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Register a new userDirective Emission Obtained by Coordinate Transformation
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We use coordinate transformation theory to realize substrates that can modify the emission of an embedded source. Simulation results show that with proper transformation functions the energy radiated by a source embedded in these space variant media will be concentrated in a narrow beam. The thickness of the slab achieved with our transformations will no longer be restricted by the evanescent modes and the source can be placed at any position along the boundary of the substrate without affecting the radiation pattern. We also discuss the case where reduced parameters are used, which still performs well and is physically realizable.
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The coordinate transformation on the space that contains electromagnetic sources is studied. We find that, not only the permittivity and permeability tensors of the media, but also the sources inside the media will take another form in order to behave equivalently as the original case. It is demonstrated that, a source of arbitrary shape and position in the free space can be replaced by an appropriately designed metamaterial coating with current distributed on the inner surface and would not be detected by outer observers, because the emission of the source can be controlled at will in this way. As examples, we show how to design conformal antennas by covering the sources with transformation media. The method proposed in this letter provides a completely new approach to develop novel active EM devices.
The coordinate transformation technique is applied to the design of perfect lenses and superlenses. In particular, anisotropic metamaterials that magnify two-dimensional planar images beyond the diffraction limit are designed by the use of oblate spheroidal coordinates. The oblate spheroidal perfect lens or superlens can naturally be used in reverse for lithography of planar subwavelength patterns.
We calculate, by means of fluctuational electrodynamics, the thermal emission of an aperture filled by vacuum or a material at temperature T. We show that thermal emission is very different whether the aperture size is large or small compared to the thermal wavelength. Subwavelength apertures filled with vacuum (subwavelength blackbody) have their thermal emission strongly decreased compared to classical blackbodies. A simple expression of their emissivity can be calculated and their total emittance scales as T 8 instead of T 4 for large apertures. Thermal emission of disk of materials with a size comparable to the wavelength is also discussed. It is shown in particular that emissivity of such a disk is increased when the material can support surface waves such as phonon polaritons.
The Kustaanheimo-Stiefel (KS) transformation maps the non-linear and singular equations of motion of the three-dimensional Kepler problem to the linear and regular equations of a four-dimensional harmonic oscillator. It is used extensively in studies of the perturbed Kepler problem in celestial mechanics and atomic physics. In contrast to the conventional matrix-based approach, the formulation of the KS transformation in the language of geometric Clifford algebra offers the advantages of a clearer geometrical interpretation and greater computational simplicity. It is demonstrated that the geometric algebra formalism can readily be used to derive a Lagrangian and Hamiltonian description of the KS dynamics in arbitrary static electromagnetic fields. For orbits starting at the Coulomb centre, initial conditions are derived and a framework is set up that allows a discussion of the stability of these orbits.
This contribution adds to the points on the <indeterminacy of special relativity> made by De Abreu and Guerra. We show that the Lorentz Transformation can be composed by the physical observations made in a frame K of events in a frame K-prime viz i) objects in K-prime are moving at a speed v relative to K, ii) distances and time intervals measured by K-prime are at variance with those measured by K and iii) the concept of simultaneity is different in K-prime compared to K. The order in which the composition is executed determines the nature of the middle aspect (ii). This essential uncertainty of the theory can be resolved only by a universal synchronicity as discussed in [1] based on the unique frame in which the one way speed of light is constant in all directions.
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