Refraction at Media with Negative Refractive Index

We show that an electromagnetic (EM) wave undergoes negative refraction at the interface between a positive and negative refractive index material. Finite difference time domain (FDTD) simulations are used to study the time evolution of an EM wave as it hits the interface. The wave is trapped temporarily at the interface and after a long time, the wave front moves eventually in the negative direction. This explains why causality and speed of light are not violated in spite of the negative refraction always present in a negative index material.Comment: 5 pages, 4 figures, submitted to Phys. Rev. Let

Negative refraction by photonic crystals

[No abstract available

EM wave propagation in two-dimensional photonic crystals: a study of anomalous refractive effects

We systematically study a collection of refractive phenomena that can possibly occur at the interface of a two-dimensional photonic crystal, with the use of the wave vector diagram formalism. Cases with a single propagating beam (in the positive or the negative direction) as well as cases with birefringence were observed. We examine carefully the conditions to obtain a single propagating beam inside the photonic crystal lattice. Our results indicate, that the presence of multiple reflected beams in the medium of incidence is neither a prerequisite nor does it imply multiple refracted beams. We characterize our results in respect to the origin of the propagating beam and the nature of propagation (left-handed or not). We identified four distinct cases that lead to a negatively refracted beam. Under these findings, the definition of phase velocity in a periodic medium is revisited and its physical interpretation discussed. To determine the ``rightness'' of propagation, we propose a wedge-type experiment. We discuss the intricate details for an appropriate wedge design for different types of cases in triangular and square structures. We extend our theoretical analysis, and examine our conclusions as one moves from the limit of photonic crystals with high index contrast between the constituent dielectrics to photonic crystals with low modulation of the refractive index. Finally, we examine the ``rightness'' of propagation in the one-dimensional multilayer medium, and obtain conditions that are different from those of two-dimensional systems.Comment: 65 pages, 17 figures, submitted to Phys. Rev.

Distance dependence of angular correlations in dense polymer solutions

Angular correlations in dense solutions and melts of flexible polymer chains are investigated with respect to the distance $r$ between the bonds by comparing quantitative predictions of perturbation calculations with numerical data obtained by Monte Carlo simulation of the bond-fluctuation model. We consider both monodisperse systems and grand-canonical (Flory-distributed) equilibrium polymers. Density effects are discussed as well as finite chain length corrections. The intrachain bond-bond correlation function $P(r)$ is shown to decay as $P(r) \sim 1/r^3$ for \xi \ll r \ll \r^* with $\xi$ being the screening length of the density fluctuations and $r^* \sim N^{1/3}$ a novel length scale increasing slowly with (mean) chain length $N$.Comment: 17 pages, 5 figures, accepted for publication at Macromolecule

Negative refraction and superlens behavior in a two-dimensional photonic crystal

We experimentally and theoretically studied a left-handed structure based on a photonic crystal (PC) with a negative refractive index. The structure consists of triangular array of rectangular dielectric bars with dielectric constant 9.61. Experimental and theoretical results demonstrate the negative refraction and the superlensing phenomena in the microwave regime. The results show high transmission for our structure for a wide range of incident angles. Furthermore, surface termination within a specific cut of the structure excite surface waves at the interface between air and PC and allow the reconstruction of evanescent waves for a better focus and better transmission. The normalized average field intensity calculated in both the source and image planes shows almost the same full width at half maximum for the source and the focused beam. © 2005 The American Physical Society

Electromagnetic-field quantization and spontaneous decay in left-handed media

We present a quantization scheme for the electromagnetic field interacting with atomic systems in the presence of dispersing and absorbing magnetodielectric media, including left-handed material having negative real part of the refractive index. The theory is applied to the spontaneous decay of a two-level atom at the center of a spherical free-space cavity surrounded by magnetodielectric matter of overlapping band-gap zones. Results for both big and small cavities are presented, and the problem of local-field corrections within the real-cavity model is addressed.Comment: 15 pages, 5 figures, RevTe

Negative refraction and left-handed behavior in two-dimensional photonic crystals

We systematically examine the conditions of obtaining left-handed (LH) behavior in photonic crystals. Detailed studies of the phase and group velocities as well as the phase np and group ng refractive index are given. The existence of negative refraction does not guarantee the existence of negative index of refraction and so LH behavior. A wedge type of experiment is suggested that can unambiguously distiguinsh between cases of negative refraction that occur when left-handed behavior is present, from cases that show negative refraction without LH behavior.Comment: 4 pages 4 figures, submitted to Phys. Rev. B Rapid Communication

Electric-field-coupled resonators for negative permittivity metamateri-als

Abstract: Complex and interesting electromagnetic behavior can be found in spaces with non-flat topology. When considering the properties of an electromagnetic medium under an arbitrary coordinate transformation an alternative interpretation presents itself. The transformed material property tensors may be interpreted as a different set of material properties in a flat, Cartesian space. We describe the calculation of these material properties for coordinate transformations that describe spaces with spherical or cylindrical holes in them. The resulting material properties can then implement invisibility cloaks in flat space. We also describe a method for performing geometric ray tracing in these materials which are both inhomogeneous and anisotropic in their electric permittivity and magnetic permeability

Compact-2D FDTD for Waveguides Including Materials with Negative Dielectric Permittivity, Magnetic Permeability and Refractive Index

An efficient compact-2D finite-difference time-domain method is presented for the numerical analysis of guided modes in waveguides that may include negative dielectric permittivity, negative magnetic permeability and negative refractive index materials. Both complex variable and real variable methods are given. The method is demonstrated for the analysis of channel-plasmon-polariton guided modes in triangular groves on a metal surface. The presented method can be used for a range of waveguide problems that were previously unsolvable analytically, due to complex geometries, or numerically, due to computational requirements of conventional three-dimensional finite-difference time-domain methods. A 3-dimensional finite-difference time-domain algorithm that also allows analysis in the presence of bound or free electric and equivalent magnetic charges is presented and an example negative refraction demonstrates the method

Numerical predictions of bubble growth in viscoelastic stretching filaments

In this study, we investigate the growth of bubbles within predominately extensional-deformation flows of thin film stretching form. This involves more than one free-surface to the flow (multiple surfaces), typically as inner (bubble) and outer (filament) boundaries that introduces fluid–gas interfacial treatment. Various bubble initial states and locations may be considered. The problem is discretised in space–time through a hybrid-finite element/volume pressure-correction formulation, coupled with an arbitrary Lagrangian–Eulerian (ALE) coupled with VOF scheme to track domain-mesh and free-surface movement. We contrast these results against the results from a complete ALE algorithm. Various fluid-filament materials have been considered, covering such properties as constant viscosity fluids (Newtonian), low-polymeric/high-solvent viscosity Boger-type (Oldroyd-B) fluids and high-polymeric/low-solvent viscosity elastic-type fluids (Oldroyd-B and Phan-Thien/Tanner). Numerical solutions are presented in terms of comparison between algorithms (ALE versus hybrid ALE/VOF), shapes (bubble shapes, filament shapes), contours of extra-stress (magnitude and location), mid-filament radius and extensional viscosity