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Electromagnetic Transformation Medium and the Effects of Microstructures

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Tutor: SunHua
School: Suzhou University
Course: Theoretical Physics
Keywords: transformation media,microstructures,scattering theory,finite©\element simulation
CLC: O441.6
Type: Master's thesis
Year:  2011
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Metamaterials are artificial structures which gain special permittivity and peameability by designing and adjusting its cell shape, size, fraction or other microstructure factors. In the designs of metamaterials, transformation theory behaves as an effective and reliable tool to find parameters profiles for controlling electromagnetic waves. The basic principle of this theory is to find the distribution of electromagnetic parameters equivalent to a certain spaital transformation according to the invariance of the Maxwell¡¯s equations. Then one can controll the propagation of electromagnetic waves effectively and obtain materials of unprecedent electromagnetic properties and functions. Media designed according to the transformation theory is called¡°transformation media¡±, of which the parameters are usually anisotropic and inhomogeneous that they can only be realized by artificial microstructures of metamaterials. Reduced paramethers or deviation from ideal original designs are inevitable in realization. Here we adopt theoretic calculations and finite©\element simulations to discucss the effects of possible deviation on functionality when one try to realize a transformation medium with particular microstures. We focus on the following topics:(1) We first discuss the effects of the deviation of the inner©\face parameters of an invisibility cloak. This is a typical transformation medium, by which an incident electromagnetic wave will flow around its cavity without any scattering. Moreover, any radiation from an inner source will by totally suppressed due to the excitation of extraordinary voltage on its inner surface. However, the inner surface of an ideal cloak should be expanded by an infinite ratio in the transformation, which cannot be satisfied by an actual microstructure and lead to additional scattering and leakage of inner radiation. Particularly, the suppression of the inner radiation may be strongly affected by this deviation. Here we discuss an imperfect cloak of which the inner surface has a finite and isotropic expanding ratio. The scattering problem of such a complex medium is turned into a a problem concerning a simple medium by using the finite©\embedded method. Then we obtain the expression of the n©\th outflowing power density of such a device containing an active source. The results from theorectical analysis agrees well with those from finite©\element simulations. Our results show that strong though not perfect suppression of inner radiation can be realized by properly adjusting the position of the internal source relative to the cloak.(2) Deviation of the inner-surface parameters of a cloak not only fails its perfect radiation suppression, but also cause additional scattering for an incident wave from exterior space. But if we can design the finite expanding ratio of the inner surface, another type of transformation medium can be obtained, that is reshapers. Such a device turn the scattering from a conductor sticking to its inner surface to that from another conductor as designed, making an exterior observer see an illlusion of the later. We propose a scheme of three dimensional reshapers which can produce reshaping effects for arbitrary shapes. Finite-element simulations are carried out to demonstrate the effects of a reshaper that can turn a spherical conductor into a virtual ellipsoid conductor: when such a transformation medium surrounds a spherical conductor, what one see is an ellipsoid conductor.(3) We further propose a reduced scheme for reshapers and the microstures which may realize the simplified parameters. Such a structure is based on arrays of spli©\ring resonators and effective permeabilities can be obtained by adjusting geomitric parameters of this structure to realize the reshaping effect for a TE incident wave. The results from finite©\element simulations show that, though the parameters are simplified and discretized in this scheme and the materials have inevitable dispersion and loss, the microsture proposed here can produce good reshaping effects at its working frequency. And the working bandwidth can be broaded effectively by adjusting the details of the structure to avoid the resonance conditions near material parameters.
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