ccri.edu/physics/keefe/light.htm ).
  2. D. L. Klipstein, (1996). The great internet light bulb book, part 1. (see also http://freespace. virgin.net/tom. baldwin/bulbguide.html ).
  3. J. J. Greffet, R. Carminati, K. Joulain, J. P. Mulet, S. Mainguy, and Y. Chen, “Coherent emission of light by thermal sources,” Nature 416(6876), 61–64 (2002).
    [Crossref] [PubMed]
  4. P. J. Hesketh, J. N. Zemel, and B. Gebhart, “Organ pipe radiant modes of periodic micromachined silicon surfaces,” Nature 324(6097), 549–551 (1986).
    [Crossref]
  5. P. J. Hesketh, J. N. Zemel, and B. Gebhart, “Polarized spectral emittance from periodic micromachined surface. I. Doped silicon: The normal direction,” Phys. Rev. B 37(18), 10795–10802 (1988).
    [Crossref]
  6. P. J. Hesketh, J. N. Zemel, and B. Gebhart, “Polarized spectral emittance from periodic micromachined surface. II. Doped silicon: angular variation,” Phys. Rev. B 37(18), 10803–10813 (1988).
    [Crossref]
  7. J. A. Schuller, T. Taubner, and M. L. Brongersma, “Optical antenna thermal emitters,” Nat. Photonics 3(11), 658–661 (2009).
    [Crossref]
  8. J. Le Gall, M. Olivier, and J.-J. Greffet, “Experimental and theoretical study of reflection and coherence thermal emission by a SiC grating supporting a surface-phonon polariton,” Phys. Rev. B 55(15), 10105–10114 (1997).
    [Crossref]
  9. S. Ingvarsson, L. Klein, Y. Y. Au, J. A. Lacey, and H. F. Hamann, “Enhanced thermal emission from individual antenna-like nanoheaters,” Opt. Express 15(18), 11249–11254 (2007).
    [Crossref] [PubMed]
  10. F. Kusunoki, T. Kohama, T. Hiroshima, S. Fukumoto, J. Takahara, and T. Kobayashi, “Narrow-band thermal radiation with low directivity by resonant modes inside tungsten microcavity,” Jpn. J. Appl. Phys. 43(No. 8A), 5253–5258 (2004).
    [Crossref]
  11. S. Tay, A. Kropachev, I. E. Araci, T. Skotheim, R. A. Norwood, and N. Peyghambarian, “Plasmonic thermal IR emitters based on nanoamorphous carbon,” Appl. Phys. Lett. 94(7), 071113 (2009).
    [Crossref]
  12. H. Sai, Y. Kanamori, and H. Yugami, “High temperature resistive surface grating for spectral control of thermal radiation,” Appl. Phys. Lett. 82(11), 1685–1687 (2003).
    [Crossref]
  13. Y. C. Chang, C. M. Wang, M. N. Abbas, M. H. Shih, and D. P. Tsai, “T-shaped plasmonic array as a narrow-band thermal emitter or biosensor,” Opt. Express 17(16), 13526–13531 (2009).
    [Crossref] [PubMed]
  14. S. Maruyama, T. Kashiwa, H. Yugami, and M. Esashi, “Thermal radiation from two dimensionally confined mode in microcavities,” Appl. Phys. Lett. 79(9), 1393–1395 (2001).
    [Crossref]
  15. I. Puscasu and W. L. Schaich, “Narrow-band tunable infrared emission from arrays of microstrip patches,” Appl. Phys. Lett. 92(23), 233102 (2008).
    [Crossref]
  16. H. T. Miyazaki, K. Ikeda, T. Kasaya, K. Yamamoto, Y. Inoue, K. Fujimura, T. Kanakugi, M. Okada, K. Hatade, and S. Kitagawa, “Thermal emission of two-color polarized infrared waves from integrated plasmon cavities,” Appl. Phys. Lett. 92(14), 141114 (2008).
    [Crossref]
  17. M. U. Pralle, N. Moelders, M. P. McNeal, I. Puscasu, A. C. Greenwald, J. T. Daly, E. A. Johnson, T. George, D. S. Choi, I. El-Kady, and R. Biswas, “Photonic crystal enhanced narrow-band infrared emitters,” Appl. Phys. Lett. 81(25), 4685–4687 (2002).
    [Crossref]
  18. S. Y. Lin, J. G. Fleming, E. Chow, J. Bur, K. K. Choi, and A. Goldberg, “Enhancement and supression of thermal emission by a three-dimensional photonic crystal,” Phys. Rev. B 62(4), R2243–R2246 (2000).
    [Crossref]
  19. F. Kusunoki, H. Kawabata, T. Hiroshima, J. Takahara, T. Kobayashi, T. Sumida, and S. Yanagida, “Suppression of total radiant flux by three-dimensional photonic crystal coatings,” Electron. Lett. 39(7), 622–623 (2003).
    [Crossref]
  20. J. G. Fleming, S. Y. Lin, I. El-Kady, R. Biswas, and K. M. Ho, “All-metallic three-dimensional photonic crystals with a large infrared bandgap,” Nature 417(6884), 52–55 (2002).
    [Crossref] [PubMed]
  21. J. H. Lee, W. Leung, T. G. Kim, K. Constant, and K. M. Ho, “Polarized thermal radiation by layer-by-layer metallic emitters with sub-wavelength grating,” Opt. Express 16(12), 8742–8747 (2008).
    [Crossref] [PubMed]
  22. S. Y. Lin, J. G. Fleming, and I. El-Kady, “Three-dimensional photonic-crystal emission through thermal excitation,” Opt. Lett. 28(20), 1909–1911 (2003).
    [Crossref] [PubMed]
  23. S. Y. Lin, J. G. Fleming, and I. El-Kady, “Highly efficient light emission at λ = 1.5 microm by a three-dimensional tungsten photonic crystal,” Opt. Lett. 28(18), 1683–1685 (2003).
    [Crossref] [PubMed]
  24. J. C. C. Fan and P. M. Zavracky, “Selective black absorbers using MgO/Au cermet films,” Appl. Phys. Lett. 29(8), 478–480 (1976).
    [Crossref]
  25. J. C. C. Fan and S. A. Spura, “Selective black absorbers using rf-sputtered Cr2O3/Cr cermet films,” Appl. Phys. Lett. 30(10), 511–513 (1977).
    [Crossref]
  26. G. Zajac, G. B. Smith, and A. Ignatiev, “Refinement of solar absorbing black chrome microstructure and its relationship to optical degradation mechanism,” J. Appl. Phys. 51(10), 5544–5554 (1980).
    [Crossref]
  27. A. Ignatiev, P. O’Neill, C. Doland, and G. Zajac, “Microstructure dependence of the optical properties of solar absorbing black chrome,” Appl. Phys. Lett. 34(1), 42–44 (1979).
    [Crossref]
  28. T. Smith and J. Guild, “The C. I. E. colorimetric standards and their use,” Trans. Opt. Soc. 33(3), 73–134 (1932).
    [Crossref]
  29. D. G. Fink, and H. W. Beaty, Standard Handbook for Electric Engineers, 11th Edition, McGraw-Hill, New York, 1978, p. 22.
  30. Magazine Online, (see also http://www.homelighting.com/article.cfm?intarticleID=880 ).

