Numerical methods for computing Casimir interactions

We review several different approaches for computing Casimir forces and related fluctuation-induced interactions between bodies of arbitrary shapes and materials. The relationships between this problem and well known computational techniques from classical electromagnetism are emphasized. We also review the basic principles of standard computational methods, categorizing them according to three criteria---choice of problem, basis, and solution technique---that can be used to classify proposals for the Casimir problem as well. In this way, mature classical methods can be exploited to model Casimir physics, with a few important modifications.Comment: 46 pages, 142 references, 5 figures. To appear in upcoming Lecture Notes in Physics book on Casimir Physic

Isotropic-medium three-dimensional cloaks for acoustic and electromagnetic waves

We propose a generalization of the two-dimensional eikonal-limit cloak derived from a conformal transformation to three dimensions. The proposed cloak is a spherical shell composed of only isotropic media; it operates in the transmission mode and requires no mirror or ground plane. Unlike the well-known omnidirectional spherical cloaks, it may reduce visibility of an arbitrary object only for a very limited range of observation angles. In the short-wavelength limit, this cloaking structure restores not only the trajectories of incident rays, but also their phase, which is a necessary ingredient to complete invisibility. Both scalar-wave (acoustic) and transverse vector-wave (electromagnetic) versions are presented.Comment: 17 pages, 12 figure

Progressive Transient Photon Beams

In this work we introduce a novel algorithm for transient rendering in participating media. Our method is consistent, robust, and is able to generate animations of time-resolved light transport featuring complex caustic light paths in media. We base our method on the observation that the spatial continuity provides an increased coverage of the temporal domain, and generalize photon beams to transient-state. We extend the beam steady-state radiance estimates to include the temporal domain. Then, we develop a progressive version of spatio-temporal density estimations, that converges to the correct solution with finite memory requirements by iteratively averaging several realizations of independent renders with a progressively reduced kernel bandwidth. We derive the optimal convergence rates accounting for space and time kernels, and demonstrate our method against previous consistent transient rendering methods for participating media

Cloaking and anamorphism for light and mass diffusion

We first review classical results on cloaking and mirage effects for electromagnetic waves. We then show that transformation optics allows the masking of objects or produces mirages in diffusive regimes. In order to achieve this, we consider the equation for diffusive photon density in transformed coordinates, which is valid for diffusive light in scattering media. More precisely, generalizing transformations for star domains introduced in [Diatta and Guenneau, J. Opt. 13, 024012, 2011] for matter waves, we numerically demonstrate that infinite conducting objects of different shapes scatter diffusive light in exactly the same way. We also propose a design of external light-diffusion cloak with spatially varying sign-shifting parameters that hides a finite size scatterer outside the cloak. We next analyse non-physical parameter in the transformed Fick's equation derived in [Guenneau and Puvirajesinghe, R. Soc. Interface 10, 20130106, 2013], and propose to use a non-linear transform that overcomes this problem. We finally investigate other form invariant transformed diffusion-like equations in the time domain, and touch upon conformal mappings and non-Euclidean cloaking applied to diffusion processes.Comment: 42 pages, Latex, 14 figures. V2: Major changes : some formulas corrected, some extra cases added, overall length extended from 21 pages (V1) to 42 pages (present version V2). The last version will appear at Journal of Optic

Study on Electromagnetic Scattering of Cylinders Buried in a Half Space with Random Rough Surfaces of Finite/Infinite Length

Analysis of electromagnetic scattering of buried objects is a subject of great interest due to its practical importance in both military and civil applications, such as subsurface investigation and target detection. In reality, the earth is of layered structure of random rough interfaces, which leads to a greatly increased complexity of the analysis. However, it is necessary to incorporate the nature of random rough surface and the layered structure because they both have substantial impact on the scattered signature and hence affect the study of inverse scattering and detection of buried objects. In this dissertation, a Monte-Carlo multidomain pseudospectral time domain (MPSTD) method is developed for investigating the scattering from cylinders buried below a random rough surface separating two half spaces under various conditions. As a prelude, the formulation of multidomain PSTD algorithm is presented. Then, this formulation is extended and combined with the Monte-Carlo approach to analyze the scattering of an object buried below a random rough surface of finite length. In the analysis, special attention is paid to the treatments of the random rough surface including its profile generation, matching with CGL points, and subdomain patching. Next, the scattering of a cylinder buried below a random rough surface of infinite length is studied and a two-step computation model based on the Monte-Carlo MPSTD method is developed. Further, in order to better simulate the real situation, the analysis is then extended to study the scattering from one or more cylinders embedded in a layered half space with random rough surfaces. Finally, a near-zone field to far-zone field transformation technique is developed and presented. Sample numerical results under different conditions, involving random rough surface of various roughness, lower half space with different permittivities, and cylinders of circular and rectangular shapes are presented, validated, and analyzed. Throughout this research, a numerical technique based on Monte-Carlo method and MPSTD approach has been developed and validated for investigating cylinders buried in a half space with random rough surfaces. It is observed that the roughness of the random rough surface and the electromagnetic properties of the lower half space can significantly affect the scattered signature of the buried object

Full-wave simulations of electromagnetic cloaking structures

Based on a coordinate transformation approach, Pendry {\it et al.} have reported electromagnetically anisotropic and inhomogeneous shells that, in theory, completely shield an interior structure of arbitrary size from electromagnetic fields without perturbing the external fields. We report full-wave simulations of the cylindrical version of this cloaking structure using ideal and nonideal (but physically realizable) electromagnetic parameters in an effort to understand the challenges of realizing such a structure in practice. The simulations indicate that the performance of the electromagnetic cloaking structure is not especially sensitive to modest permittivity and permeability variations. This is in contrast to other applications of engineered electromagnetic materials, such as subwavelength focusing using negative refractive index materials. The cloaking performance degrades smoothly with increasing loss, and effective low-reflection shielding can be achieved with a cylindrical shell composed of an eight (homogeneous) layer approximation of the ideal continuous medium