Transformation Electromagnetics: An Overview of the Theory and Applications

The recently introduced transformation-electromagnetics techniques provide a new methodology for designing devices that possess novel wave-material interaction properties. They are based on the form invariance of Maxwell's equations under coordinate transformations. These methods provide an extremely versatile set of design tools that employ spatial-coordinate transformations, where the compression and dilation of space in different coordinate directions are interpreted as appropriate scalings of the material parameters. The most famous transformation-optics device is the cloak of invisibility. However, a wide variety of other devices are also possible, such as field concentrators, polarization rotators, beam splitters, beam collimators, and flat lenses. In this paper, an overview of transformation-electromagnetics device design techniques is presented. The paper begins by introducing the underlying design principle behind transformation electromagnetics. Several novel transformation-based device designs are then summarized, starting with electromagnetic-cloaks that have spherical shell or cylindrical annular shapes. More general cloaking designs of noncircular annular geometries are treated, and the application of cloaking to RF/microwave antenna shielding is also discussed. Following this, device designs that employ transformations that have discontinuities on the domain boundary are presented. Unlike those used for cloaks, this type of transformation is capable of modifying the fields outside of the device. Examples of this type of transformation-electromagnetics device are presented, which include flat near-field and far-field focusing lenses, wave collimators for embedded sources (e. g., antennas), polarization splitters and rotators, and right-angle beam benders.