# A Phased Array Antenna with New Elements Designed Using Source Transformations
## 1 Introduction  
The concept of transformation electromagnetics/optics (TE/TO), introduced by [PERSON] et al. [1] and [PERSON] [2], refers to the manipulation of electromagnetic fields through a complex electromagnetic medium whose constitutive parameters are distinctly determined by the transformation. The transformation-based approach has led to numerous electromagnetic passive device designs [3, 4, 5, 6, 7, 8, 9, 10, 11] that exhibit unconventional and unusual propagation characteristics. This technique is based on the key assumption of form-invariance of Maxwell's equations under coordinate transformations [12]. The same coordinate transformation technique can also be applied to a region with sources (e.g., current and charge distributions), where the sources will be transformed along with the material and behave exactly the same way as the original untransformed source [13, 14, 15]. The use of source transformations yields fascinating opportunities for the design of complex radiation structures by enabling the fabrication of unique structures with engineered material properties, allowing the transformed geometries to mimic the performance of original ones, which is especially useful when physical constraints require spatial changes to be made to the source. One of the first applications of this technique was suggested by [PERSON] et al. [13], who transformed a dipole current source into a completely new distribution while preserving its properties as a dipole antenna. [PERSON] et al. [14] took this concept further and introduced an optical source transformation using a \"pinwheel\" transformation, where they approximated the sheet current of a simple dipole as a volumecurrent and transformed it to a new current distribution using a \"pinwheel\" coordinate transformation. Based on these pioneering works, several conformal arrays have been proposed [16; 17; 18]. [PERSON] et al. [16] proposed a conformal array design, where a nonuniform circular array radiates as a uniformly spaced linear array. [PERSON] [17] proposed a TO-based circular array design, which performs as a series of line sources embedded in a rectangular metamaterial media. However, these designs used \"point\" charges or electric line sources as the radiating sources in their numerical solution to validate their proposed concept. A more practical antenna source was not considered in these TO-based phased array designs. In this paper, the source transformation approach is used to design a new linear array, where each individual antenna element is transformed from a single dipole element in free-space (as shown in Figure 1a). The result is an antenna array that radiates the same field as the linear dipole array depicted in Figure 1b. As shown in Figure 1a, the individual antenna element of the transformed linear array is a relatively extreme demonstration of a \"pinwheel\" shaped antenna which is transformed from a dipole antenna element similar to the transformation introduced in [14]. Furthermore, the transformed antenna element in the array is surrounded by a complex electromagnetic media as prescribed by the transformation (shown as dotted grey circle in Figure 1). Specifically, through numerical simulations, it is shown that a linear array of complex \"pinwheel\" antenna elements can perform as an array of linear dipole antennas in free-space for potential applications in structurally integrated and conformal phased arrays, where the antenna performance is a function of structural and mechanical restraints. The finite element analysis (FEA)-based full-wave simulations via COMSOL Multiphysics (r) are used to numerically analyze and demonstrate the performance of the proposed TO-based antenna array for phased array scanning. The proposed \"pinwheel\" antenna array has potential applications in structurally integrated and conformal phased array antennas where the antenna performance is a function of structural and mechanical restraints.