Geometric effects on blackbody radiation

Abstract

Planck's formula for blackbody radiation was formulated subject to the assumption that the radiating body is much larger than the emitted wavelength. We demonstrate that thermal radiation exceeding Planck's law may occur in a narrow spectral range when the local radius of curvature is comparable with the wavelength of the emitted radiation. Although locally the spectral enhancement may be of several orders of magnitude, the deviation from the Stefan-Boltzmann law is less than one order of magnitude. The fluctuation-dissipation theorem needs to be employed for adequate assessment of the spectrum in this regime. Several simple examples are presented as well as experimental results demonstrating the effect. For each configuration a geometric form factor needs to be incorporated into Planck's formula in order to properly describe the emitted radiation.

Measurements of single-state and state-ensemble lifetimes of high-lying Rb Rydberg levels

“…This leaves a variation in the black-body spectrum itself as a plausible explanation (other possible causes for enhanced decay, such as superradiance [29][30][31][32], are unlikely to play a role in our system due to the small number of excitations involved and the narrow range of parameters for which such effects are expected to occur in multi-level systems [33]). In fact, it is well known that the assumptions made in the derivation of the Planck formula for black-body radiation are no longer valid when the wavelength of the radiation becomes comparable to the size of the black body, as the density of modes is strongly modified close to the longest-wavelength modes supported by the cavity [34][35][36] (signatures of such an effect were detected experimentally in [37]). The dimensions of our vacuum cell (internal cross-section 1.8 cm x 2.4 cm, with a thin coating of adsorbed Rb atoms on the inner walls) and of the surrounding support structures and coils are of order a few centimetres.…”

Overcoming black body radiation limit in free space: metamaterial superemitter

“…Therefore, when dealing with an impedance matched emitter, we may approximate F lm by unity when l N max  , and by zero when l N max > when N a 2 1 max p l =  . This excludes the modes with l N max > from summation (10), and we obtain the following closed-form expression for the power spectral density:…”

“…[6][7][8][9]. Similarly, resonant absorption by shape irregularities with curvature radius a l  on a surface of a large body [10] makes the absorption cross section associated with an irregularity larger than its geometric cross section.…”

Scaling laws, pressure anisotropy, and thermodynamic effects for blackbody radiation in a finite cavity

“…In [14] it was shown that the experimental detection of deviations from the Planck's formula is within the reach of current experimental capabilities. Finally, in [12] the experimental observation of such deviations was reported: it was detected that in narrow spectral range thermal radiation may exceed the value predicted by the Planck's formula.…”

“…• Consideration of radiation from small particles, exploration of a particle size influence on thermal radiation spectrum ( [11], [12]). …”