Computation and visualization of Casimir forces in arbitrary geometries: non-monotonic lateral forces and failure of proximity-force approximations

We present a method of computing Casimir forces for arbitrary geometries, with any desired accuracy, that can directly exploit the efficiency of standard numerical-electromagnetism techniques. Using the simplest possible finite-difference implementation of this approach, we obtain both agreement with past results for cylinder-plate geometries, and also present results for new geometries. In particular, we examine a piston-like problem involving two dielectric and metallic squares sliding between two metallic walls, in two and three dimensions, respectively, and demonstrate non-additive and non-monotonic changes in the force due to these lateral walls.Comment: Accepted for publication in Physical Review Letters. (Expected publication: Vol. 99 (8) 2007

Photonic crystal optical waveguides for on-chip Bose-Einstein condensates

We propose an on-chip optical waveguide for Bose-Einstein condensates based on the evanescent light fields created by surface states of a photonic crystal. It is shown that the modal properties of these surface states can be tailored to confine the condensate at distances from the chip surface significantly longer that those that can be reached by using conventional index-contrast guidance. We numerically demonstrate that by index-guiding the surface states through two parallel waveguides, the atomic cloud can be confined in a two-dimensional trap at about 1$\mu$m above the structure using a power of 0.1mW.Comment: 5 pages, 4 figure

Theoretical analysis of acoustic stop bands in two-dimensional periodic scattering arrays

This paper presents a theoretical analysis of the recently reported observation of acoustic stop bands in two-dimensional scattering arrays (Robertson and Rudy, J. Acoust. Soc. Am. {\bf 104}, 694, 1998). A self-consistent wave scattering theory, incorporating all orders of multiple scattering, is used to obtain the wave transmission. The band structures for the regular arrays of cylinders are computed using the plane wave expansion method. The theoretical results compare favorably with the experimental data.Comment: 18 pages, 4 page

A fundamental relation between phase and group velocity, and application to the failure of perfectly matched layers in backward-wave structures

http://link.aps.org/doi/10.1103/PhysRevE.79.065601We demonstrate that the ratio of group to phase velocity has a simple relationship to the orientation of the electromagnetic field. In nondispersive materials, opposite group and phase velocity corresponds to fields that are mostly oriented in the propagation direction. More generally, this relationship (including the case of dispersive and negative-index materials) offers a perspective on the phenomena of backward waves and left-handed media. As an application of this relationship, we demonstrate and explain an irrecoverable failure of perfectly matched layer absorbing boundaries in computer simulations for constant cross-section waveguides with backward-wave modes and suggest an alternative in the form of adiabatic isotropic absorbers

Virtual photons in imaginary time: Computing exact Casimir forces via standard numerical-electromagnetism techniques

We describe a numerical method to compute Casimir forces in arbitrary geometries, for arbitrary dielectric and metallic materials, with arbitrary accuracy (given sufficient computational resources). Our approach, based on well-established integration of the mean stress tensor evaluated via the fluctuation-dissipation theorem, is designed to directly exploit fast methods developed for classical computational electromagnetism, since it only involves repeated evaluation of the Green's function for imaginary frequencies (equivalently, real frequencies in imaginary time). We develop the approach by systematically examining various formulations of Casimir forces from the previous decades and evaluating them according to their suitability for numerical computation. We illustrate our approach with a simple finite-difference frequency-domain implementation, test it for known geometries such as a cylinder and a plate, and apply it to new geometries. In particular, we show that a piston-like geometry of two squares sliding between metal walls, in both two and three dimensions with both perfect and realistic metallic materials, exhibits a surprising non-monotonic ``lateral'' force from the walls.Comment: Published in Physical Review A, vol. 76, page 032106 (2007

Wide-band optical field concentrator for low-index core propagation

We propose a novel chirped structure consisting of a low index polymer core bounded by modulated multilayer claddings, to realize an optical field concentrator with virtually zero propagation losses in a wide spectral range, independent of wave polarization. In spite of the absence of the total internal reflection mechanism, properly designed multilayer claddings ensure the achievement of unitary transmittance in a wide spectral range, including the widely used wavelengths for optical communications. Several cladding geometries obtained by varying the thicknesses of the cladding layers are reported and discussed.Comment: submitted to the Journal of the European Optical Societ

Paired modes of heterostructure cavities in photonic crystal waveguides with split band edges

We investigate the modes of double heterostructure cavities where the underlying photonic crystal waveguide has been dispersion engineered to have two band-edges inside the Brillouin zone. By deriving and using a perturbative method, we show that these structures possess two modes. For unapodized cavities, the relative detuning of the two modes can be controlled by changing the cavity length, and for particular lengths, a resonant-like effect makes the modes degenerate. For apodized cavities no such resonances exist and the modes are always non-degenerate. © 2010 Optical Society of America

Results of the Ontology Alignment Evaluation Initiative 2022

The Ontology Alignment Evaluation Initiative (OAEI) aims at comparing ontology matching systems on precisely defined test cases. These test cases can be based on ontologies of different levels of complexity and use different evaluation modalities. The OAEI 2022 campaign offered 14 tracks and was attended by 18 participants. This paper is an overall presentation of that campaign

Results of the Ontology Alignment Evaluation Initiative 2023

The Ontology Alignment Evaluation Initiative (OAEI) aims at comparing ontology matching systems on precisely defined test cases. These test cases can be based on ontologies of different levels of complexity and use different evaluation modalities. The OAEI 2023 campaign offered 15 tracks and was attended by 16 participants. This paper is an overall presentation of that campaign