Basics of Near-Field Thermal Radiation

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Thermal Radiation

Conventionally, the theory of thermal radiation is based on the concept of blackbody, cast by Gustav Kirchhoff in 1860. A blackbody absorbs all energy of the radiation rays reaching it geometrically. Among all objects at the same temperature with the same geometry, a blackbody emits the largest amount of energy when measured in the same angular and spectral ranges. As such, the Stefan-Boltzmann law and Planck’s law provide descriptions of the total and spectral characteristics of blackbodies. A blackbody is a diffuse emitter and the emitted intensity does not depend on the direction of emission. Thermal emission from real materials can be described by comparison with that emitted by a blackbody at the same temperature using a property called emissivity (also called emittance). Care should be taken as regards to the proper definition of emissivity (spectral, total, directional, individual polarization versus polarization averaged, etc.) [1-3].

Near-Field versus Far-Field

Near field optics refers to the situation when the geometric features or distances are smaller than the characteristic wavelength. In the near-field regime, conventional radiative transfer approaches are often not applicable. For very small objects such as particles with dimensions less than the wavelength, its interaction with the electromagnetic (EM) wave field is very different and cannot be modeled with geometric optics. Consider a solid sphere of diameter D in air. When a monochromatic EM plane wave passes by, the particle can scatter or absorb the energy of the EM wave. As it turns out, when the wavelength (λ) is much smaller than the diameter, λ << D, the absorbed radiation cannot exceed the product, G×Ac, where G is the irradiance (energy flux) of the incident field and Ac is the cross-sectional area. The situation is very different when λ is comparable with or larger than D. The interaction between the particle and the EM field is well described by Maxwell’s equations [4,5]. In such case, the particle can absorb more energy than a “blackbody” [5]. Here, the concept of blackbody breaks down. The same is true when dealing with other nanostructures such as nanoslits or nanoapertures, where the energy transmittance can exceed unity due to diffraction effect. Near-field effect can also affect the far-field properties of nanostructured surfaces or objects. In the far-field, no matter how complex the structure is, the emissivity and transmittance cannot exceed unity. However, unique spectral- and angular-dependent radiative properties can be achieved by engineering nano/microstructures. Surface waves and photonic band structures are often utilized to enable unique optical properties of nano/microstructures.

Near-Field Thermal Radiation

Planck [6] noted that the derivation of the spectral distribution of blackbody radiation is based on the assumption that the geometric dimensions of the enclosure (also called a blackbody cavity) are much greater than the characteristic wavelength of thermal radiation. It should also be noted that the energy density obtained by Planck’s law is only applicable away from the surface of any objects, i.e., in the far field. At distances much smaller than the characteristic wavelength of thermal radiation, which can be estimated based on the Wien’s displacement law [7], the energy density can be greatly enhanced due to near-field effect [3,8,9].

In essence, thermal radiation can be thought as due to the random fluctuation of charges (free or bound) in the material, forming dipoles that can emit EM waves. While the average of the field component such as the electric field or magnetic field is zero, the energy density and Poynting vector (which characterizes the energy flux) are nonzero and depend on the temperature and the dielectric and magnetic properties of materials. All but a very few naturally occurring materials are nonmagnetic in the optical and thermal radiation spectra from the ultraviolet to far-infrared. On the other hand, nanoengineered materials can exhibit diamagnetism, resulting in magnetic responses [10]. These materials are called metamaterials, which may possess negative refraction as well as other exotic properties [11]. The study of nanophotonics, plasmonics, and metamaterials are among the frontiers in optical and thermal radiation research [12].

Applications

Near-field radiation holds promise for applications in energy systems, nanofabrication and near-field imaging. Rapidly depleting reserves of fossil fuels and the concern of the level of greenhouse gases have placed a great demand of alternative power generation technologies. One of such technology is thermophotovoltaic (TPV) systems, which operate on the principle similar to that of solar cells (but with a lower bandgap) to generate electricity from thermal emission. A possible method of improving the performance of TPV systems is to employ near-field thermal radiation to the energy conversion [13]. Near-field thermal radiation has also been used for imaging beyond the diffraction limit [14,15]. Furthermore, the concept of using near-field radiation as thermal rectifier has also been suggested [16,17]. Limiting the magnitude of near-field radiation is critical for improving the performance of thermal tunneling devices [18].

Another important application of near-field radiation is in the field of nanomanufacturing. Enhanced transmission of metallic films perforated with subwavelength holes stirred the interest in studying light transmission through nanostructures. Nanolithography techniques based on the surface plasmon waves have been demonstrated for patterning structures of less than 50 nm [19,20]. Furthermore, nanoscale direct writing has also been demonstrated using near-field optics coupled with femtosecond laser [21].