2009 (3)

J. A. Schuller, T. Taubner, and M. L. Brongersma, “Optical antenna thermal emitters,” Nat. Photonics 3(11), 658–661 (2009).
[Crossref]

S. Tay, A. Kropachev, I. E. Araci, T. Skotheim, R. A. Norwood, and N. Peyghambarian, “Plasmonic thermal IR emitters based on nanoamorphous carbon,” Appl. Phys. Lett. 94(7), 071113 (2009).
[Crossref]

Y. C. Chang, C. M. Wang, M. N. Abbas, M. H. Shih, and D. P. Tsai, “T-shaped plasmonic array as a narrow-band thermal emitter or biosensor,” Opt. Express 17(16), 13526–13531 (2009).
[Crossref] [PubMed]

2008 (3)

I. Puscasu and W. L. Schaich, “Narrow-band tunable infrared emission from arrays of microstrip patches,” Appl. Phys. Lett. 92(23), 233102 (2008).
[Crossref]

H. T. Miyazaki, K. Ikeda, T. Kasaya, K. Yamamoto, Y. Inoue, K. Fujimura, T. Kanakugi, M. Okada, K. Hatade, and S. Kitagawa, “Thermal emission of two-color polarized infrared waves from integrated plasmon cavities,” Appl. Phys. Lett. 92(14), 141114 (2008).
[Crossref]

J. H. Lee, W. Leung, T. G. Kim, K. Constant, and K. M. Ho, “Polarized thermal radiation by layer-by-layer metallic emitters with sub-wavelength grating,” Opt. Express 16(12), 8742–8747 (2008).
[Crossref] [PubMed]

2007 (1)

2004 (1)

F. Kusunoki, T. Kohama, T. Hiroshima, S. Fukumoto, J. Takahara, and T. Kobayashi, “Narrow-band thermal radiation with low directivity by resonant modes inside tungsten microcavity,” Jpn. J. Appl. Phys. 43(No. 8A), 5253–5258 (2004).
[Crossref]

2003 (4)

H. Sai, Y. Kanamori, and H. Yugami, “High temperature resistive surface grating for spectral control of thermal radiation,” Appl. Phys. Lett. 82(11), 1685–1687 (2003).
[Crossref]

S. Y. Lin, J. G. Fleming, and I. El-Kady, “Three-dimensional photonic-crystal emission through thermal excitation,” Opt. Lett. 28(20), 1909–1911 (2003).
[Crossref] [PubMed]

S. Y. Lin, J. G. Fleming, and I. El-Kady, “Highly efficient light emission at λ = 1.5 microm by a three-dimensional tungsten photonic crystal,” Opt. Lett. 28(18), 1683–1685 (2003).
[Crossref] [PubMed]

F. Kusunoki, H. Kawabata, T. Hiroshima, J. Takahara, T. Kobayashi, T. Sumida, and S. Yanagida, “Suppression of total radiant flux by three-dimensional photonic crystal coatings,” Electron. Lett. 39(7), 622–623 (2003).
[Crossref]

2002 (3)

J. G. Fleming, S. Y. Lin, I. El-Kady, R. Biswas, and K. M. Ho, “All-metallic three-dimensional photonic crystals with a large infrared bandgap,” Nature 417(6884), 52–55 (2002).
[Crossref] [PubMed]

M. U. Pralle, N. Moelders, M. P. McNeal, I. Puscasu, A. C. Greenwald, J. T. Daly, E. A. Johnson, T. George, D. S. Choi, I. El-Kady, and R. Biswas, “Photonic crystal enhanced narrow-band infrared emitters,” Appl. Phys. Lett. 81(25), 4685–4687 (2002).
[Crossref]

J. J. Greffet, R. Carminati, K. Joulain, J. P. Mulet, S. Mainguy, and Y. Chen, “Coherent emission of light by thermal sources,” Nature 416(6876), 61–64 (2002).
[Crossref] [PubMed]

2001 (1)

S. Maruyama, T. Kashiwa, H. Yugami, and M. Esashi, “Thermal radiation from two dimensionally confined mode in microcavities,” Appl. Phys. Lett. 79(9), 1393–1395 (2001).
[Crossref]

2000 (1)

S. Y. Lin, J. G. Fleming, E. Chow, J. Bur, K. K. Choi, and A. Goldberg, “Enhancement and supression of thermal emission by a three-dimensional photonic crystal,” Phys. Rev. B 62(4), R2243–R2246 (2000).
[Crossref]

1997 (1)

J. Le Gall, M. Olivier, and J.-J. Greffet, “Experimental and theoretical study of reflection and coherence thermal emission by a SiC grating supporting a surface-phonon polariton,” Phys. Rev. B 55(15), 10105–10114 (1997).
[Crossref]

1988 (2)

P. J. Hesketh, J. N. Zemel, and B. Gebhart, “Polarized spectral emittance from periodic micromachined surface. I. Doped silicon: The normal direction,” Phys. Rev. B 37(18), 10795–10802 (1988).
[Crossref]

P. J. Hesketh, J. N. Zemel, and B. Gebhart, “Polarized spectral emittance from periodic micromachined surface. II. Doped silicon: angular variation,” Phys. Rev. B 37(18), 10803–10813 (1988).
[Crossref]

1986 (1)

P. J. Hesketh, J. N. Zemel, and B. Gebhart, “Organ pipe radiant modes of periodic micromachined silicon surfaces,” Nature 324(6097), 549–551 (1986).
[Crossref]

1980 (1)

G. Zajac, G. B. Smith, and A. Ignatiev, “Refinement of solar absorbing black chrome microstructure and its relationship to optical degradation mechanism,” J. Appl. Phys. 51(10), 5544–5554 (1980).
[Crossref]

1979 (1)

A. Ignatiev, P. O’Neill, C. Doland, and G. Zajac, “Microstructure dependence of the optical properties of solar absorbing black chrome,” Appl. Phys. Lett. 34(1), 42–44 (1979).
[Crossref]

1977 (1)

J. C. C. Fan and S. A. Spura, “Selective black absorbers using rf-sputtered Cr2O3/Cr cermet films,” Appl. Phys. Lett. 30(10), 511–513 (1977).
[Crossref]

1976 (1)

J. C. C. Fan and P. M. Zavracky, “Selective black absorbers using MgO/Au cermet films,” Appl. Phys. Lett. 29(8), 478–480 (1976).
[Crossref]

1932 (1)

T. Smith and J. Guild, “The C. I. E. colorimetric standards and their use,” Trans. Opt. Soc. 33(3), 73–134 (1932).
[Crossref]

Abbas, M. N.

