A Theoretical Study on the Effect of Curvature on Near-field Radiative Transfer

The dissertation focuses on the theoretical analysis of near-field electromagnetic wave effects in thermal radiative transfer i.e. wave effects like interference, diffraction, and tunneling effects, that become important when analyzing energy transfer via electromagnetic waves over sub-wavelength distances. In particular, the focus will be on the enhanced thermal radiative transfer between bodies made of polar dielectric materials which support surface phonon polaritons (SPPs). When two such bodies are brought in close proximity to each other, the enhanced near-field radiation due to tunneling of SPPs can exceed the classical black body limit by several orders of magnitude. This enhanced radiation at nano-scale gaps finds applications in near-field thermophotovoltaics, heat assisted magnetic recording and near-field radiative cooling. While the dependence of near-field radiative transfer on the gap between two planar objects is well understood, the effect of curvature on near-field radiative transfer is unclear. In particular, the relevance of an approximate method to predict the near-field interaction between curved bodies (called the proximity approximate method) is disputed. Hence, the computation of near-field radiative transfer between curved bodies, such as between two spherical bodies, become important. The existing method for computing near-field radiative transfer between two spheres is highly inefficient in probing small gaps where the near-field enhancement is most observed. The objective of this work is not only to simplify this computational framework which would enable us to probe smaller gaps and understand the effect of curvature on near-field radiative transfer better, but also to provide a method to extend this to unequal sized spheres with large size disparities, so that comparison can be made with existing experimental measurements for near-field radiative transfer between a sphere and a plane. In this regard a simplified form of vector translation addition theorem has been proposed which is valid for general near-field electromagnetic scattering problems. The range of validity of this approximation for the translation addition theorem has been discussed and recursion relations have been derived for computing the translation coefficients under this approximation. A method for normalizing the translation coefficients has also been proposed, and the computation of these normalized translation coefficients has been shown to depend only on ratios of successive orders of Bessel and Hankel functions which are computationally inexpensive. An analysis of the dependence of normalized translation coefficients on the size ratio of the two spheres has allowed us to extend the computation of near-field radiative transfer calculations to spheres with large size disparities. Based on the computations, I have shown that the surface phonon polariton mediated radiative transfer between two spheres of effective radius R = (R_1 R_2)/(R_1 + R_2), where R_1 and R_2 are the radii of the individual spheres, and minimum gap, d, scales as R/d as the non-dimensional gap d/R goes to 0. I have proposed a modified form of proximity approximation to satisfy the continuity requirement between far-field and near-field radiative transfer between the spheres. The validity of this modified form of proximity approximation at different frequencies has also been discussed. This method can be applied to approximate the near-field radiative transfer between, not just spherical surfaces, but other general curved surfaces such as between cylindrical or conical surfaces