Study Of Invisibility, Scattering And Antenna Based On Coordinate Transformation Method

Transformation optics/electromagnetics which is based on the form invariance of Maxwell's equations under a coordinate transformation provides us a totally new and powerful tool to manipulate light/electromagnetic (EM) wave in almost any desired manner. One only needs to build up a kind of spatial mapping according to the requirement for the light/EM wave propagation, and to then find a proper coordinate transformation to calculate the transformation media where the light would be guided as one desires. This method is initially applied to design invisibility cloak by which incident light will be guided around the concealed object smoothly, and return to its original trajectory when it comes out of the cloak. It seems the light travels in the same direction as if it had passed through an empty space, and invisibility is thus achieved. This design was soon validated by a practical metamaterial cloak at microwave frequency. Hence, a great progress is made in both transformation optics/electromagnetics and invisibility technology. Undoubtedly, the theory of transformation optics/electromagnetics helps us to understand and manipulate light and acoustic wave better.With this background, this dissertation carefully studies and discusses several issues concerning on invisibility, scattering, and antenna in transformation optics. And the main work and contributions of this dissertation are detailed as follows:1. The major strategies for cloaking are summarized and described. One can crush the concealed object to a point to achieve perfect invisibility; or crush the object to a sheet sit on another conducting sheet to obtain a ground-plane cloak; besides, with the help of folded transformation and complementary media, one can conceal targets outside the cloak device. With the first strategy this dissertation designs perfect elliptical cloak whose inner and outer boundaries are non-conformal ellipses. It also describes the method to design perfect cloak with arbitrary non-conformal boundaries. Meanwhile, with the second cloaking strategy this dissertation designs a ground-plane cloak whose inner boundary is a parabola and outer boundary is rectangule.2. Cloaks with multiple invisible regions are proposed. It is noticeable that with the first and second cloaking strategies one can design perfect invisibility cloaks; however, cloaking region in these kinds of cloaks is isolated from its external surrounding, so concealed object cannot receive or transmit any electromagnetic (EM) signal. On the contrary, in the third cloaking strategy object is concealed outside the cloak, where is a non-zero field region. This implies that concealed object is invisible to the surrounding space, but is still capable of observing efficiently. Unfortunately, "anti-object" has to be designed for each concealed object, and this is not suitable for metallic and absorbing objects. To overcome, at least in some extent, the disadvantages of previous strategies, cloaks with multiple invisible regions are proposed in this dissertation. There are several invisible regions especially with different kind of cloaking capabilities in the proposed cloak, which would provide more flexible choices for the objects to be hidden depending on their own properties or special demands.3. Scattering-shifting cloaks are proposed. Different from invisibility optics, illusion optics does not make concealed object invisible, but instead make it "look like" another totally different object. On this topic, a kind of scattering-shifting cloaks is proposed here, which will have the same scattering pattern as any desired object including metallic, dielectric or absorbing object. This implies that any target coated with the cloak will look like the mimicked object. In particular, curve-mapping method and geometrical approximation are proposed to imitate arbitrary conducting line segment, an area which remains problematic.4. Conic reflectors with planar profile are proposed. It is known that conic reflectors and planar reflectors have different optical properties. This dissertation presents a general and rigorous transformation method to tailor planar conic reflectors. The proposed method enables the designed reflectors to scatter or reflect incident light in the same manner as a conic reflector dose while the whole device as well as the reflector would maintain planar profiles. In order to reduce the overall size, especially the aperture of the reflector, it further applies a set of compressed and folded spatial mapping to the planar reflectors. Planar reflectors with reduced sizes are finally obtained which may be useful in several optical and electromagnetic applications.5. Multi-source co-beam system is proposed. Using folded transformation and spatial overlapping, equivalent multi-source system is designed, in which sources in different location will have the same radiation pattern. When the sources operate at the same frequency, the system can be used to synthesize the radiation power; and when the sources operate at different frequencies, it can be used in multi-frequency co-beam antenna. This dissertation further combines the multi-source co-beam system with planar conic reflectors to construct a multi-source co-beam planar reflector system which may be useful in several engeneering applications.