Araci, I. E.

S. Tay, A. Kropachev, I. E. Araci, T. Skotheim, R. A. Norwood, and N. Peyghambarian, “Plasmonic thermal IR emitters based on nanoamorphous carbon,” Appl. Phys. Lett. 94(7), 071113 (2009).
[Crossref]

Au, Y. Y.

Biswas, R.

M. U. Pralle, N. Moelders, M. P. McNeal, I. Puscasu, A. C. Greenwald, J. T. Daly, E. A. Johnson, T. George, D. S. Choi, I. El-Kady, and R. Biswas, “Photonic crystal enhanced narrow-band infrared emitters,” Appl. Phys. Lett. 81(25), 4685–4687 (2002).
[Crossref]

J. G. Fleming, S. Y. Lin, I. El-Kady, R. Biswas, and K. M. Ho, “All-metallic three-dimensional photonic crystals with a large infrared bandgap,” Nature 417(6884), 52–55 (2002).
[Crossref] [PubMed]

Brongersma, M. L.

J. A. Schuller, T. Taubner, and M. L. Brongersma, “Optical antenna thermal emitters,” Nat. Photonics 3(11), 658–661 (2009).
[Crossref]

Bur, J.

S. Y. Lin, J. G. Fleming, E. Chow, J. Bur, K. K. Choi, and A. Goldberg, “Enhancement and supression of thermal emission by a three-dimensional photonic crystal,” Phys. Rev. B 62(4), R2243–R2246 (2000).
[Crossref]

Carminati, R.

J. J. Greffet, R. Carminati, K. Joulain, J. P. Mulet, S. Mainguy, and Y. Chen, “Coherent emission of light by thermal sources,” Nature 416(6876), 61–64 (2002).
[Crossref] [PubMed]

Chang, Y. C.

Chen, Y.

J. J. Greffet, R. Carminati, K. Joulain, J. P. Mulet, S. Mainguy, and Y. Chen, “Coherent emission of light by thermal sources,” Nature 416(6876), 61–64 (2002).
[Crossref] [PubMed]

Choi, D. S.

M. U. Pralle, N. Moelders, M. P. McNeal, I. Puscasu, A. C. Greenwald, J. T. Daly, E. A. Johnson, T. George, D. S. Choi, I. El-Kady, and R. Biswas, “Photonic crystal enhanced narrow-band infrared emitters,” Appl. Phys. Lett. 81(25), 4685–4687 (2002).
[Crossref]

Choi, K. K.

S. Y. Lin, J. G. Fleming, E. Chow, J. Bur, K. K. Choi, and A. Goldberg, “Enhancement and supression of thermal emission by a three-dimensional photonic crystal,” Phys. Rev. B 62(4), R2243–R2246 (2000).
[Crossref]

Chow, E.

S. Y. Lin, J. G. Fleming, E. Chow, J. Bur, K. K. Choi, and A. Goldberg, “Enhancement and supression of thermal emission by a three-dimensional photonic crystal,” Phys. Rev. B 62(4), R2243–R2246 (2000).
[Crossref]

Constant, K.

Daly, J. T.

M. U. Pralle, N. Moelders, M. P. McNeal, I. Puscasu, A. C. Greenwald, J. T. Daly, E. A. Johnson, T. George, D. S. Choi, I. El-Kady, and R. Biswas, “Photonic crystal enhanced narrow-band infrared emitters,” Appl. Phys. Lett. 81(25), 4685–4687 (2002).
[Crossref]

Doland, C.

A. Ignatiev, P. O’Neill, C. Doland, and G. Zajac, “Microstructure dependence of the optical properties of solar absorbing black chrome,” Appl. Phys. Lett. 34(1), 42–44 (1979).
[Crossref]

El-Kady, I.

S. Y. Lin, J. G. Fleming, and I. El-Kady, “Three-dimensional photonic-crystal emission through thermal excitation,” Opt. Lett. 28(20), 1909–1911 (2003).
[Crossref] [PubMed]

S. Y. Lin, J. G. Fleming, and I. El-Kady, “Highly efficient light emission at λ = 1.5 microm by a three-dimensional tungsten photonic crystal,” Opt. Lett. 28(18), 1683–1685 (2003).
[Crossref] [PubMed]

J. G. Fleming, S. Y. Lin, I. El-Kady, R. Biswas, and K. M. Ho, “All-metallic three-dimensional photonic crystals with a large infrared bandgap,” Nature 417(6884), 52–55 (2002).
[Crossref] [PubMed]

M. U. Pralle, N. Moelders, M. P. McNeal, I. Puscasu, A. C. Greenwald, J. T. Daly, E. A. Johnson, T. George, D. S. Choi, I. El-Kady, and R. Biswas, “Photonic crystal enhanced narrow-band infrared emitters,” Appl. Phys. Lett. 81(25), 4685–4687 (2002).
[Crossref]

Esashi, M.

S. Maruyama, T. Kashiwa, H. Yugami, and M. Esashi, “Thermal radiation from two dimensionally confined mode in microcavities,” Appl. Phys. Lett. 79(9), 1393–1395 (2001).
[Crossref]

Fan, J. C. C.

J. C. C. Fan and S. A. Spura, “Selective black absorbers using rf-sputtered Cr2O3/Cr cermet films,” Appl. Phys. Lett. 30(10), 511–513 (1977).
[Crossref]

J. C. C. Fan and P. M. Zavracky, “Selective black absorbers using MgO/Au cermet films,” Appl. Phys. Lett. 29(8), 478–480 (1976).
[Crossref]

Fleming, J. G.

S. Y. Lin, J. G. Fleming, and I. El-Kady, “Three-dimensional photonic-crystal emission through thermal excitation,” Opt. Lett. 28(20), 1909–1911 (2003).
[Crossref] [PubMed]

S. Y. Lin, J. G. Fleming, and I. El-Kady, “Highly efficient light emission at λ = 1.5 microm by a three-dimensional tungsten photonic crystal,” Opt. Lett. 28(18), 1683–1685 (2003).
[Crossref] [PubMed]

J. G. Fleming, S. Y. Lin, I. El-Kady, R. Biswas, and K. M. Ho, “All-metallic three-dimensional photonic crystals with a large infrared bandgap,” Nature 417(6884), 52–55 (2002).
[Crossref] [PubMed]

S. Y. Lin, J. G. Fleming, E. Chow, J. Bur, K. K. Choi, and A. Goldberg, “Enhancement and supression of thermal emission by a three-dimensional photonic crystal,” Phys. Rev. B 62(4), R2243–R2246 (2000).
[Crossref]

Fujimura, K.

