21 research outputs found
Transformation Acoustics in Generic Elastic Media
In this work a transformation acoustics scheme for generic elastic media is
developed. Our approach starts form the decomposition of the elasticity tensor
in terms of its eigentensors, an idea previously used by Norris. While Norris'
transformation acoustics is restricted to the special class of so-called
pentamode materials, we show that a similar scheme can be defined for the most
general elasticity tensor. As in case of Norris' model (and in sharp contrast
to transformation optics), the compatibility equations of the transformation
medium are not purely algebraic and it is not guaranteed that solutions to
these equations exist for any choice of material parameters and coordinate
transformation. Nonetheless, it is shown that our scheme yields new cloaking
solutions for certain classes of materials. In particular, we present the first
application of a transformation based device for a non-scalar wave equation
outside of the field of electromagnetics.Comment: 14 pages, LaTe
Negative index of refraction, perfect lenses and transformation optics -- some words of caution
In this paper we show that a negative index of refraction is not a direct
implication of transformation optics with orientation-reversing
diffeomorphisms. Rather a negative index appears due to a specific choice of
sign freedom. Furthermore, we point out that the transformation designed lens,
which relies on the concept of spacetime folding, does not amplify evanescent
modes, in contrast to the Pendry-Veselago lens. Instead, evanescent modes at
the image point are produced by a duplicated source and thus no imaging of the
near field (perfect lensing) takes place.Comment: 13 pages, 3 figures, LaTe
Black Hole Thermodynamics and Hamilton-Jacobi Counterterm
We review the construction of the universal Hamilton-Jacobi counterterm for
dilaton gravity in two dimensions, derive the corresponding result in the
Cartan formulation and elaborate further upon black hole thermodynamics and
semi-classical corrections. Applications include spherically symmetric black
holes in arbitrary dimensions with Minkowski- or AdS-asymptotics, the BTZ black
hole and black holes in two-dimensional string theory.Comment: 9 pages, proceedings contribution to QFEXT07 submitted to IJMPA, v2:
added Re
Decomposable medium conditions in four-dimensional representation
The well-known TE/TM decomposition of time-harmonic electromagnetic fields in
uniaxial anisotropic media is generalized in terms of four-dimensional
differential-form formalism by requiring that the field two-form satisfies an
orthogonality condition with respect to two given bivectors. Conditions for the
electromagnetic medium in which such a decomposition is possible are derived
and found to define three subclasses of media. It is shown that the previously
known classes of generalized Q-media and generalized P-media are particular
cases of the proposed decomposable media (DCM) associated to a quadratic
equation for the medium dyadic. As a novel solution, another class of special
decomposable media (SDCM) is defined by a linear dyadic equation. The paper
further discusses the properties of medium dyadics and plane-wave propagation
in all the identified cases of DCM and SDCM
Generalized transformation optics from triple spacetime metamaterials
In this paper various extensions of the design strategy of transformation
media are proposed. We show that it is possible to assign different transformed
spaces to the field strength tensor (electric field and magnetic induction) and
to the excitation tensor (displacement field and magnetic field), resp. In this
way, several limitations of standard transformation media can be overcome. In
particular it is possible to provide a geometric interpretation of
non-reciprocal as well as indefinite materials. We show that these
transformations can be complemented by a continuous version of
electric-magnetic duality and comment on the relation to the complementary
approach of field-transforming metamaterials.Comment: 11 pages, 3 figures, v2: typos, new figures, REVTeX, v3: typos, new
example added, final versio
Graded Poisson-Sigma Models and Dilaton-Deformed 2D Supergravity Algebra
Fermionic extensions of generic 2d gravity theories obtained from the graded
Poisson-Sigma model (gPSM) approach show a large degree of ambiguity. In
addition, obstructions may reduce the allowed range of fields as given by the
bosonic theory, or even prohibit any extension in certain cases. In our present
work we relate the finite W-algebras inherent in the gPSM algebra of
constraints to algebras which can be interpreted as supergravities in the usual
sense (Neuveu-Schwarz or Ramond algebras resp.), deformed by the presence of
the dilaton field. With very straightforward and natural assumptions on them
--like demanding rigid supersymmetry in a certain flat limit, or linking the
anti-commutator of certain fermionic charges to the Hamiltonian constraint-- in
the ``genuine'' supergravity obtained in this way the ambiguities disappear, as
well as the obstructions referred to above. Thus all especially interesting
bosonic models (spherically reduced gravity, the Jackiw-Teitelboim model etc.)\
under these conditions possess a unique fermionic extension and are free from
new singularities. The superspace supergravity model of Howe is found as a
special case of this supergravity action. For this class of models the relation
between bosonic potential and prepotential does not introduce obstructions as
well.Comment: 22 pages, LaTeX, JHEP class. v3: Final version, to appear in JHE