Transformation Electromagnetics in Antenna Engineering: Theory and Implementation Yang Hao School of Electronic Engineering and Computer Science, Queen Mary University of London, London E1 4NS, UK. e-mail: yang.hao@eecs.qmul.ac.uk Abstract Current designs of electromagnetic cloaks are largely based on the use of metamaterials and a technique called “transformation optics/electromagnetics”. Free space cloaks require materials with extreme properties and, hence, they are difficult to implement in practice. However, the theory of “transformation optics/electromagnetics” offers a useful design tool for antenna engineers, and enables them to develop novel antennas. In this paper, we will review some research activities at Queen Mary, University of London, regarding applications of transformation electromagnetics in the antenna and microwave engineering. Design examples such as flat reflectors, lenses and sub-wavelength antennas will be introduced. Novel FDTD techniques to deal with the design of gradient index metamaterials will be also demonstrated and used to evaluate the performance of transformation-based antennas. In particular, the tradeoff in antenna performance whether or not metamaterials are required in the design will be discussed. 1. Introduction Electromagnetic Transformation utilizes a symmetry property of EM fields embodied in the fact that Maxwell’s equations are form-invariant under coordinate transformations. The power of Electromagnetic Transformation is that it may be used to specify the required electromagnetic properties of a material in order to control in a predefined manner the path of an electromagnetic beam. These specifications typically require anisotropic and exotic material parameters that can only be achieved by the fabrication of novel materials, but lead to novel ways to control “electromagnetic space”. In addition to the well-publicised cloaking phenomenon [1], [2], other applications of transformation electromagnetics include all-angle absorbers [3] and retro-reflectors [4], reflection-less beam shifters and beam-splitters [5], and “flat” parabolic mirrors [6]. Many of these applications have been also confirmed by numerical simulations [7, 8]. Some recent work at Queen Mary, University of London demonstrates how electromagnetic transformation concepts can be employed by distorting EM space using an all-dielectric approach [9]. In this paper, some design examples such as flat reflectors, lenses and sub-wavelength antennas will be presented. They are characterized by using gradient index metamaterials, based on both numerical modeling and experiments. In particular, the tradeoff in antenna performance whether or not metamaterials are required in the design will be discussed. 2. Theoretical Background Let’s assume a 3D volume of space described by a Cartesian coordinate system (x, y, z), and a second volume described by a distorted coordinate system (x′, y′, z′). 2D cut-planes in those spaces are shown in Fig. 1. The two coordinate systems are related through a general transformation function x′ = x′(x, y, z), y′ = y′(x, y, z), z′ = z′(x, y, z). Assume that, in the original space (x, y, z), it contains materials having and . According to the theory of transformation electromagnetics [1], the resulting permittivity and permeability tensors in a distorted coordinate system (x′, y′, z′) are given by (1) where J is the Jacobian transformation matrix between the two coordinate systems, defined as (2) 978-1-4244-6051-9/11/$26.00 ©2011 IEEE