H. T. Miyazaki, K. Ikeda, T. Kasaya, K. Yamamoto, Y. Inoue, K. Fujimura, T. Kanakugi, M. Okada, K. Hatade, and S. Kitagawa, “Thermal emission of two-color polarized infrared waves from integrated plasmon cavities,” Appl. Phys. Lett. 92(14), 141114 (2008).
[Crossref]

Fukumoto, S.

F. Kusunoki, T. Kohama, T. Hiroshima, S. Fukumoto, J. Takahara, and T. Kobayashi, “Narrow-band thermal radiation with low directivity by resonant modes inside tungsten microcavity,” Jpn. J. Appl. Phys. 43(No. 8A), 5253–5258 (2004).
[Crossref]

Gebhart, B.

P. J. Hesketh, J. N. Zemel, and B. Gebhart, “Polarized spectral emittance from periodic micromachined surface. I. Doped silicon: The normal direction,” Phys. Rev. B 37(18), 10795–10802 (1988).
[Crossref]

P. J. Hesketh, J. N. Zemel, and B. Gebhart, “Polarized spectral emittance from periodic micromachined surface. II. Doped silicon: angular variation,” Phys. Rev. B 37(18), 10803–10813 (1988).
[Crossref]

P. J. Hesketh, J. N. Zemel, and B. Gebhart, “Organ pipe radiant modes of periodic micromachined silicon surfaces,” Nature 324(6097), 549–551 (1986).
[Crossref]

George, T.

M. U. Pralle, N. Moelders, M. P. McNeal, I. Puscasu, A. C. Greenwald, J. T. Daly, E. A. Johnson, T. George, D. S. Choi, I. El-Kady, and R. Biswas, “Photonic crystal enhanced narrow-band infrared emitters,” Appl. Phys. Lett. 81(25), 4685–4687 (2002).
[Crossref]

Goldberg, A.

S. Y. Lin, J. G. Fleming, E. Chow, J. Bur, K. K. Choi, and A. Goldberg, “Enhancement and supression of thermal emission by a three-dimensional photonic crystal,” Phys. Rev. B 62(4), R2243–R2246 (2000).
[Crossref]

Greenwald, A. C.

M. U. Pralle, N. Moelders, M. P. McNeal, I. Puscasu, A. C. Greenwald, J. T. Daly, E. A. Johnson, T. George, D. S. Choi, I. El-Kady, and R. Biswas, “Photonic crystal enhanced narrow-band infrared emitters,” Appl. Phys. Lett. 81(25), 4685–4687 (2002).
[Crossref]

Greffet, J. J.

J. J. Greffet, R. Carminati, K. Joulain, J. P. Mulet, S. Mainguy, and Y. Chen, “Coherent emission of light by thermal sources,” Nature 416(6876), 61–64 (2002).
[Crossref] [PubMed]

Greffet, J.-J.

J. Le Gall, M. Olivier, and J.-J. Greffet, “Experimental and theoretical study of reflection and coherence thermal emission by a SiC grating supporting a surface-phonon polariton,” Phys. Rev. B 55(15), 10105–10114 (1997).
[Crossref]

Guild, J.

T. Smith and J. Guild, “The C. I. E. colorimetric standards and their use,” Trans. Opt. Soc. 33(3), 73–134 (1932).
[Crossref]

Hamann, H. F.

Hatade, K.

H. T. Miyazaki, K. Ikeda, T. Kasaya, K. Yamamoto, Y. Inoue, K. Fujimura, T. Kanakugi, M. Okada, K. Hatade, and S. Kitagawa, “Thermal emission of two-color polarized infrared waves from integrated plasmon cavities,” Appl. Phys. Lett. 92(14), 141114 (2008).
[Crossref]

Hesketh, P. J.

P. J. Hesketh, J. N. Zemel, and B. Gebhart, “Polarized spectral emittance from periodic micromachined surface. II. Doped silicon: angular variation,” Phys. Rev. B 37(18), 10803–10813 (1988).
[Crossref]

P. J. Hesketh, J. N. Zemel, and B. Gebhart, “Polarized spectral emittance from periodic micromachined surface. I. Doped silicon: The normal direction,” Phys. Rev. B 37(18), 10795–10802 (1988).
[Crossref]

P. J. Hesketh, J. N. Zemel, and B. Gebhart, “Organ pipe radiant modes of periodic micromachined silicon surfaces,” Nature 324(6097), 549–551 (1986).
[Crossref]

Hiroshima, T.

F. Kusunoki, T. Kohama, T. Hiroshima, S. Fukumoto, J. Takahara, and T. Kobayashi, “Narrow-band thermal radiation with low directivity by resonant modes inside tungsten microcavity,” Jpn. J. Appl. Phys. 43(No. 8A), 5253–5258 (2004).
[Crossref]

F. Kusunoki, H. Kawabata, T. Hiroshima, J. Takahara, T. Kobayashi, T. Sumida, and S. Yanagida, “Suppression of total radiant flux by three-dimensional photonic crystal coatings,” Electron. Lett. 39(7), 622–623 (2003).
[Crossref]

Ho, K. M.

J. H. Lee, W. Leung, T. G. Kim, K. Constant, and K. M. Ho, “Polarized thermal radiation by layer-by-layer metallic emitters with sub-wavelength grating,” Opt. Express 16(12), 8742–8747 (2008).
[Crossref] [PubMed]

J. G. Fleming, S. Y. Lin, I. El-Kady, R. Biswas, and K. M. Ho, “All-metallic three-dimensional photonic crystals with a large infrared bandgap,” Nature 417(6884), 52–55 (2002).
[Crossref] [PubMed]

Ignatiev, A.

G. Zajac, G. B. Smith, and A. Ignatiev, “Refinement of solar absorbing black chrome microstructure and its relationship to optical degradation mechanism,” J. Appl. Phys. 51(10), 5544–5554 (1980).
[Crossref]

A. Ignatiev, P. O’Neill, C. Doland, and G. Zajac, “Microstructure dependence of the optical properties of solar absorbing black chrome,” Appl. Phys. Lett. 34(1), 42–44 (1979).
[Crossref]

Ikeda, K.

