Transformation optics was born of the realization that lines of force are effectively glued to the coordinate system. As the system is distorted it carries with it all the associated fields. Hence to guide the trajectory of a ray of light, only a distortion in the underlying coordinate system is needed, automatically taking with it the light ray. Knowledge of the transformation in turn provides the values of μ and ε required to steer the light in this way.

Invisibility
Figure 3 (top left) shows a ray of light travelling in free space. We wish to hide the contents of a sphere radius R1 by directing the rays around this region, but requiring that any distortion of trajectories is confined within a larger sphere radius R2 (Fig. 3, top right). In this way an external observer would be aware neither of the presence of the cloak nor its contents. The illusion of empty space has been created.

Metamaterials
The idea behind metamaterials is that electromagnetic properties can be altered by changing the physical structure of an existing material. A simple example would be to create a series of voids in a dielectric. If the voids are much smaller than the relevant wavelength, incident light will see only an average response and a reduced effective permittivity. More complex structures, such as tiny metallic resonators, can produce more exotic effects, including negative refractive indices. Provided that the structure remains much smaller than the wavelength, properties can be interpreted in terms of an effective ε and μ. As it happens, nature has not been generous with the electromagnetic properties of materials: only a limited range is on offer and some properties, such as a negative refraction, are entirely absent in naturally occurring materials. In fact, it was the ability of metamaterials to produce negative refractive indices that first drove them to prominence. Since that time, the concept of function through structure has been deployed to implement many theoretical schemes previously thought to be beyond reach.

This has been #Cloaking101 part 1 of #InterstellarTravel101

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