Study On "Non-double-blind" Superlens Cloaking Device

Recently, the investigations of transformation optics, as well as its derived counterpart transformation acoustics, have received more and more attention. Transformation acoustics is based on the fact that acoustic wave function can keep its form under coordinate transformation, expect for the distributions of the parameters of the materials. Suppose we know the materials distributions in a virtual space and the propagating of the acoustic wave can be easily obtained in that space. The virtual space can be mapped to the real physical space by a certain mapping relationship. The distributions of the materials in the physical world are determined by those in the virtual world and the mapping relationship. In that case, the propagating of acoustic field in the physical world will follow that mapping relationship. However, parameters of the materials in the physical space are often beyond those in the nature, such as a mass density with negative value or anisotropic mass density. Lucky, the recently popular topic "metamaterial" could provide such materials for us. Thus, the trajectory of acoustic waves can easily be manipulated by changing the distributions of materials. A large number of fascinate devices can be designed by this scheme. Among all these, the most interesting one is the famous "invisibility cloak". However, most cloaking devices isolate the cloaked objects from incident fields to hide the objects. As a result, the cloaked objects lost the contact from outside world. Later, some "none-double-blind" cloaking schemes, in which the cloaked object can receive external information have been proposed. But those schemes always refer to plenty’s of single-negative-index materials (materials with negative mass density or negative bulk modulus), or even double-negative-index materials (materials with simultaneously negative mass density and bulk modulus) which may bring a great challenge to experimental realizations. Consequently, the number of required negative materials of such a device shall be reduced to simplify the experimental realizations.This dissertation proposes a new "superlens" cloaking strategy which only consists of a pair of complementary single-negative-index materials. This should be the minimal requirement to form such devices. The dissertation is divided into following sections:In Chapter Ⅰ, we start from the Veselago lens and review the background as well as the developments of optical and acoustical metamaterial. Cloaking structures based on different theory are discussed and compared. Those cloaking structures and some other applications based on transformation optics and acoustics are briefly discussed.In Chapter Ⅱ, the theory of transformation acoustics are introduced. The formulas are detailed deduced in the Cartesian coordinates and are convent to a reduced way in the orthogonal curvilinear coordinate. Finally, a perfectly matched layer which can adapt boundary is designed through transformation acoustics. In Chapter III, two numerical methods used in this article, the finite element method and the acoustic scattering theory are introduced.In Chapter IV, the development in the domain of acoustic cloaking is briefly introduced. Then, a new "superlens" cloaking strategy which only consists of a pair of complementary single-negative-index materials is proposed and is verified by numerical method. The proposed device is a multi-layered structure consists of a pair of complementary materials which are arranged alternately. Numerical results show the multi-layered structure can remarkably reduce the scattering of the cloaked object when the thickness of each layer is much smaller than the wavelength of the incident wave, while the cloaked object can receive outside information. Thus this structure can be used to hide an acoustic sensor. Then, we discuss the influences to the scattering-reducing effect when the parameters of the cloaked object and the complementary materials are changed. At last, the proposed scheme is extended to three dimensions; and a preliminary scheme for a similar three-dimensional superlens cloaking is proposed.Finally, in Chapter V, the main conclusions of the dissertation and the prospect of the future work are presented.The principal contribution of the present study is summarized as below:1. A new strategy to design acoustic cloaking device is proposed. Compared to "double-blind" invisibility cloaks, this structure can hide the cloaked object from outside obverses while this object can receive undistorted external information. The proposed structure only requires a pair of complementary materials which are independent with the parameters of background medium as well as the cloaked object. The only need of the scheme is the thickness of each layer should be much smaller than the wavelength of incident wave. Therefore, compared to the previous "non-double-blind" cloaking structure, the proposed structure should notably reduce the technical difficulties in experimental realization.2. The robustness of the parameters of the cloaked object has been studied. When the mass density and the bulk modulus are multiplied by the same robust factor simultaneously, it is shown the scatter wave can be reduced almost an order of magnitude by the proposed multi-layered structure, provided the robust factor is between0.5and2.3. The situation when single-negative-index layers of the multi-layered structure exists dissipation has been studied. It is pointed that the scatter wave caused by the cloaked object can be remarkably reduced when the loss of the single-negative-index layers is less than10%.