טכניון מכון טכנולוגי לישראל
הטכניון מכון טכנולוגי לישראל - בית הספר ללימודי מוסמכים  
M.Sc Thesis
M.Sc StudentShamir Shay
SubjectEnhanced Emission of Thermal Radiation in 2D
Wavelength-Scale Cylinders
DepartmentDepartment of Electrical Engineering
Supervisor Professor Levi Schachter
Full Thesis textFull thesis text - English Version


Abstract

Planck’s Law of Blackbody Radiation (BBR), usually taken as the bounding limit for the spectrum of Thermal Radiation, has been formulated subject to the assumption of dimensions much greater than wavelength. It is founded upon the approximation of a continuous Density of States (DOS), calculated for a large cavity. This, however, we know to be irrelevant for wavelength-scale bodies, whose dimensions allow for a finite amount of radiating states. The question of what the Blackbody Energy spectrum is for miniscule structures has been investigated, with emphasis on closed structures (resonant cavities). We methodically extend these results to open structures - investigating the thermal radiation of wavelength-scale bodies. Eminently, we aim to exceed the Blackbody limit, which is to say that we shall demonstrate how simple material configurations may emit more thermal radiation than a same-size Blackbody, at least in particular parts of the spectrum.

Such an enhancement could be practically useful in the field of Thermo-Photovoltaics (TPV), wherein heat energy (solar or other) is converted to IR radiation, which is itself tuned to match a solar cell's band-gap energy for maximum efficiency. In this context it is desirable to enhance emission within the wanted band of wavelengths, and a super-Planckian radiator could potentially improve a device's efficiency.

In this thesis, we study the thermal radiation given off in 2D by cylindrical structures, as they constitute a convenient platform for the subject at hand. To calculate thermal emissions it is necessary to use Rytov’s extension of the Fluctuation Dissipation Theorem (FDT) for continuous media. This relates the second moments of fluctuational fields and fluctuational sources to the operators that relate the two - essentially the problem’s Greens functions and their inverse operators. Furthermore it is shown by utilizing the reciprocity theorem that the emission coefficient (emission relative to Planck's Law, known as emissivity) is equal to the normalized absorption cross section, thereby extending the well-known Kirchhoff Law from the geometric optics regime to the wavelength scale regime.

The results obtained for cylinder radiation show that emissivity may exceed unity by many orders of magnitude through use of appropriate materials. We clarify that this is the result of electromagnetic modes entering resonance, which behaves differently for low-loss materials and high-loss materials. Finally, we demonstrate how metallic nano-rods (using real material data relevant for TPV applications at high temperatures) may achieve this enhanced emission, and analyze the counter-intuitive result that thermal radiation may be naturally polarized under some conditions. Further theoretical improvement achieved by coating the nano-rods with a dielectric layer is also shown and analyzed. In particular, we show that contrary to what one might suspect, the coating layer can in principle act as more than a mere filter, since it may enhance the overall emission of the compound structure (radiator together with the coating layer) relative to a Blackbody of the same dimensions as the compound structure, and not only when compared to the emission of the base radiator by itself.