97,582 research outputs found

    A method for creating materials with a desired refraction coefficient

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    It is proposed to create materials with a desired refraction coefficient in a bounded domain D⊂R3D\subset \R^3 by embedding many small balls with constant refraction coefficients into a given material. The number of small balls per unit volume around every point x∈Dx\in D, i.e., their density distribution, is calculated, as well as the constant refraction coefficients in these balls. Embedding into DD small balls with these refraction coefficients according to the calculated density distribution creates in DD 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

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    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

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    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

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    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

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    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 ϵ1<0\epsilon_1<0, 0<ϵ2≠ϵ30<\epsilon_2\neq\epsilon_3. 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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