1,666 research outputs found
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
Josephson surface plasmons in spatially confined cuprate superconductors
In this work, we generalize the theory of localized surface plasmons to the
case of high-Tc cuprate superconductors, spatially confined in the form of
small spherical particles. At variance from ordinary metals, cuprate
superconductors are characterized by a low-energy bulk excitation known as the
Josephson plasma wave (JPW), arising from interlayer tunneling of the
condensate along the c-axis. The effect of the JPW is revealed in a
characteristic spectrum of surface excitations, which we call Josephson surface
plasmons. Our results, which apply to any material with a strongly anisotropic
electromagnetic response, are worked out in detail for the case of multilayered
superconductors supporting both low-frequency (acoustic) and transverse-optical
JPW. Spatial confinement of the Josephson plasma waves may represent a new
degree of freedom to engineer their frequencies and to explore the link between
interlayer tunnelling and high-Tc superconductivity
Acoustic cloaking and mirages with flying carpets
Carpets under consideration here, in the context of pressure acoustic waves
propagating in a compressible fluid, do not touch the ground: they levitate in
mid-air (or float in mid-water), which leads to approximate cloaking for an
object hidden underneath, or touching either sides of a square cylinder on, or
over, the ground. The tentlike carpets attached to the sides of a square
cylinder illustrate how the notion of a carpet on a wall naturally generalizes
to sides of other small compact objects. We then extend the concept of flying
carpets to circular cylinders. However, instead of reducing its scattering
cross-section like in acoustic cloaks, we rather mimic that of another
obstacle, say a square rigid cylinder. For instance, show that one can hide any
type of defects under such circular carpets, and yet they still scatter waves
just like a smaller cylinder on its own. Interestingly, all these carpets are
described by non-singular acoustic parameters. To exemplify this important
aspect, we propose a multi-layered carpet consisting of isotropic homogeneous
fluids with constant bulk modulus and varying density which works over a finite
range of wavelengths. We have discussed some applications, with the sonar boats
or radars cases as typical examples. For instance, we would like to render a
pipeline lying on the bottom of the sea or floating in mid-water undetectable
for a boat with a sonar at rest just above it on the surface of the sea.
Another possible application would be protecting parabolic antennas.Comment: 26 pages, 9 figures. Key words: Mathematical methods in physics;
Mathematical Physics, electromagnetic theory; Metamaterials;Anisotropic
optical materials; invisibility; cloa
Numerical Analysis of Three-dimensional Acoustic Cloaks and Carpets
We start by a review of the chronology of mathematical results on the
Dirichlet-to-Neumann map which paved the way towards the physics of
transformational acoustics. We then rederive the expression for the
(anisotropic) density and bulk modulus appearing in the pressure wave equation
written in the transformed coordinates. A spherical acoustic cloak consisting
of an alternation of homogeneous isotropic concentric layers is further
proposed based on the effective medium theory. This cloak is characterised by a
low reflection and good efficiency over a large bandwidth for both near and far
fields, which approximates the ideal cloak with a inhomogeneous and anisotropic
distribution of material parameters. The latter suffers from singular material
parameters on its inner surface. This singularity depends upon the sharpness of
corners, if the cloak has an irregular boundary, e.g. a polyhedron cloak
becomes more and more singular when the number of vertices increases if it is
star shaped. We thus analyse the acoustic response of a non-singular spherical
cloak designed by blowing up a small ball instead of a point, as proposed in
[Kohn, Shen, Vogelius, Weinstein, Inverse Problems 24, 015016, 2008]. The
multilayered approximation of this cloak requires less extreme densities
(especially for the lowest bound). Finally, we investigate another type of
non-singular cloaks, known as invisibility carpets [Li and Pendry, Phys. Rev.
Lett. 101, 203901, 2008], which mimic the reflection by a flat ground.Comment: Latex, 21 pages, 7 Figures, last version submitted to Wave Motion.
OCIS Codes: (000.3860) Mathematical methods in physics; (260.2110)
Electromagnetic theory; (160.3918) Metamaterials; (160.1190) Anisotropic
optical materials; (350.7420) Waves; (230.1040) Acousto-optical devices;
(160.1050) Acousto-optical materials; (290.5839) Scattering,invisibility;
(230.3205) Invisibility cloak
Scattering in Multilayered Structures: Diffraction from a Nanohole
The spectral expansion of the Green's tensor for a planar multilayered
structure allows us to semi analytically obtain the angular spectrum
representation of the field scattered by an arbitrary dielectric perturbation
present in the structure. In this paper we present a method to find the
expansion coefficients of the scattered field, given that the electric field
inside the perturbation is available. The method uses a complete set of
orthogonal vector wave functions to solve the structure's vector wave equation.
In the two semi-infinite bottom and top media, those vector wave functions
coincide with the plane-wave basis vectors, including both propagating and
evanescent components. The technique is used to obtain the complete angular
spectrum of the field scattered by a nanohole in a metallic film under Gaussian
illumination. We also show how the obtained formalism can easily be extended to
spherically and cylindrically multilayered media. In those cases, the expansion
coefficients would multiply the spherical and cylindrical vector wave
functions.Comment: 9 pages, 5 figure
Coupled mode theory for on-channel nonlinear microcavities
We consider a nonlinear microcavity separating a waveguide channel into two
parts so as the coupling between them is possible only due to the resonant
properties of the microcavity. We provide a rigorous derivation of the
equations used in the phenomenological coupled mode theory for such systems.
This allows us to find the explicit formulas for all fitting parameters such as
decay rates, coupling coefficients and characteristic intensities in terms of
the mode profiles. The advantages of using the semi-analytical approach are
discussed, and the accuracy of the results is compared with the strictly
numerical methods. A particular attention is paid to multilayered structures
since they represent the simplest realization of on-channel microcavities.Comment: 21 pages, 4 figure
Excitation Theory for Space-Dispersive Active Media Waveguides
A unified electrodynamic approach to the guided-wave excitation theory is
generalized to the waveguiding structures containing a hypothetical
space-dispersive medium with drifting charge carriers possessing simultaneously
elastic, piezoelectric and magnetic properties. Substantial features of our
electrodynamic approach are: (i) the allowance for medium losses and (ii) the
separation of potential fields peculiar to the slow quasi-static waves. It is
shown that the orthogonal complementary fields appearing inside the external
source region are just associated with a contribution of the potential fields
inherent in exciting sources. Taking account of medium losses converts the
usual orthogonality relation into a novel form called the quasi-orthogonality
relation. It is found that the separation of potential fields reveals the fine
structure of interaction between the exciting sources and mode eigenfields: in
addition to the exciting currents interacting with the curl fields, the
exciting charges and the double charge (surface dipole) layers appear to
interact with the quasi-static potentials and the displacement currents,
respectively.Comment: LaTeX 2.09, 28 pages with mathematical appendi
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