At visible and infrared frequencies, metals show tantalizing promise for strong subwavelength resonances, but material loss typically dampens the response. We derive fundamental limits to the optical response of absorptive systems, bounding the large
st enhancements possible given intrinsic material losses. Through basic conservation-of-energy principles, we derive geometry-independent limits to per-volume absorption and scattering rates, and to local-density-of-states enhancements that represent the power radiated or expended by a dipole near a material body. We provide examples of structures that approach our absorption and scattering limits at any frequency, by contrast, we find that common antenna structures fall far short of our radiative LDOS bounds, suggesting the possibility for significant further improvement. Underlying the limits is a simple metric, $|chi|^2 / operatorname{Im} chi$ for a material with susceptibility $chi$, that enables broad technological evaluation of lossy materials across optical frequencies.
We present a generic technique, automated by computer-algebra systems and available as open-source software cite{scuff-em}, for efficient numerical evaluation of a large family of singular and nonsingular 4-dimensional integrals over triangle-product
domains, such as those arising in the boundary-element method (BEM) of computational electromagnetism. To date, practical implementation of BEM solvers has often required the aggregation of multiple disparate integral-evaluation schemes 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 emph{same} algorithm and the same code implementation. Our method is a significant generalization of the Taylor--Duffy approach cite{Taylor2003,Duffy1982}, 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 emph{dimension} of the final numerical integral may often be 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).
We show that there are shape-independent upper bounds to the extinction cross section per unit volume of randomly oriented nanoparticles, given only material permittivity. Underlying the limits are restrictive sum rules that constrain the distributio
n of quasistatic eigenvalues. Surprisingly, optimally-designed spheroids, with only a single quasistatic degree of freedom, reach the upper bounds for four permittivity values. Away from these permittivities, we demonstrate computationally-optimized structures that surpass spheroids and approach the fundamental limits.
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 met
hod (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.
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 fi
elds. 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.
This paper presents a new method for the efficient numerical computation of Casimir interactions between objects of arbitrary geometries, composed of materials with arbitrary frequency-dependent electrical properties. Our method formulates the Casimi
r effect as an interaction between effective electric and magnetic current distributions on the surfaces of material bodies, and obtains Casimir energies, forces, and torques from the spectral properties of a matrix that quantifies the interactions of these surface currents. The method can be formulated and understood in two distinct ways: textbf{(1)} as a consequence of the familiar textit{stress-tensor} approach to Casimir physics, or, alternatively, textbf{(2)} as a particular case of the textit{path-integral} approach to Casimir physics, and we present both formulations in full detail. In addition to providing an algorithm for computing Casimir interactions in geometries that could not be efficiently handled by any other method, the framework proposed here thus achieves an explicit unification of two seemingly disparate approaches to computational Casimir physics.
We examine the non-equilibrium radiative heat transfer between a plate and finite cylinders and cones, making the first accurate theoretical predictions for the total heat transfer and the spatial heat flux profile for three-dimensional compact objec
ts including corners or tips. We find qualitatively different scaling laws for conical shapes at small separations, and in contrast to a flat/slightly-curved object, a sharp cone exhibits a local emph{minimum} in the spatially resolved heat flux directly below the tip. The method we develop, in which a scattering-theory formulation of thermal transfer is combined with a boundary-element method for computing scattering matrices, can be applied to three-dimensional objects of arbitrary shape.
We extend a previous result [Phys. Rev. Lett. 105, 090403 (2010)] on Casimir repulsion between a plate with a hole and a cylinder centered above it to geometries in which the central object can no longer be treated as a point dipole. We show through
numerical calculations that as the distance between the plate and central object decreases, there is an intermediate regime in which the repulsive force increases dramatically. Beyond this, the force rapidly switches over to attraction as the separation decreases further to zero, in line with the proximity force approximation. We demonstrate that this effect can be understood as a competition between an increased repulsion due to a larger polarizability of the central object interacting with increased fringing fields near the edge of the plate, and attractive forces due primarily to the nonzero thickness of the plate. In comparison with our previous work, we find that using the same plate geometry but replacing the single cylinder with a ring of cylinders, or more generally an extended uniaxial conductor, the repulsive force can be enhanced by a factor of approximately $10^3$. We conclude that this enhancement, although quite dramatic, is still too small to yield detectable repulsive Casimir forces.
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 i
mperfect 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.
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 non-spheroidal, non-axisymmetric 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.
