Transformation Optics and Cloaking

An extraordinary range of electromagnetic properties can be engineered in artificially structured metamaterials, with a flexibility unmatched by any conventional material. While metamaterials can be designed that have properties beyond any of those in existing materials-such as negative refractive index-it is the ability to control these properties at will that makes the field of metamaterials truly exciting. We can, for example, control exactly the degrees of electric and magnetic responses of a metamaterial point-by-point. The concept of a graded material is far from unprecedented; materials in which the refractive index varies spatially are well known in optics, forming the basis of a class of lenses and other optical devices. What is unprecedented is that we now can create carefully controlled and independent spatial gradients in the electric and magnetic properties of a metamaterial, with a greater precision and wider range of variation than has ever been possible. Taking full advantage of this enormous flexibility has led to the recent development of transformation optics.

What is transformation optics? Transformation optics is a unique means of designing an optical device. Rather than relying on the standard tools of optics, such as ray-tracing or full-wave simulations, we instead imagine warping space in a manner so as to control the trajectories of light rays. The process can be easily understood by visualizing a set of grid lines drawn on a sheet of rubber. By stretching, squishing, shearing or otherwise distorting the rubber sheet, the grid lines will be distorted accordingly. Light, which would follow a straight line on the undistorted grid, instead will follow the curved path on the distorted grid. If we could warp space like the sheet of rubber, we could control the flow of light.

While space cannot be transformed in this manner, we can still make use of the coordinate transformation that connects the undistorted and distorted grids. Applying the transformation to Maxwell's equations-the equations that govern electromagnetic waves-we arrive at a straightforward prescription for a material that will accomplish the same result in terms of controlling the trajectories of the rays of light. If we can make the material, we can make light flow just in the manner as the lines on the distorted rubber sheet.

CMIP is currently studying the unusual and intriguing properties of a wide range of components and devices based on transformation optical designs. CMIP faculty and students are currently developing the tools to realize transformation optical structures, from fundamental theory to eventual metamaterial implementation. Perhaps one of the most compelling transformation optical structures yet conjectured and demonstrated is the invisibility cloak-a structure that can be used to conceal objects from detection by electromagnetic waves. When we make use of the transformation optical approach, the design of a cloak is almost trivial: poke a hole in the sheet of rubber, and push outwards. The grid lines will now appear to flow around the hole. Any objects placed within the hole are not part of the "space," and are therefore undetectable. In 2006, David Schurig, David Smith and Steve Cummer of CMIP demonstrated a metamaterial cloak that successfully approximated this transformation. We continue to study electromagnetic cloaks and other advanced structures enabled by metamaterial implementations of transformation optical designs.