101 research outputs found
Approaches to Three-Dimensional Transformation Optical Media Using Quasi-Conformal Coordinate Transformations
We introduce an approach to the design of three-dimensional transformation
optical (TO) media based on a generalized quasi-conformal mapping approach. The
generalized quasi-conformal TO (QCTO) approach enables the design of media that
can, in principle, be broadband and low-loss, while controlling the propagation
of waves with arbitrary angles of incidence and polarization. We illustrate the
method in the design of a three-dimensional "carpet" ground plane cloak and of
a flattened Luneburg lens. Ray-trace studies provide a confirmation of the
performance of the QCTO media, while also revealing the limited performance of
index-only versions of these devices
Quantum Electric Circuits Analogous to Ballistic Conductors
The conductance steps in a constricted two-dimensional electron gas and the
minimum conductivity in graphene are related to a new uncertainty relation
between electric charge and conductance in a quantized electric circuit that
mimics the electric transport in mesoscopic systems. This uncertainty relation
makes specific use of the discreteness of electric charge. Quantum electric
circuits analogous to both constricted two-dimensional electron gas and
graphene are introduced. In the latter case a new insight into the origin of
minimum conductivity is obtained.Comment: 14 page
Collimating lenses from non-Euclidean transformation optics
Based on the non-Euclidean transformation optics, we design a thin
metamaterial lens that can achieve wide-beam radiation by embedding a simple
source (a point source in three-dimensional case or a line current source in
two-dimensional case). The scheme is performed on a layer-by-layer geometry to
convert curved surfaces in virtual space to flat sheets, which pile up and form
the entire lens in physical space. Compared to previous designs, the lens has
no extreme material parameters. Simulation results confirm its functionality.Comment: 12 pages, 6 figure
Perfect imaging with positive refraction in three dimensions
Maxwell's fish eye has been known to be a perfect lens within the validity
range of ray optics since 1854. Solving Maxwell's equations we show that the
fish-eye lens in three dimensions has unlimited resolution for electromagnetic
waves
Perfect imaging with geodesic waveguides
Transformation optics is used to prove that a spherical waveguide filled with
an isotropic material with radial refractive index n=1/r has radial polarized
modes (i.e. the electric field has only radial component) with the same perfect
focusing properties as the Maxwell Fish-Eye lens. The approximate version of
that device using a thin waveguide with a homogenous core paves the way to
experimentally prove perfect imaging in the Maxwell Fish Eye lens
Snell's Law from an Elementary Particle Viewpoint
Snell's law of light deflection between media with different indices of
refraction is usually discussed in terms of the Maxwell electromagnetic wave
theory. Snell's law may also be derived from a photon beam theory of light
rays. This latter particle physics view is by far the most simple one for
understanding the laws of refraction.Comment: ReVTeX Format 2 *.eps figure
Perfect imaging: they don't do it with mirrors
Imaging with a spherical mirror in empty space is compared with the case when
the mirror is filled with the medium of Maxwell's fish eye. Exact
time-dependent solutions of Maxwell's equations show that perfect imaging is
not achievable with an electrical ideal mirror on its own, but with Maxwell's
fish eye in the regime when it implements a curved geometry for full
electromagnetic waves
Notes on Conformal Invisibility Devices
As a consequence of the wave nature of light, invisibility devices based on
isotropic media cannot be perfect. The principal distortions of invisibility
are due to reflections and time delays. Reflections can be made exponentially
small for devices that are large in comparison with the wavelength of light.
Time delays are unavoidable and will result in wave-front dislocations. This
paper considers invisibility devices based on optical conformal mapping. The
paper shows that the time delays do not depend on the directions and impact
parameters of incident light rays, although the refractive-index profile of any
conformal invisibility device is necessarily asymmetric. The distortions of
images are thus uniform, which reduces the risk of detection. The paper also
shows how the ideas of invisibility devices are connected to the transmutation
of force, the stereographic projection and Escheresque tilings of the plane
Absolute instruments and perfect imaging in geometrical optics
We investigate imaging by spherically symmetric absolute instruments that
provide perfect imaging in the sense of geometrical optics. We derive a number
of properties of such devices, present a general method for designing them and
use this method to propose several new absolute instruments, in particular a
lens providing a stigmatic image of an optically homogeneous region and having
a moderate refractive index range.Comment: 20 pages, 9 image
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