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 \textit{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 in a number of example geometries. Free, open-source software implementations of our formulas are available for download online

Computation of Casimir Interactions between Arbitrary 3D Objects with Arbitrary Material Properties

We extend a recently introduced method for computing Casimir forces between arbitrarily--shaped metallic objects [M. T. H. Reid et al., Phys. Rev. Lett._103_ 040401 (2009)] to allow treatment of objects with arbitrary material properties, including imperfect conductors, dielectrics, and magnetic materials. Our original method considered electric currents on the surfaces of the interacting objects; the extended method considers both electric and magnetic surface current distributions, and obtains the Casimir energy of a configuration of objects in terms of the interactions of these effective surface currents. Using this new technique, we present the first predictions of Casimir interactions in several experimentally relevant geometries that would be difficult to treat with any existing method. In particular, we investigate Casimir interactions between dielectric nanodisks embedded in a dielectric fluid; we identify the threshold surface--surface separation at which finite--size effects become relevant, and we map the rotational energy landscape of bound nanoparticle diclusters

Fluctuating surface-current formulation of radiative heat transfer: theory and applications

We describe a novel fluctuating-surface current formulation of radiative heat transfer between bodies of arbitrary shape that exploits efficient and sophisticated techniques from the surface-integral-equation formulation of classical electromagnetic scattering. Unlike previous approaches to non-equilibrium fluctuations that involve scattering matrices---relating "incoming" and "outgoing" waves from each body---our approach is formulated in terms of "unknown" surface currents, laying at the surfaces of the bodies, that need not satisfy any wave equation. We show that our formulation can be applied as a spectral method to obtain fast-converging semi-analytical formulas in high-symmetry geometries using specialized spectral bases that conform to the surfaces of the bodies (e.g. Fourier series for planar bodies or spherical harmonics for spherical bodies), and can also be employed as a numerical method by exploiting the generality of surface meshes/grids to obtain results in more complicated geometries (e.g. interleaved bodies as well as bodies with sharp corners). In particular, our formalism allows direct application of the boundary-element method, a robust and powerful numerical implementation of the surface-integral formulation of classical electromagnetism, which we use to obtain results in new geometries, including the heat transfer between finite slabs, cylinders, and cones

Transformation Optics scheme for two-dimensional materials

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

Photon Emission Rate Engineering using Graphene Nanodisc Cavities

In this work, we present a systematic study of the plasmon modes in a system of vertically stacked pair of graphene discs. Quasistatic approximation is used to model the eigenmodes of the system. Eigen-response theory is employed to explain the spatial dependence of the coupling between the plasmon modes and a quantum emitter. These results show a good match between the semi-analytical calculation and full-wave simulations. Secondly, we have shown that it is possible to engineer the decay rates of a quantum emitter placed inside and near this cavity, using Fermi level tuning, via gate voltages and variation of emitter location and polarization. We highlighted that by coupling to the bright plasmon mode, the radiative efficiency of the emitter can be enhanced compared to the single graphene disc case, whereas the dark plasmon mode suppresses the radiative efficiency

Fluctuation-Induced Phenomena in Nanoscale Systems: Harnessing the Power of Noise

The famous Johnson-Nyquist formula relating noise current to conductance has a microscopic generalization relating noise current density to microscopic conductivity, with corollary relations governing noise in the components of the electromagnetic fields. These relations, known collectively in physics as fluctuation-dissipation relations, form the basis of the modern understanding of fluctuation-induced phenomena, a field of burgeoning importance in experimental physics and nanotechnology. In this review, we survey recent progress in computational techniques for modeling fluctuation-induced phenomena, focusing on two cases of particular interest: near-field radiative heat transfer and Casimir forces. In each case we review the basic physics of the phenomenon, discuss semi-analytical and numerical algorithms for theoretical analysis, and present recent predictions for novel phenomena in complex material and geometric configurations.Comment: Accepted for publication in a forthcoming special issue of Proceedings of the IEEE. Corrected numbering of references in Figure

New algorithm for efficient prediction of Casimir interactions among arbitrary materials in arbitrary geometries

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Physics, 2011.Cataloged from PDF version of thesis.Includes bibliographical references (p. 161-163).For most of its 60 year history, the Casimir effect was an obscure theoretical backwater, but technological advances over the past decade have promoted this curious manifestation of quantum and thermal fluctuations to a position of central importance in modern experimental physics. Dramatic progress in the measurement of Casimir forces since 1997 has created a demand for theoretical tools that can predict Casimir interactions in realistic experimental geometries and in materials with realistic frequency-dependent electrical properties. This work presents a new paradigm for efficient numerical computation of Casimir interactions. Our new technique, which we term the fluctuating-surface-current (FSC) approach to computational Casimir physics, borrows ideas from the boundary-element method of computational electromagnetism to express Casimir energies, forces, and torques between bodies of arbitrary shapes and materials in terms of interactions among effective electric and magnetic surface currents flowing on the surfaces of the objects. We demonstrate that the master equations of the FSC approach arise as logical consequences of either of two seemingly disparate Casimir paradigms-the stress-tensor approach and the path-integral (or scattering) approach-and this work thus achieves an unexpected unification of these two otherwise quite distinct theoretical frameworks. But a theoretical technique is only as relevant as its practical implementations are useful, and for this reason we present three distinct numerical implementations of the FSC formulae, each of which poses a series of unique technical challenges. Finally, using our new theoretical paradigm and our practical implementations of it, we obtain new predictions of Casimir interactions in a number of experimentally relevant geometric and material configurations that would be difficult or impossible to treat with any other existing Casimir method.by M. T. Homer Reid.Ph.D