Controlling the radiative properties has important applications in photonic and energy conversion systems such as solar cells and solar absorbers, thermophotovoltaic (TPV) devices, radiation filters, selective emitters, photodetectors, semiconductor processing, and optoelectronics [12,13,22,23]. The performance of various devices can be greatly enhanced by the modification of the reflection, transmission, absorption and emission spectra using one-, two-, or three-dimensional micro/nanostructures. Surface microstructures can also strongly affect the directional behavior of absorption and emission due to multiple reflections and diffraction, allowing the radiative properties to be tailored. Because of the important applications to energy transport and conversion, the study of engineered surfaces with desired thermal radiative characteristics has become an active research area.

References

[1] Howell, J. R., Siegel, R, and Menguc, M. P., 2010, Thermal Radiation Heat Transfer, 5th edn., CRC Press/Taylor & Francis Group, New York.

[2] Modest, M. F., 2003, Radiative Heat Transfer, 2nd ed., Academic Press, San Diego, 2003.

[3] Zhang, Z. M., 2007, Nano/Microscale Heat Transfer, McGraw-Hill, New York.

[4] Van de Hulst, H. C., 1957, Light Scattering by Small Particles, John Wiley & Sons, New York.

[5] Bohren, C. F., and Huffman, D. R., 1983, Absorption and Scattering of Light by Small Particles, Wiley & Sons, New York.

[6] Planck, M., 1959, The Theory of Heat Radiation, Dover Publ., New York.

[7] Zhang, Z. M., and Wang, X. J., 2010, "Unified Wien’s Displacement Law in Terms of the Logarithmic Frequency or Wavelength Scale," Journal of Thermophysics and Heat Transfer, 24, pp. 222-224.

[8] Fu, C. J., and Zhang, Z. M., 2006, "Nanoscale Radiation Heat Transfer for Silicon at Different Doping Levels," International Journal of Heat and Mass Transfer, 49, pp. 1703-1718.

[9] Basu, S., Zhang, Z. M., and Fu, C. J., 2009, "Review of Near-Field Thermal Radiation and Its Application to Energy Conversion," International Journal of Energy Research, 33, pp. 1203-1232.

[10] Wang, L.P., and Zhang, Z.M., 2011, “Phonon-Mediated Magnetic Polaritons in the Infrared Region,” Optics Express, 19, pp. A126–A135.

[11] Fu, C. J., and Zhang, Z.M., 2009, “Thermal Radiative Properties of Metamaterials and Other Nanostructured Materials: A Review,” Frontiers of Energy and Power Engineering in China, 3, pp. 11-26.

[12] Zhang, Z. M., and Wang, L. P., 2011, "Measurements and Modeling of the Spectral and Directional Radiative Properties of Micro/Nanostructured Materials," International Journal of Thermophysics, DOI: 10.1007/s10765-011-1036-5 (available online).

[13] Basu, S., Chen, Y. -B., and Zhang, Z. M., 2007, “Microscale Radiation in Thermophotovoltaic Devices – A Review,” International Journal of Energy Research, 31, pp. 689-716.

[14] De Wilde, Y., Formanek, F., Carminati, R., Gralak, B., Lemoine, P. A., Joulain, K., Mulet, J.-P., Chen, Y., and Greffet, J.-J., 2006, "Thermal Radiation Scanning Tunnelling Microscopy," Nature, 444, pp. 740-743.

[15] Kittel, A., Muller-Hirsch, W., Parisi, J., Biehs, S. A., Reddig, D., and Holthaus, M., 2005, "Near-Field Heat Transfer in a Scanning Thermal Microscope," Physics Review Letters, 95, p. 224301.

[16] Otey, C. R., Lau, W. T., and Fan, S., 2010, "Thermal Rectification through Vacuum," Physics Review Letters, 104, p. 154301.

[17] Basu, S., and Francoeur, M., 2011, "Near-Field Radiative Transfer Based Thermal Rectification Using Doped Silicon," Applied Physics Letters, 98, p. 113106.

[18] Dillner, U., 2008, "The Effect of Thermotunneling on the Thermoelectric Figure of Merit," Energy Conversion and Management, 19, pp. 3409-3416.

[19] Liu, Z. W., Wei, Q. H., and Zhang, X., 2005, “Surface Plasmon Interference Nanolithography,” Nano Letters, 5, pp. 957-961.

[20] Wang, L., Uppuluri, S. M., Jin, E. X., and Xu, X. F., 2006, “Nanolithography Using High Transmission Nanoscale Bowtie Apertures,” Nano Letters, 6, pp. 361-364.

[21] Grigoropoulos, C. P., Hwang, D. J., and Chimmalgi, A., 2007, "Nanometer-Scale Direct-Writing using Near-Field Optics," MRS Bulletin, 32, pp. 16–22.

[22] Zhang, Z. M., Fu, C. J., and Zhu, Q. Z., 2003 “Optical and Thermal Radiative Properties of Semiconductors Related to Micro/Nanotechnology,” in Advances in Heat Transfer, Academic Press, San Diego, 37, pp. 179-296.

[23] Zhu, Q. Z., Lee, H. J., and Zhang, Z. M., 2009, “Radiative Properties of Materials with Surface Scattering or Volume Scattering: A Review,” Frontiers of Energy and Power Engineering in China, 3, pp. 60-79.