97,582 research outputs found
A method for creating materials with a desired refraction coefficient
It is proposed to create materials with a desired refraction coefficient in a
bounded domain by embedding many small balls with constant
refraction coefficients into a given material. The number of small balls per
unit volume around every point , i.e., their density distribution, is
calculated, as well as the constant refraction coefficients in these balls.
Embedding into small balls with these refraction coefficients according to
the calculated density distribution creates in a material with a desired
refraction coefficient
A computational method for the Helmholtz equation in unbounded domains based on the minimization of an integral functional
We study a new approach to the problem of transparent boundary conditions for
the Helmholtz equation in unbounded domains. Our approach is based on the
minimization of an integral functional arising from a volume integral
formulation of the radiation condition. The index of refraction does not need
to be constant at infinity and may have some angular dependency as well as
perturbations. We prove analytical results on the convergence of the
approximate solution. Numerical examples for different shapes of the artificial
boundary and for non-constant indexes of refraction will be presented
Weyl asymptotics of the transmission eigenvalues for a constant index of refraction
We prove Weyl type of asymptotic formulas for the real and the complex
internal transmission eigenvalues when the domain is a ball and the index of
refraction is constant
Anomalous character of the axion-photon coupling in a magnetic field distorted by a pp-wave gravitational background
We study the problem of axion-photon coupling in the magnetic field
influenced by gravitational radiation. We focus on exact solutions to the
equations for axion electrodynamics in the pp-wave gravitational background for
two models with initially constant magnetic field. The first model describes
the response of an initially constant magnetic field in a gravitational-wave
vacuum with unit refraction index; the second model is characterized by a
non-unit refraction index prescribed to the presence of ordinary and/or dark
matter. We show that both models demonstrate anomalous behavior of the
electromagnetic field generated by the axion-photon coupling in the presence of
magnetic field, evolving in the gravitational wave background. The role of
axionic dark matter in the formation of the anomalous response of this
electrodynamic system is discussed.Comment: 26 pages, no figure
Conical diffraction and the dispersion surface of hyperbolic metamaterials
Hyperbolic metamaterials are materials in which at least one principal
dielectric constant is negative. We describe the refractive index surface, and
the resulting refraction effects, for a biaxial hyperbolic metamaterial, with
principal dielectric constants , . In
this general case the two sheets of the index surface intersect forming conical
singularities. We derive the ray description of conical refraction in these
materials, and show that it is topologically and quantitatively distinct from
conical refraction in a conventional biaxial material. We also develop a wave
optics description, which allows us to obtain the diffraction patterns formed
from arbitrary beams incident close to the optic axis. The resulting patterns
lack circular symmetry, and hence are qualitatively different from those
obtained in conventional, positive index materials.Comment: 10 pages, 7 figure
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