H. T. Miyazaki, K. Ikeda, T. Kasaya, K. Yamamoto, Y. Inoue, K. Fujimura, T. Kanakugi, M. Okada, K. Hatade, and S. Kitagawa, “Thermal emission of two-color polarized infrared waves from integrated plasmon cavities,” Appl. Phys. Lett. 92(14), 141114 (2008).
[Crossref]

Ingvarsson, S.

Inoue, Y.

H. T. Miyazaki, K. Ikeda, T. Kasaya, K. Yamamoto, Y. Inoue, K. Fujimura, T. Kanakugi, M. Okada, K. Hatade, and S. Kitagawa, “Thermal emission of two-color polarized infrared waves from integrated plasmon cavities,” Appl. Phys. Lett. 92(14), 141114 (2008).
[Crossref]

Johnson, E. A.

M. U. Pralle, N. Moelders, M. P. McNeal, I. Puscasu, A. C. Greenwald, J. T. Daly, E. A. Johnson, T. George, D. S. Choi, I. El-Kady, and R. Biswas, “Photonic crystal enhanced narrow-band infrared emitters,” Appl. Phys. Lett. 81(25), 4685–4687 (2002).
[Crossref]

Joulain, K.

J. J. Greffet, R. Carminati, K. Joulain, J. P. Mulet, S. Mainguy, and Y. Chen, “Coherent emission of light by thermal sources,” Nature 416(6876), 61–64 (2002).
[Crossref] [PubMed]

Kanakugi, T.

H. T. Miyazaki, K. Ikeda, T. Kasaya, K. Yamamoto, Y. Inoue, K. Fujimura, T. Kanakugi, M. Okada, K. Hatade, and S. Kitagawa, “Thermal emission of two-color polarized infrared waves from integrated plasmon cavities,” Appl. Phys. Lett. 92(14), 141114 (2008).
[Crossref]

Kanamori, Y.

H. Sai, Y. Kanamori, and H. Yugami, “High temperature resistive surface grating for spectral control of thermal radiation,” Appl. Phys. Lett. 82(11), 1685–1687 (2003).
[Crossref]

Kasaya, T.

H. T. Miyazaki, K. Ikeda, T. Kasaya, K. Yamamoto, Y. Inoue, K. Fujimura, T. Kanakugi, M. Okada, K. Hatade, and S. Kitagawa, “Thermal emission of two-color polarized infrared waves from integrated plasmon cavities,” Appl. Phys. Lett. 92(14), 141114 (2008).
[Crossref]

Kashiwa, T.

S. Maruyama, T. Kashiwa, H. Yugami, and M. Esashi, “Thermal radiation from two dimensionally confined mode in microcavities,” Appl. Phys. Lett. 79(9), 1393–1395 (2001).
[Crossref]

Kawabata, H.

F. Kusunoki, H. Kawabata, T. Hiroshima, J. Takahara, T. Kobayashi, T. Sumida, and S. Yanagida, “Suppression of total radiant flux by three-dimensional photonic crystal coatings,” Electron. Lett. 39(7), 622–623 (2003).
[Crossref]

Kim, T. G.

Kitagawa, S.

H. T. Miyazaki, K. Ikeda, T. Kasaya, K. Yamamoto, Y. Inoue, K. Fujimura, T. Kanakugi, M. Okada, K. Hatade, and S. Kitagawa, “Thermal emission of two-color polarized infrared waves from integrated plasmon cavities,” Appl. Phys. Lett. 92(14), 141114 (2008).
[Crossref]

Klein, L.

Kobayashi, T.

F. Kusunoki, T. Kohama, T. Hiroshima, S. Fukumoto, J. Takahara, and T. Kobayashi, “Narrow-band thermal radiation with low directivity by resonant modes inside tungsten microcavity,” Jpn. J. Appl. Phys. 43(No. 8A), 5253–5258 (2004).
[Crossref]

F. Kusunoki, H. Kawabata, T. Hiroshima, J. Takahara, T. Kobayashi, T. Sumida, and S. Yanagida, “Suppression of total radiant flux by three-dimensional photonic crystal coatings,” Electron. Lett. 39(7), 622–623 (2003).
[Crossref]

Kohama, T.

F. Kusunoki, T. Kohama, T. Hiroshima, S. Fukumoto, J. Takahara, and T. Kobayashi, “Narrow-band thermal radiation with low directivity by resonant modes inside tungsten microcavity,” Jpn. J. Appl. Phys. 43(No. 8A), 5253–5258 (2004).
[Crossref]

Kropachev, A.

S. Tay, A. Kropachev, I. E. Araci, T. Skotheim, R. A. Norwood, and N. Peyghambarian, “Plasmonic thermal IR emitters based on nanoamorphous carbon,” Appl. Phys. Lett. 94(7), 071113 (2009).
[Crossref]

Kusunoki, F.

F. Kusunoki, T. Kohama, T. Hiroshima, S. Fukumoto, J. Takahara, and T. Kobayashi, “Narrow-band thermal radiation with low directivity by resonant modes inside tungsten microcavity,” Jpn. J. Appl. Phys. 43(No. 8A), 5253–5258 (2004).
[Crossref]

F. Kusunoki, H. Kawabata, T. Hiroshima, J. Takahara, T. Kobayashi, T. Sumida, and S. Yanagida, “Suppression of total radiant flux by three-dimensional photonic crystal coatings,” Electron. Lett. 39(7), 622–623 (2003).
[Crossref]

Lacey, J. A.

Le Gall, J.

J. Le Gall, M. Olivier, and J.-J. Greffet, “Experimental and theoretical study of reflection and coherence thermal emission by a SiC grating supporting a surface-phonon polariton,” Phys. Rev. B 55(15), 10105–10114 (1997).
[Crossref]

Lee, J. H.

Leung, W.

Lin, S. Y.

S. Y. Lin, J. G. Fleming, and I. El-Kady, “Three-dimensional photonic-crystal emission through thermal excitation,” Opt. Lett. 28(20), 1909–1911 (2003).
[Crossref] [PubMed]

S. Y. Lin, J. G. Fleming, and I. El-Kady, “Highly efficient light emission at λ = 1.5 microm by a three-dimensional tungsten photonic crystal,” Opt. Lett. 28(18), 1683–1685 (2003).
[Crossref] [PubMed]

J. G. Fleming, S. Y. Lin, I. El-Kady, R. Biswas, and K. M. Ho, “All-metallic three-dimensional photonic crystals with a large infrared bandgap,” Nature 417(6884), 52–55 (2002).
[Crossref] [PubMed]

S. Y. Lin, J. G. Fleming, E. Chow, J. Bur, K. K. Choi, and A. Goldberg, “Enhancement and supression of thermal emission by a three-dimensional photonic crystal,” Phys. Rev. B 62(4), R2243–R2246 (2000).
[Crossref]

Mainguy, S.

