75,930 research outputs found
Flat lens without optical axis: Theory of imaging
We derive a general theory for imaging by a flat lens without optical axis.
We show that the condition for imaging requires a material having elliptic
dispersion relations with negative group refraction, equivalent to an effective
anisotropic refractive index n(theta). Imaging can be achieved with both
negative (n0) refractive indices. The Veselago-Pendry lens
is a special case with isotropic negative refractive index of n(theta)=-1.
Realizations of the imaging conditions using anisotropic media and
inhomogeneous media, particularly photonic crystals, are discussed. Numerical
examples of imaging and requirements for sub-wavelength imaging are also
presented.Comment: 5 pages, 4 figure
Alternative approach to all-angle negative refraction in two-dimensional photonic crystals
We show that with an appropriate surface modification, a slab of photonic
crystal can be made to allow wave transmission within the band gap.
Furthermore, negative refraction and all-angle-negative-refraction (AANR) can
be achieved by this surface modification in frequency windows that were not
realized before in two-dimensional photonic crystals [C. Luo et al, Phys. Rev.
B 65, 201104 (2002)]. This approach to AANR leads to new applications in flat
lens imaging. Previous flat lens using photonic crystals requires object-image
distance u+v less than or equal to the lens thickness d, u+v d. Our approach
can be used to design flat lens with u+v=sd with s>>1, thus being able to image
large and/or far away objects. Our results are confirmed by FDTD simulations.Comment: 5 pages, 9 eps figs in RevTex forma
On the rooted Tutte polynomial
The Tutte polynomial is a generalization of the chromatic polynomial of graph
colorings. Here we present an extension called the rooted Tutte polynomial,
which is defined on a graph where one or more vertices are colored with
prescribed colors. We establish a number of results pertaining to the rooted
Tutte polynomial, including a duality relation in the case that all roots
reside around a single face of a planar graph. The connection with the Potts
model is also reviewed.Comment: plain latex, 14 pages, 2 figs., to appear in Annales de l'Institut
Fourier (1999
GRB 060206: hints of precession of the central engine?
Aims. The high-redshift (z=4.048) gamma-ray burst GRB 060206 showed unusual behavior, with a significant rebrightening by a factor of ~4 at about 3000 s after the burst. We argue that this rebrightening implies that the central engine became active again after the main burst produced by the first ejecta, then drove another more collimated jet-like ejecta with a larger viewing angle. The two ejecta both interacted with the ambient medium, giving rise to forward shocks that propagated into the ambient medium and reverse shocks that penetrated into the ejecta. The total emission was a combination of the emissions from the reverse- and forward- shocked regions. We discuss how this combined emission accounts for the observed rebrightening.
Methods. We apply numerical models to calculate the light curves from the shocked regions, which include a forward shock originating in the first ejecta and a forward-reverse shock for the second ejecta.
Results. We find evidence that the central engine became active again 2000 s after the main burst. The combined emission produced by interactions of these two ejecta with the ambient medium can describe the properties of the afterglow of this burst. We argue that the rapid rise in brightness at ~3000 s in the afterglow is due to the off-axis emission from the second ejecta. The precession of the torus or accretion disk of the central engine is a natural explanation for the departure of the second ejecta from the line of sight
Soluble kagome Ising model in a magnetic field
An Ising model on the kagome lattice with super-exchange interactions is
solved exactly under the presence of a nonzero external magnetic field. The
model generalizes the super-exchange model introduced by Fisher in 1960 and is
analyzed in light of a free-fermion model. We deduce the critical condition and
present detailed analyses of its thermodynamic and magnetic properties. The
system is found to exhibit a second-order transition with logarithmic
singularities at criticality.Comment: 8 pages, 8 figures, references adde
GRB 060206: Evidence of Precession of Central Engine
The high-redshift (z = 4.048) gamma-ray burst GRB 060206 showed unusual behavior, with a significant re-brightening about 3000 s after the burst. We assume that the central engine became active again 2000 s after the main burst and drove another more collimated off-axis jet. The two jets both interacted with the ambient medium and contributed to the whole emission. We numerically fit this optical afterglow from the two jets using the forward-shock model and the forward-reverse shock model. Combining with the zero time effect, we suggest that the fast rise at ~3000 s in the afterglow was due to the off-axis emission from the second jet. The precession of the torus or accretion disk of the gamma ray burst engine is the natural explanation for the symmetry axes of these two jets not to lie on the same line
Negative refraction and plano-concave lens focusing in one-dimensional photonic crystals
Negative refraction is demonstrated in one-dimensional (1D) dielectric
photonic crystals (PCs) at microwave frequencies. Focusing by plano-concave
lens made of 1D PC due to negative refraction is also demonstrated. The
frequency-dependent negative refractive indices, calculated from the
experimental data matches very well with those determined from band structure
calculations. The easy fabrication of one-dimensional photonic crystals may
open the door for new applications.Comment: 3 pages and 5 figure
Generalized Fibonacci numbers and dimer statistics
We establish new product identities involving the -analogue of the
Fibonacci numbers. We show that the identities lead to alternate expressions of
generating functions for close-packed dimers on non-orientable surfaces.Comment: 4 pages, no figure, International Symposium on Frontiers of Science -
In celebration of the 80th birthday of C. N. Yang, to appear in Modern
Physics Letters
Superconductivity mediated by the antiferromagnetic spin-wave in chalcogenide iron-base superconductors
The ground state of KFeSe and other iron-based
selenide superconductors are doped antiferromagnetic semiconductors. There are
well defined iron local moments whose energies are separated from those of
conduction electrons by a large band gap in these materials. We propose that
the low energy physics of this system is governed by a model Hamiltonian of
interacting electrons with on-site ferromagnetic exchange interactions and
inter-site superexchange interactions. We have derived the effective pairing
potential of electrons under the linear spin-wave approximation and shown that
the superconductivity can be driven by mediating coherent spin wave excitations
in these materials. Our work provides a natural account for the coexistence of
superconducting and antiferromagnetic long range orders observed by neutron
scattering and other experiments.Comment: 4 pages, 3 figure
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