Modal analysis of wave propagation in dispersive media

Surveys on wave propagation in dispersive media have been limited since the pioneering work of Sommerfeld [Ann. Phys. 349, 177 (1914)] by the presence of branches in the integral expression of the wave function. In this article, a method is proposed to eliminate these critical branches and hence to establish a modal expansion of the time-dependent wave function. The different components of the transient waves are physically interpreted as the contributions of distinct sets of modes and characterized accordingly. Then, the modal expansion is used to derive a modified analytical expression of the Sommerfeld precursor improving significantly the description of the amplitude and the oscillating period up to the arrival of the Brillouin precursor. The proposed method and results apply to all waves governed by the Helmholtz equations.Comment: 10 pages, 9 figure

Macroscopic Maxwell's equations and negative index materials

We study the linear phenomenological Maxwell's equations in the presence of a polarizable and magnetizable medium (magnetodielectric). For a dispersive, non-absorptive, medium with equal electric and magnetic permeabilities, the latter can assume the value -1 (+1 is their vacuum value) for a discrete set of frequencies, i.e., for these frequencies the medium behaves as a negative index material (NIM). We show that such systems have a well-defined time evolution. In particular the fields remain square integrable (and the electromagnetic energy finite) if this is the case at some initial time. Next we turn to the Green's function (a tensor), associated with the electric Helmholtz operator, for a set of parallel layers filled with a material. We express it in terms of the well-known scalar s and p ones. For a half space filled with the material and with a single dispersive Lorentz form for both electric and magnetic permeabilities we obtain an explicit form for the Green's function. We find the usual behavior for negative index materials, there is no refection outside the evanescent regime and the transmission (refraction) shows the usual NIM behavior. We find that the Green's function has poles, which lead to a modulation of the radiative decay probability of an excited atom. The formalism is free from ambiguities in the sign of the refractive index.Comment: 22 pages, accepted for publication in J. Math. Phys

Discrete dipole approximation in time domain through the Laplace transform

We present a form of the discrete dipole approximation for electromagnetic scattering computations in time domain. We show that the introduction of complex frequencies, through the Laplace transform, significantly improves the computation time. We also show that the Laplace transform and its inverse can be combined to extract the field inside a scatterer at a real resonance frequenc

Design of metallic nanoparticles gratings for filtering properties in the visible spectrum

Plasmonic resonances in metallic nanoparticles are exploited to create efficient optical filtering functions. A Finite Element Method is used to model metallic nanoparticles gratings. The accuracy of this method is shown by comparing numerical results with measurements on a two-dimensional grating of gold nanocylinders with elliptic cross section. Then a parametric analysis is performed in order to design efficient filters with polarization dependent properties together with high transparency over the visible range. The behavior of nanoparticle gratings is also modelled using the Maxwell-Garnett homogenization theory and analyzed by comparison with the diffraction by a single nanoparticle. The proposed structures are intended to be included in optical systems which could find innovative applications.Comment: submitted to Applied Optic

Semi-analytical design of antireflection gratings for photonic crystals

This article concerns the design of antireflection structures which, placed on a photonic crystal surface, significantly diminish the fraction of energy lost to reflected waves. After a review of the classes of these structures proposed to date, a new method is presented in detail for the design of antireflection gratings operating in a wide range of angles of incidence. The proposed algorithm is illustrated by means of several examples, showing the advantages and limitations.Comment: Submitted to Phys. Rev.

Photonic crystal carpet: Manipulating wave fronts in the near field at 1550 nm

Ground-plane cloaks, which transform a curved mirror into a flat one, and recently reported at wavelengths ranging from the optical to the visible spectrum, bring the realm of optical illusion a step closer to reality. However, all carpet-cloaking experiments have thus far been carried out in the far-field. Here, we demonstrate numerically and experimentally that a dielectric photonic crystal (PC) of a complex shape made of a honeycomb array of air holes can scatter waves in the near field like a PC with a at boundary at stop band frequencies. This mirage effect relies upon a specific arrangement of dielectric pillars placed at the nodes of a quasi-conformal grid dressing the PC. Our carpet is shown to work throughout the range of wavelengths 1500nm to 1650nm within the stop band extending from 1280 to 1940 nm. The device has been fabricated using a single- mask advanced nanoelectronics technique on III-V semiconductors and the near field measurements have been carried out in order to image the wave fronts's curvatures around the telecommunication wavelength 1550 nm.Comment: 6 page

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

Assessment of genetically modified maize\ua04114 for food and feed uses, under Regulation (EC) No\ua01829/2003 (application EFSA-GMO-NL-2014-123)

Maize\ua04114 was developed through Agrobacterium\ua0tumefaciens-mediated transformation to provide protection against certain lepidopteran and coleopteran pests by expression of the Cry1F, Cry34Ab1 and Cry35Ab1 proteins derived from Bacillus\ua0thuringiensis, and tolerance to the herbicidal active ingredient glufosinate-ammonium by expression of the PAT protein derived from Streptomyces viridochromogenes. The molecular characterisation data did not identify issues requiring assessment for food/feed safety. None of the compositional, agronomic and phenotypic differences identified between maize\ua04114 and the non-genetically modified (GM) comparator(s) required further assessment. There were no concerns regarding the potential toxicity and allergenicity of the newly expressed proteins Cry1F, Cry34Ab1, Cry35Ab1 and PAT, and no evidence that the genetic modification might significantly change the overall allergenicity of maize 4114. The nutritional value of food/feed derived from maize 4114 is not expected to differ from that derived from non-GM maize varieties and no post-market monitoring of food/feed is considered necessary. In the case of accidental release of viable maize\ua04114 grains into the environment, maize\ua04114 would not raise environmental safety concerns. The post-market environmental monitoring plan and reporting intervals are in line with the intended uses of maize\ua04114. The genetically modified organism (GMO) Panel\ua0concludes that maize\ua04114 is as safe as the non-GM comparator(s) and non-GM reference varieties with respect to potential effects on human and animal health and the environment in the context of the scope of this application