J. J. Greffet, R. Carminati, K. Joulain, J. P. Mulet, S. Mainguy, and Y. Chen, “Coherent emission of light by thermal sources,” Nature 416(6876), 61–64 (2002).
[Crossref] [PubMed]

Maruyama, S.

S. Maruyama, T. Kashiwa, H. Yugami, and M. Esashi, “Thermal radiation from two dimensionally confined mode in microcavities,” Appl. Phys. Lett. 79(9), 1393–1395 (2001).
[Crossref]

McNeal, M. P.

M. U. Pralle, N. Moelders, M. P. McNeal, I. Puscasu, A. C. Greenwald, J. T. Daly, E. A. Johnson, T. George, D. S. Choi, I. El-Kady, and R. Biswas, “Photonic crystal enhanced narrow-band infrared emitters,” Appl. Phys. Lett. 81(25), 4685–4687 (2002).
[Crossref]

Miyazaki, H. T.

H. T. Miyazaki, K. Ikeda, T. Kasaya, K. Yamamoto, Y. Inoue, K. Fujimura, T. Kanakugi, M. Okada, K. Hatade, and S. Kitagawa, “Thermal emission of two-color polarized infrared waves from integrated plasmon cavities,” Appl. Phys. Lett. 92(14), 141114 (2008).
[Crossref]

Moelders, N.

M. U. Pralle, N. Moelders, M. P. McNeal, I. Puscasu, A. C. Greenwald, J. T. Daly, E. A. Johnson, T. George, D. S. Choi, I. El-Kady, and R. Biswas, “Photonic crystal enhanced narrow-band infrared emitters,” Appl. Phys. Lett. 81(25), 4685–4687 (2002).
[Crossref]

Mulet, J. P.

J. J. Greffet, R. Carminati, K. Joulain, J. P. Mulet, S. Mainguy, and Y. Chen, “Coherent emission of light by thermal sources,” Nature 416(6876), 61–64 (2002).
[Crossref] [PubMed]

Norwood, R. A.

S. Tay, A. Kropachev, I. E. Araci, T. Skotheim, R. A. Norwood, and N. Peyghambarian, “Plasmonic thermal IR emitters based on nanoamorphous carbon,” Appl. Phys. Lett. 94(7), 071113 (2009).
[Crossref]

O’Neill, P.

A. Ignatiev, P. O’Neill, C. Doland, and G. Zajac, “Microstructure dependence of the optical properties of solar absorbing black chrome,” Appl. Phys. Lett. 34(1), 42–44 (1979).
[Crossref]

Okada, M.

H. T. Miyazaki, K. Ikeda, T. Kasaya, K. Yamamoto, Y. Inoue, K. Fujimura, T. Kanakugi, M. Okada, K. Hatade, and S. Kitagawa, “Thermal emission of two-color polarized infrared waves from integrated plasmon cavities,” Appl. Phys. Lett. 92(14), 141114 (2008).
[Crossref]

Olivier, M.

J. Le Gall, M. Olivier, and J.-J. Greffet, “Experimental and theoretical study of reflection and coherence thermal emission by a SiC grating supporting a surface-phonon polariton,” Phys. Rev. B 55(15), 10105–10114 (1997).
[Crossref]

Peyghambarian, N.

S. Tay, A. Kropachev, I. E. Araci, T. Skotheim, R. A. Norwood, and N. Peyghambarian, “Plasmonic thermal IR emitters based on nanoamorphous carbon,” Appl. Phys. Lett. 94(7), 071113 (2009).
[Crossref]

Pralle, M. U.

M. U. Pralle, N. Moelders, M. P. McNeal, I. Puscasu, A. C. Greenwald, J. T. Daly, E. A. Johnson, T. George, D. S. Choi, I. El-Kady, and R. Biswas, “Photonic crystal enhanced narrow-band infrared emitters,” Appl. Phys. Lett. 81(25), 4685–4687 (2002).
[Crossref]

Puscasu, I.

I. Puscasu and W. L. Schaich, “Narrow-band tunable infrared emission from arrays of microstrip patches,” Appl. Phys. Lett. 92(23), 233102 (2008).
[Crossref]

M. U. Pralle, N. Moelders, M. P. McNeal, I. Puscasu, A. C. Greenwald, J. T. Daly, E. A. Johnson, T. George, D. S. Choi, I. El-Kady, and R. Biswas, “Photonic crystal enhanced narrow-band infrared emitters,” Appl. Phys. Lett. 81(25), 4685–4687 (2002).
[Crossref]

Sai, H.

H. Sai, Y. Kanamori, and H. Yugami, “High temperature resistive surface grating for spectral control of thermal radiation,” Appl. Phys. Lett. 82(11), 1685–1687 (2003).
[Crossref]

Schaich, W. L.

I. Puscasu and W. L. Schaich, “Narrow-band tunable infrared emission from arrays of microstrip patches,” Appl. Phys. Lett. 92(23), 233102 (2008).
[Crossref]

Schuller, J. A.

J. A. Schuller, T. Taubner, and M. L. Brongersma, “Optical antenna thermal emitters,” Nat. Photonics 3(11), 658–661 (2009).
[Crossref]

Shih, M. H.

Skotheim, T.

S. Tay, A. Kropachev, I. E. Araci, T. Skotheim, R. A. Norwood, and N. Peyghambarian, “Plasmonic thermal IR emitters based on nanoamorphous carbon,” Appl. Phys. Lett. 94(7), 071113 (2009).
[Crossref]

Smith, G. B.

G. Zajac, G. B. Smith, and A. Ignatiev, “Refinement of solar absorbing black chrome microstructure and its relationship to optical degradation mechanism,” J. Appl. Phys. 51(10), 5544–5554 (1980).
[Crossref]

Smith, T.

T. Smith and J. Guild, “The C. I. E. colorimetric standards and their use,” Trans. Opt. Soc. 33(3), 73–134 (1932).
[Crossref]

Spura, S. A.

J. C. C. Fan and S. A. Spura, “Selective black absorbers using rf-sputtered Cr2O3/Cr cermet films,” Appl. Phys. Lett. 30(10), 511–513 (1977).
[Crossref]

Sumida, T.

F. Kusunoki, H. Kawabata, T. Hiroshima, J. Takahara, T. Kobayashi, T. Sumida, and S. Yanagida, “Suppression of total radiant flux by three-dimensional photonic crystal coatings,” Electron. Lett. 39(7), 622–623 (2003).
[Crossref]

Takahara, J.

