Proximity Effects in Radiative Heat Transfer

Though the dependence of near-field radiative transfer on the gap between two planar objects is well understood, that between curved objects is still unclear. We show unequivocally that the surface polariton mediated radiative transfer between two spheres of equal radii R and minimum gap d scales as R/d as the nondimensional gap d/R→0. We discuss the proximity approximation form that is being used at present to compare with experimental observations and suggest a modified form in order to satisfy the continuity requirement between far-field and near-field radiative transfer between the spheres

Convergence of Vector Spherical Wave Expansion Method Applied to Near-Field Radiative Transfer

Near-field radiative transfer between two objects can be computed using Rytov’s theory of fluctuational electrodynamics in which the strength of electromagnetic sources is related to temperature through the fluctuation-dissipation theorem, and the resultant energy transfer is described using the dyadic Green’s function of the vector Helmholtz equation. When the two objects are spheres, the dyadic Green’s function can be expanded in a series of vector spherical waves. Based on comparison with the convergence criterion for the case of radiative transfer between two parallel surfaces, we derive a relation for the number of vector spherical waves required for convergence in the case of radiative transfer between two spheres. We show that when electromagnetic surface waves are active at a frequency the number of vector spherical waves required for convergence is proportional to Rmax /d when d/Rmax → 0, where Rmax is the radius of the larger sphere, and d is the smallest gap between the two spheres. This criterion for convergence applies equally well to other near-field electromagnetic scattering problems

Convergence of Vector Spherical Wave Expansion Method Applied to Near-Field Radiative Transfer

Near-field radiative transfer between two objects can be computed using Rytov’s theory of fluctuational electrodynamics in which the strength of electromagnetic sources is related to temperature through the fluctuation-dissipation theorem, and the resultant energy transfer is described using the dyadic Green’s function of the vector Helmholtz equation. When the two objects are spheres, the dyadic Green’s function can be expanded in a series of vector spherical waves. Based on comparison with the convergence criterion for the case of radiative transfer between two parallel surfaces, we derive a relation for the number of vector spherical waves required for convergence in the case of radiative transfer between two spheres. We show that when electromagnetic surface waves are active at a frequency the number of vector spherical waves required for convergence is proportional to Rmax /d when d/Rmax → 0, where Rmax is the radius of the larger sphere, and d is the smallest gap between the two spheres. This criterion for convergence applies equally well to other near-field electromagnetic scattering problems

Near-field radiative transfer between two unequal sized spheres with large size disparities

We compute near-field radiative transfer between two spheres of unequal radii R1 and R2 such that R2 ≲ 40R1. For R2 = 40R1, the smallest gap to which we have been able to compute radiative transfer is d = 0.016R1. To accomplish these computations, we have had to modify existing methods for computing near-field radiative transfer between two spheres in the following ways: (1) exact calculations of coefficients of vector translation theorem are replaced by approximations valid for the limit d ≪ R1, and (2) recursion relations for a normalized form of translation coefficients are derived which enable us to replace computations of spherical Bessel and Hankel functions by computations of ratios of spherical Bessel or spherical Hankel functions. The results are then compared with the predictions of the modified proximity approximation

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

A surface-scattering model satisfying energy conservation and reciprocity

In order for surface scattering models to be accurate they must necessarily satisfy energy conservation and reciprocity principles. Roughness scattering models based on Kirchoff's approximation or perturbation theory do not satisfy these criteria in all frequency ranges. Here we present a surface scattering model based on analysis of scattering from a layer of particles on top of a substrate in the dipole approximation which satisfies both energy conservation and reciprocity and is thus accurate in all frequency ranges. The model takes into account the absorption in the substrate induced by the particles but does not take into account the near-field interactions between the particles.Comment: 15 pages, 10 figure

Proximity Effects in Radiative Transfer

Though the dependence of near-field radiative transfer on the gap between two planar objects is well understood, that between curved objects is still unclear. We show, based on the analysis of the surface polariton mediated radiative transfer between two spheres of equal radii $R$ and minimum gap $d$, that the near--field radiative transfer scales as $R/d$ as $d/R \rightarrow 0$ and as $\ln(R/d)$ for larger values of $d/R$ up to the far--field limit. We propose a modified form of the proximity approximation to predict near--field radiative transfer between curved objects from simulations of radiative transfer between planar surfaces.Comment: 5 journal pages, 4 figure

Phonon Transport Across a Vacuum Gap

Phonon transport across a silicon/vacuum-gap/silicon structure is modeled using lattice dynamics calculations and Landauer theory. The phonons transmit thermal energy across the vacuum gap via atomic interactions between the leads. Because the incident phonons do not encounter a classically impenetrable potential barrier, this mechanism is not a tunneling phenomenon. While some incident phonons transmit across the vacuum gap and remain in their original mode, many are annihilated and excite different modes. We show that the heat flux due to phonon transport can be 4 orders of magnitude larger than that due to photon transport predicted from near-field radiation theory