Research On Some Electromagnetic Problems Based On Coordinate Transformation

In recent years, transformation optics has attracted great attention of scientists and engineers. Transformation optics has become a theory to control the electromagnetic fields accurately to design new electromagnetic devices, such as electromagnetic cloaks, electromagnetic concentrators, electromagnetic rotators, electromagnetic shifters. However the electrical parameters (relative permittivity, relative permeability) of these devices based on the theory-TO are inhomogeneous and anisotropic, difficult to be designed. So, scientists and engineers have proposed two methods to simplify the electrical parameters in the TO design. One is linear transformation optics by which the electrical parameters are homogeneous and anisotropic, the homogeneous parameters are easier to realize than inhomogeneous ones. This paper designs arbitrary shape homogeneous electromagnetic shifters by this method. Also this paper proposes and designs homogeneous electromagnetic rotators based on this method and do further discussion aiming to explore the nature of the linear method. Another method is based on conformal mapping method. The electric parameters of the electric devices, such as waveguide adapter, invisible carpets are inhomogeneous and isotropic based on this method. This paper designs waveguide adapter based on the second method by choosing suitable transforming function. This paper improves the fraction transforming function to design the high directional antenna. High directional antenna based on sine function conformal mapping is proposed and designed. This paper puts the complex series theory into the theory of conformal mapping to design multi-beam antenna. This method, compared with the Schwarz-Christoffel transformation and fraction transformation method attached in reference documentation, greatly simplifies the derivation process to design multiple-beam antenna. This paper successfully designs three-beam antenna, four-beam antenna, five-beam antenna, six-beam antenna, and eight-beam antenna. This paper deduces complete transformation optics theory from the integral loop invariance of electric field and magnetic field. The design procedures are presented in the appendix.