F. Kusunoki, T. Kohama, T. Hiroshima, S. Fukumoto, J. Takahara, and T. Kobayashi, “Narrow-band thermal radiation with low directivity by resonant modes inside tungsten microcavity,” Jpn. J. Appl. Phys. 43(No. 8A), 5253–5258 (2004).
[Crossref]

F. Kusunoki, H. Kawabata, T. Hiroshima, J. Takahara, T. Kobayashi, T. Sumida, and S. Yanagida, “Suppression of total radiant flux by three-dimensional photonic crystal coatings,” Electron. Lett. 39(7), 622–623 (2003).
[Crossref]

Taubner, T.

J. A. Schuller, T. Taubner, and M. L. Brongersma, “Optical antenna thermal emitters,” Nat. Photonics 3(11), 658–661 (2009).
[Crossref]

Tay, S.

S. Tay, A. Kropachev, I. E. Araci, T. Skotheim, R. A. Norwood, and N. Peyghambarian, “Plasmonic thermal IR emitters based on nanoamorphous carbon,” Appl. Phys. Lett. 94(7), 071113 (2009).
[Crossref]

Tsai, D. P.

Wang, C. M.

Yamamoto, K.

H. T. Miyazaki, K. Ikeda, T. Kasaya, K. Yamamoto, Y. Inoue, K. Fujimura, T. Kanakugi, M. Okada, K. Hatade, and S. Kitagawa, “Thermal emission of two-color polarized infrared waves from integrated plasmon cavities,” Appl. Phys. Lett. 92(14), 141114 (2008).
[Crossref]

Yanagida, S.

F. Kusunoki, H. Kawabata, T. Hiroshima, J. Takahara, T. Kobayashi, T. Sumida, and S. Yanagida, “Suppression of total radiant flux by three-dimensional photonic crystal coatings,” Electron. Lett. 39(7), 622–623 (2003).
[Crossref]

Yugami, H.

H. Sai, Y. Kanamori, and H. Yugami, “High temperature resistive surface grating for spectral control of thermal radiation,” Appl. Phys. Lett. 82(11), 1685–1687 (2003).
[Crossref]

S. Maruyama, T. Kashiwa, H. Yugami, and M. Esashi, “Thermal radiation from two dimensionally confined mode in microcavities,” Appl. Phys. Lett. 79(9), 1393–1395 (2001).
[Crossref]

Zajac, G.

G. Zajac, G. B. Smith, and A. Ignatiev, “Refinement of solar absorbing black chrome microstructure and its relationship to optical degradation mechanism,” J. Appl. Phys. 51(10), 5544–5554 (1980).
[Crossref]

A. Ignatiev, P. O’Neill, C. Doland, and G. Zajac, “Microstructure dependence of the optical properties of solar absorbing black chrome,” Appl. Phys. Lett. 34(1), 42–44 (1979).
[Crossref]

Zavracky, P. M.

J. C. C. Fan and P. M. Zavracky, “Selective black absorbers using MgO/Au cermet films,” Appl. Phys. Lett. 29(8), 478–480 (1976).
[Crossref]

Zemel, J. N.

P. J. Hesketh, J. N. Zemel, and B. Gebhart, “Polarized spectral emittance from periodic micromachined surface. II. Doped silicon: angular variation,” Phys. Rev. B 37(18), 10803–10813 (1988).
[Crossref]

P. J. Hesketh, J. N. Zemel, and B. Gebhart, “Polarized spectral emittance from periodic micromachined surface. I. Doped silicon: The normal direction,” Phys. Rev. B 37(18), 10795–10802 (1988).
[Crossref]

P. J. Hesketh, J. N. Zemel, and B. Gebhart, “Organ pipe radiant modes of periodic micromachined silicon surfaces,” Nature 324(6097), 549–551 (1986).
[Crossref]

Appl. Phys. Lett. (9)

S. Tay, A. Kropachev, I. E. Araci, T. Skotheim, R. A. Norwood, and N. Peyghambarian, “Plasmonic thermal IR emitters based on nanoamorphous carbon,” Appl. Phys. Lett. 94(7), 071113 (2009).
[Crossref]

H. Sai, Y. Kanamori, and H. Yugami, “High temperature resistive surface grating for spectral control of thermal radiation,” Appl. Phys. Lett. 82(11), 1685–1687 (2003).
[Crossref]

S. Maruyama, T. Kashiwa, H. Yugami, and M. Esashi, “Thermal radiation from two dimensionally confined mode in microcavities,” Appl. Phys. Lett. 79(9), 1393–1395 (2001).
[Crossref]

I. Puscasu and W. L. Schaich, “Narrow-band tunable infrared emission from arrays of microstrip patches,” Appl. Phys. Lett. 92(23), 233102 (2008).
[Crossref]

H. T. Miyazaki, K. Ikeda, T. Kasaya, K. Yamamoto, Y. Inoue, K. Fujimura, T. Kanakugi, M. Okada, K. Hatade, and S. Kitagawa, “Thermal emission of two-color polarized infrared waves from integrated plasmon cavities,” Appl. Phys. Lett. 92(14), 141114 (2008).
[Crossref]

M. U. Pralle, N. Moelders, M. P. McNeal, I. Puscasu, A. C. Greenwald, J. T. Daly, E. A. Johnson, T. George, D. S. Choi, I. El-Kady, and R. Biswas, “Photonic crystal enhanced narrow-band infrared emitters,” Appl. Phys. Lett. 81(25), 4685–4687 (2002).
[Crossref]

A. Ignatiev, P. O’Neill, C. Doland, and G. Zajac, “Microstructure dependence of the optical properties of solar absorbing black chrome,” Appl. Phys. Lett. 34(1), 42–44 (1979).
[Crossref]

J. C. C. Fan and P. M. Zavracky, “Selective black absorbers using MgO/Au cermet films,” Appl. Phys. Lett. 29(8), 478–480 (1976).
[Crossref]

J. C. C. Fan and S. A. Spura, “Selective black absorbers using rf-sputtered Cr2O3/Cr cermet films,” Appl. Phys. Lett. 30(10), 511–513 (1977).
[Crossref]

Electron. Lett. (1)

F. Kusunoki, H. Kawabata, T. Hiroshima, J. Takahara, T. Kobayashi, T. Sumida, and S. Yanagida, “Suppression of total radiant flux by three-dimensional photonic crystal coatings,” Electron. Lett. 39(7), 622–623 (2003).
[Crossref]

J. Appl. Phys. (1)

G. Zajac, G. B. Smith, and A. Ignatiev, “Refinement of solar absorbing black chrome microstructure and its relationship to optical degradation mechanism,” J. Appl. Phys. 51(10), 5544–5554 (1980).
[Crossref]

Jpn. J. Appl. Phys. (1)

F. Kusunoki, T. Kohama, T. Hiroshima, S. Fukumoto, J. Takahara, and T. Kobayashi, “Narrow-band thermal radiation with low directivity by resonant modes inside tungsten microcavity,” Jpn. J. Appl. Phys. 43(No. 8A), 5253–5258 (2004).
[Crossref]

