At this point, there are three distinctly different approaches to cloaking: transformation optics, scattering cancellation, and conformal mapping. All three methods depend on specialized materials to achieve their goals.
The most promising class of these specialized materials, known as metamaterials, interacts differently with the electromagnetic waves that make up visible light. Instead of absorbing some light and reflecting other light to our eyes so that we can see the object, or refracting light so that we can see at least partway through the object, these objects bend the light so we can see around the object.
With metamaterials, the inherent properties of the material are important, but it's also important how the materials are put together at the atomic scale. The fundamental compositions of the metamaterial have to be smaller than the wavelengths they are trying to bend. Materials like this are already in use for longer wavelengths such as radar (this is the concept behind the stealth bomber, visible to humans but not to radar).
To make a stealth bomber invisible to the human eye, we have to transfer this effect into the shorter wavelength visible light range, between 380 and 780 nanometers (nm). Thus, the basic structure of the metamaterial has to be below this range for cloaking to occur. Worse still, this material has to cover the entire visible range to be useful; otherwise we would see it as a specific color (for example, a red object is red to us because it reflects the red wavelengths back to our eye and absorbs the other wavelengths).
This is quite a design challenge for materials scientists. The common thread in all cloaking approaches is to minimizing what is known as the scattering cross section. In simplistic terms, that means to keep the light smoothly flowing around the object and eliminate reflections and refractions that could alert us to the object's presence (or in the case of scattering cancellation, produce a complementary scattering, similar to the effect of noise-cancelling headphones).
All of these strategies also currently use a forward design process, where the properties of a cloaking device can't be worked out until the design process is finished. This can be a slow, iterative process.
The authors are suggesting an inverse design method. Forward design focuses more on the task and finding a material that fills that need (for example, cloaking a tank). Inverse design focuses on the material-find the most useful class of materials with the broadest application, then adapt to a specific case (this works well in the general case, now how can I modify it to cloak a tank?). This approach often reduces screening time significantly, and the authors believe this will accelerate the practical development process.
These are exciting developments, but the practical applications are still far away. Don't run down to the department store looking for your Harry Potter Invisibility Cloak anytime soon. (Don't forget your spouse's birthday either, and you won't need one.)