Thermal radiation is traditionally considered to be incoherent. However, it has been shown that the electromagnetic waves thermally emitted by a medium can be highly correlated in both near-field and far-field regimes depending on the geometry, material, and observation distance. While the spatial coherence of thermal emission has been widely studied for planar media, spatial coherence for finite non-planar media is almost unexplored. The spectral and spatial properties of thermal emission by spheres are of importance as they are the building blocks for many man-made materials such as Mie-resonance-based metamaterials. In this study, we develop analytical expressions for the energy density and spatial correlation function of thermal emission by a homogeneous and isothermal sphere with an arbitrary size and material. The energy density and spatial coherence of the thermal emission are explored for silicon carbide (dielectric), silicon (semiconducting), and tungsten (metallic) spheres in the extreme near-field, intermediate near-field, and far-field regimes, and the effects of size parameter (*X*), material, and localized surface phonons (LSPhs) are investigated in each regime. It is shown that the energy density follows a power law of *d*^-2^ (*d* is the observation distance) in the far field. The near-field energy density by spheres with *X*\<\<1 and *d*/*a*\>\>1 (*a* is the radius of the sphere) varies with the distance as *d*^-6^  which is similar to the power law for an electric point dipole. With increasing *X* or decreasing *d*/*a*, the power law deviates from that for a dipole and eventually converges to the one for a semi-infinite medium (*d*^-2.5^, *d*^-0.5^, and *d*^-3.5^ for silicon carbide, silicon, and tungsten, respectively, in the intermediate near field, and *d*^-3.5^, *d*^-3.5^, and *d*^-2.5^ for silicon carbide, silicon, and tungsten, respectively, in the extreme near field). Moreover, it is found that the correlation length in the radial direction when normalized by the wavelength is in the order of 0.001, 0.1, and 1 in the extreme near-field, intermediate near-field, and far-field regimes, respectively. In the polar direction, the correlation angle is strongly size-dependent in the extreme near-field regime, and, when normalized by a factor of pi, it varies from 0.5 to 0.001 as *X* increases from 0.002 to 5. The normalized correlation angle retains an order of magnitude of 0.1 for all size parameters in the intermediate near-field and far-field regimes. Finally, it is shown that the multipolar LSPhs reduce the spatial coherence along both radial and polar directions in the extreme and intermediate near field, while the dipolar LSPh has no effect on the spatial coherence.


Energy Density and Spatial Coherence of Thermal Emission by Single Spheres

Division / Sponsors: 
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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