Man-made materials engineered at the sub-wavelength scale (the dominant wavelength of thermal radiation at room temperature is about 10 mm) offer great potential for tuning the magnitude and the spectrum of near-field thermal emission. Nanowire arrays are a class of man-made materials that have attracted significant attention as they can support both hyperbolic modes resulting in a broadband enhancement of thermal emission and surface phonons resulting in narrow-band peaks in the spectrum of thermal radiation. Near-field radiative properties of nanowire arrays are usually studied using the effective medium theory (EMT). Using EMT, the nanowire array is modeled as an anisotropic homogeneous film with effective parallel (to the optical axis which is along the nanowires axis) and perpendicular dielectric functions. The EMT is assumed to be valid in the long-wavelength regime (i.e., when the nanowires and the array pitch are much smaller than the thermal wavelength) at observation distances, *z~o~*, greater than the array pitch, *L*, by a factor of 1/pi. However, this assumption has not been fully examined. In this study, the validity of the Maxwell-Garnett (MG) and Bruggeman (BR) EMTs for modeling near-field thermal emission by nanowire arrays is inspected. Near-field energy density emitted by various nanowire arrays with various filling factors, nanowire heights, and diameters is calculated using the MG and BR EMTs at different perpendicular and lateral observation distances. Quartz nanowires are selected for this study as they support both hyperbolic and surface phonon-polariton modes based on the EMT. The calculated near-field emission spectra using the EMTs are compared to numerical simulations using the thermal discrete dipole approximation (T-DDA), which is a numerically exact solution of the Maxwell equations augmented by the thermally fluctuating current given by the fluctuation-dissipation theorem. It is concluded that neither MG nor BR EMT can accurately predict the spectrum and the magnitude of near-field thermal emission by nanowire arrays for *L*/*z~o~* greater than pi. Although it is assumed that the EMT is valid when *L*/*z~o~* is less than pi, it is shown that this theory deviates significantly from the T-DDA when *L*/*z~o~* is smaller than 1. Among the two EMTs, it is observed that MG EMT is slightly more consistent with T-DDA numerical simulations than the BR EMT. Finally, the T-DDA numerical simulations show that the variations of near-field thermal emission by nanowire arrays in lateral directions can be very significant. These variations, however, cannot be captured using the EMTs.


Validity of the Effective Medium Theory for Modeling Near-Field Thermal Emission by Nanowire Arrays

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Aerospace, Bioengineering, Applied Mechanics, Design Engineering Division, Advanced Energy Systems, Manufacturing Engineering Division, Noise Control and Acoustics, Nondestructive Evaluation, Diagnosis, and Prognosis (NDPD), Nuclear Engineering Division, Process Industries Division, Fluids Engineering, Heat Transfer, Materials, Microelectromechanical Systems, Safety Engineering and Risk Analysis, Computers & Information in Engineering


Paper Proceedings: https://asmedigitalcollection.asme.org/IMECE/IMECE2020/volume/84478

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