Nat. Photonics (1)

J. A. Schuller, T. Taubner, and M. L. Brongersma, “Optical antenna thermal emitters,” Nat. Photonics 3(11), 658–661 (2009).
[Crossref]

Nature (3)

J. J. Greffet, R. Carminati, K. Joulain, J. P. Mulet, S. Mainguy, and Y. Chen, “Coherent emission of light by thermal sources,” Nature 416(6876), 61–64 (2002).
[Crossref] [PubMed]

P. J. Hesketh, J. N. Zemel, and B. Gebhart, “Organ pipe radiant modes of periodic micromachined silicon surfaces,” Nature 324(6097), 549–551 (1986).
[Crossref]

J. G. Fleming, S. Y. Lin, I. El-Kady, R. Biswas, and K. M. Ho, “All-metallic three-dimensional photonic crystals with a large infrared bandgap,” Nature 417(6884), 52–55 (2002).
[Crossref] [PubMed]

Opt. Express (3)

Opt. Lett. (2)

Phys. Rev. B (4)

S. Y. Lin, J. G. Fleming, E. Chow, J. Bur, K. K. Choi, and A. Goldberg, “Enhancement and supression of thermal emission by a three-dimensional photonic crystal,” Phys. Rev. B 62(4), R2243–R2246 (2000).
[Crossref]

P. J. Hesketh, J. N. Zemel, and B. Gebhart, “Polarized spectral emittance from periodic micromachined surface. I. Doped silicon: The normal direction,” Phys. Rev. B 37(18), 10795–10802 (1988).
[Crossref]

P. J. Hesketh, J. N. Zemel, and B. Gebhart, “Polarized spectral emittance from periodic micromachined surface. II. Doped silicon: angular variation,” Phys. Rev. B 37(18), 10803–10813 (1988).
[Crossref]

J. Le Gall, M. Olivier, and J.-J. Greffet, “Experimental and theoretical study of reflection and coherence thermal emission by a SiC grating supporting a surface-phonon polariton,” Phys. Rev. B 55(15), 10105–10114 (1997).
[Crossref]

Trans. Opt. Soc. (1)

T. Smith and J. Guild, “The C. I. E. colorimetric standards and their use,” Trans. Opt. Soc. 33(3), 73–134 (1932).
[Crossref]

Other (4)

D. G. Fink, and H. W. Beaty, Standard Handbook for Electric Engineers, 11th Edition, McGraw-Hill, New York, 1978, p. 22.

Magazine Online, (see also http://www.homelighting.com/article.cfm?intarticleID=880 ).

T. J. Keefe, (2007). The nature of light. (see also http://www.ccri.edu/physics/keefe/light.htm ).

D. L. Klipstein, (1996). The great internet light bulb book, part 1. (see also http://freespace. virgin.net/tom. baldwin/bulbguide.html ).

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Figures (4)

Fig. 1
Fig. 1 Emitter reflectance spectrum. The reflectance spectrum is a step-function-like structure designed to shift the resulting radiation toward the visible. The lower inset shows the optical thin-film structure observed by a transmission electron microscope (TEM). The upper inset presents the quantitative model for the modification of the blackbody radiation. The black line represents the reflectance spectrum, the blue line is the emissivity spectrum described by ε(λ) = 1 - R(λ), the green line is the blackbody radiation spectrum, and the red line is the modulated thermal radiation created by the product of the blackbody radiation spectrum and the emissivity ε(λ).
Fig. 2
Fig. 2 Thermal radiation spectrum from the emitter obtained by a FTIR spectrometer at 580 K (red circles), 670 K (yellow circles), 785 K (green circles), and 870 K (blue circles). For comparison, the thermal radiation spectrum from a copper plate (emissivity ε0 = 0.13) is shown (open squares). The thermal radiation spectrum of the plate obeys Planck’s law, and the results are fit by solid curves. The arrows mark the peak positions of the thermal radiation spectrum for the emitter and the plate for each temperature. The inset shows the 580 K thermal radiation spectrum from the emitter (solid circles) and the plate (open squares). The radiation spectrum of the emitter was fit using the product of the wavelength-dependent emissivity and Planck’s law, and the results were fit with theoretical curves obtained using Eq. (5).
Fig. 3
Fig. 3 The total radiation intensity as a function of temperature (T4) for the copper plates (blue circles) and the emitters (red circles). The Stefan–Boltzmann law, I∝T4, is clearly shown for the plate. The red line is the theoretical fit determined by Eq. (6). The inset shows the change in temperature as a function of input power for the plates (blue circles) and for the emitters (red circles) to estimate the ratio of the energy dissipation between the thermal radiation and the conduction. The solid blue line is the curve obtained using Eq. (7), given the linear dependence of conduction loss on temperature, denoted by the solid black line. The solid red line is the theoretical fit to the power dissipation curve of the emitters obtained by Eq. (8). This leads to the conclusion that almost 80% of the input power can be converted into thermal radiation at shorter wavelengths using the emitter.
Fig. 4
Fig. 4 The blue line represents the theoretical temperature change as a function of input power generated from Eq. (8), given an emitter with a cutoff wavelength of λ0 = 0.7 μm. The black line is the heat dissipation term due to conduction from electric wires. The broken red line is the extracted radiative power from the emitter given the step-function reflectance spectrum described in the upper inset. The red curve in the upper inset is a theoretically derived radiation spectrum, and the green line is the spectral luminous efficiency curve. The chromaticity of the incandescent lamp investigated here centers on the red circle of the inset CIE chromaticity diagram, and its correlated color temperature is beyond 9000 K.

Equations (8)

Equations on this page are rendered with MathJax. Learn more.

Pin = Pcond + Prad,
ε   ​ ​ ( λ )   ​ ​ = 1 R ​ ​ ​ ( λ ) .
Φ   ​ ​ ( λ )   ​ ​ = ε   ​ ​ ( λ ) B   ​ ​ ( λ ) ,
B ( λ ) = α λ −5 exp ( β / λ T ) 1 ,
Φ ( λ ) = ε ( λ ) α λ 5 exp ( β / λ T ) 1 .
I e m i t ( T ) = ε 0 0 ( λ λ 0 ) α λ 5 exp ( β / λ T ) 1 d λ ,
P C u ( T ) = ε σ S ( T 4 T 0 4 ) + ξ ( T T 0 ) ,
P e m i t   ​ ​ ( T ) ​ ​ =   ​ { I e m i t   ​ ​ ( T ) I e m i t   ​ ​ ( T 0 ) } S + ξ   ​ ( T T 0 ) .

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