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Register a new userDesign Method for Electromagnetic Cloak with Arbitrary Shapes Based on Laplaces Equation
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In transformation optics, the space transformation is viewed as the deformation of a material. The permittivity and permeability tensors in the transformed space are found to correlate with the deformation field of the material. By solving the Laplaces equation, which describes how the material will deform during a transformation, we can design electromagnetic cloaks with arbitrary shapes if the boundary conditions of the cloak are considered. As examples, the material parameters of the spherical and elliptical cylindrical cloaks are derived based on the analytical solutions of the Laplaces equation. For cloaks with irregular shapes, the material parameters of the transformation medium are determined numerically by solving the Laplaces equation. Full-wave simulations based on the Maxwells equations validate the designed cloaks. The proposed method can be easily extended to design other transformation materials for electromagnetic and acoustic wave phenomena.
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The fact that the capacitance coefficients for a set of conductors are geometrical factors is derived in most electricity and magnetism textbooks. We present an alternative derivation based on Laplaces equation that is accessible for an intermediate course on electricity and magnetism. The properties of Laplaces equation permits to prove many properties of the capacitance matrix. Some examples are given to illustrate the usefulness of such properties.
In computational physics and mathematical physics, modal analysis method has been one of important study topics. The central purposes of this Post-Doctoral Concluding Report are (1) to reveal the core position of energy viewpoint in the realm of electromagnetic modal analysis; (2) to show how to do energy-viewpoint-based modal analysis for various electromagnetic structures. The major conclusions of this report are that: energy conservation law governs the energy utilization processes of various electromagnetic structures, and its energy source term sustains the steady energy utilization processes; the whole modal space of an electromagnetic structure is spanned by a series of energy-decoupled modes (DMs), which dont have net energy exchange in any integral period; the DMs can be effectively constructed by orthogonalizing energy source operator, which is just the operator form of the energy source term. Specifically speaking: in classical electromagnetism, energy conservation law has five different manifestation forms, that are power transport theorem (PTT), partial-structure-oriented work-energy theorem (PS-WET), entire-structure-oriented work-energy theorem (ES-WET), Poyntings theorem (PtT), and Lorentzs reciprocity theorem (LRT) forms; the energy source terms in the first four forms are formulated as input power operator (IPO), partial-structure-oriented driving power operator (PS-DPO), entire-structure-oriented driving power operator (ES-DPO), and Poyntings flux operator (PtFO); the DMs of wave-port-fed, lumped-port-driven, externally-incident-field-driven, and energy-dissipating/self-oscillating electromagnetic structures can be constructed by orthogonalizing IPO, PS-DPO, ES-DPO, and PtFO; LRT guarantees that the obtained DMs satisfy some useful Em-Hn orthogonality relations, where the Em and Hn represent the electric field of the m-th DM and the magnetic field of the n-th DM.
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An inhomogeneity into a conductive matrix deforms the flow pattern of an applied electric current. A usual current cloak can be defined as a permanent modification of the matrix properties around the inhomogeneity guaranteeing that the current flow pattern is similar before and after passing by the modified zone, so it implies the electrical invisibility of the inhomogeneous region. Here we introduce the concept of a current cloak that can be tuned --switched on and off, for example-- by means on an external field. We demonstrate analytically and using Finite Elements Simulations that a current cloak can be constructed and manipulated by an external magnetic field for a concrete system consisting in a magneto-resistive matrix with a stainless steel inclusion.
A radial-dependent dispersive finite-difference time-domain (FDTD) method is proposed to simulate electromagnetic cloaking devices. The Drude dispersion model is applied to model the electromagnetic characteristics of the cloaking medium. Both lossless and lossy cloaking materials are examined and their operating bandwidth is also investigated. It is demonstrated that the perfect invisibility from electromagnetic cloaks is only available for lossless metamaterials and within an extremely narrow frequency band.
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