M. T. Homer Reid

Radiative heat transfer in the extreme near field

Radiative transfer of energy at the nanometre length scale is of great importance to a variety of technologies including heat-assisted magnetic recording, near-field thermophotovoltaics and lithography. Although experimental advances have enabled elucidation of near-field radiative heat transfer in gaps as small as 20–30 nanometres (refs 4, 5, 6), quantitative analysis in the extreme near field (less than 10 nanometres) has been greatly limited by experimental challenges. Moreover, the results of pioneering measurements differed from theoretical predictions by orders of magnitude. Here we use custom-fabricated scanning probes with embedded thermocouples, in conjunction with new microdevices capable of periodic temperature modulation, to measure radiative heat transfer down to gaps as small as two nanometres. For our experiments we deposited suitably chosen metal or dielectric layers on the scanning probes and microdevices, enabling direct study of extreme near-field radiation between silica–silica, silicon nitride–silicon nitride and gold–gold surfaces to reveal marked, gap-size-dependent enhancements of radiative heat transfer. Furthermore, our state-of-the-art calculations of radiative heat transfer, performed within the theoretical framework of fluctuational electrodynamics, are in excellent agreement with our experimental results, providing unambiguous evidence that confirms the validity of this theory for modelling radiative heat transfer in gaps as small as a few nanometres. This work lays the foundations required for the rational design of novel technologies that leverage nanoscale radiative heat transfer.

Efficient Computation of Casimir Interactions between Arbitrary 3D Objects

We introduce an efficient technique for computing Casimir energies and forces between objects of arbitrarily complex 3D geometries. In contrast to other recently developed methods, our technique easily handles nonspheroidal, nonaxisymmetric objects, and objects with sharp corners. Using our new technique, we obtain the first predictions of Casimir interactions in a number of experimentally relevant geometries, including crossed cylinders and tetrahedral nanoparticles.

Casimir Repulsion between Metallic Objects in Vacuum

We give an example of a geometry in which two metallic objects in vacuum experience a repulsive Casimir force. The geometry consists of an elongated metal particle centered above a metal plate with a hole. We prove that this geometry has a repulsive regime using a symmetry argument and confirm it with numerical calculations for both perfect and realistic metals. The system does not support stable levitation, as the particle is unstable to displacements away from the symmetry axis.

Fluctuating-surface-current formulation of radiative heat transfer for arbitrary geometries

We describe a fluctuating-surface-current formulation of radiative heat transfer, applicable to arbitrary geometries in both the near and far field, that directly exploits efficient and sophisticated techniques from the boundary-element method. We validate as well as extend previous results for spheres and cylinders, and also compute the heat transfer in a more complicated geometry consisting of two interlocked rings. Finally, we demonstrate how this method can be adapted to compute the spatial distribution of heat flux on the surfaces of the bodies.

Efficient Computation of Power, Force, and Torque in BEM Scattering Calculations

We present concise, computationally efficient formulas for several quantities of interest-including absorbed and scattered power, optical force (radiation pressure), and torque-in scattering calculations performed using the boundary-element method (BEM) [also known as the method of moments (MoM)]. Our formulas compute the quantities of interest directly from the BEM surface currents with no need ever to compute the scattered electromagnetic fields. We derive our new formulas and demonstrate their effectiveness by computing power, force, and torque (PFT) in a number of example geometries. Free, open-source software implementations of our formulas are available for download online.

Microstructure effects for Casimir forces in chiral metamaterials

We examine a recent prediction for the chirality dependence of the Casimir force in chiral metamaterials by numerical computation of the forces between the exact microstructures, rather than homogeneous approximations. Although repulsion in the metamaterial regime is rigorously impossible, it is unknown whether a reduction in the attractive force can be achieved through suitable material engineering. We compute the exact force for a chiral bent-cross pattern, as well as forces for an idealized “omega”-particle medium in the dilute approximation and identify the effects of structural inhomogeneity i.e., proximity forces and anisotropy .W e find that these microstructure effects dominate the force for separations where chirality was predicted to have a strong influence. At separations where the homogeneous approximation is valid, in even the most ideal circumstances the effects of chirality are less than 10 �4 of the total force, making them virtually undetectable in experiments.

Generalized Taylor–Duffy Method for Efficient Evaluation of Galerkin Integrals in Boundary-Element Method Computations

We present a generic technique, automated by computer-algebra systems and available as open-source software, for efficient numerical evaluation of a large family of singular and nonsingular four-dimensional integrals over triangle-product domains, such as those arising in the boundary-element method (BEM) of computational electromagnetism. Previously, practical implementation of BEM solvers often required the aggregation of multiple disparate integral-evaluation schemes in order to treat all of the distinct types of integrals needed for a given BEM formulation; in contrast, our technique allows many different types of integrals to be handled by the same algorithm and the same code implementation. Our method is a significant generalization of the Taylor-Duffy approach, which was originally presented for just a single type of integrand; in addition to generalizing this technique to a broad class of integrands, we also achieve a significant improvement in its efficiency by showing how the dimension of the final numerical integral may often reduced by one. In particular, if n is the number of common vertices between the two triangles, in many cases we can reduce the dimension of the integral from 4-n to 3-n, obtaining a closed-form analytical result for n=3 (the common-triangle case).

Transformation optics scheme for two-dimensional materials

Two-dimensional optical materials, such as graphene, can be characterized by surface conductivity. So far, the transformation optics schemes have focused on three-dimensional properties such as permittivity ϵ and permeability μ. In this Letter, we use a scheme for transforming surface currents to highlight that the surface conductivity transforms in a way different from ϵ and μ. We use this surface conductivity transformation to demonstrate an example problem of reducing the scattering of the plasmon mode from sharp protrusions in graphene.

On the Computation of Power in Volume Integral Equation Formulations

We present simple and stable formulas for computing power (including absorbed/radiated, scattered and extinction power) in current-based volume integral equation formulations. The proposed formulas are given in terms of vector-matrix-vector products of quantities found solely in the associated linear system. In addition to their efficiency, the derived expressions can guarantee the positivity of the computed power. We also discuss the application of Poyntings theorem for the case of sources immersed in dissipative materials. The formulas are validated against results obtained both with analytical and numerical methods for scattering and radiation benchmark cases.

Limits to the Optical Response of Graphene and Two-Dimensional Materials

Two-dimensional (2D) materials provide a platform for strong light-matter interactions, creating wide-ranging design opportunities via new-material discoveries and new methods for geometrical structuring. We derive general upper bounds to the strength of such light-matter interactions, given only the optical conductivity of the material, including spatial nonlocality, and otherwise independent of shape and configuration. Our material figure-of-merit shows that highly doped graphene is an optimal material at infrared frequencies, whereas single-atomic-layer silver is optimal in the visible. For quantities ranging from absorption and scattering to near-field spontaneous-emission enhancements and radiative heat transfer, we consider canonical geometrical structures and show that in certain cases the bounds can be approached, while in others there may be significant opportunity for design improvement. The bounds can encourage systematic improvements in the design of ultrathin broadband absorbers, 2D antennas, and near-field energy harvesters.