Researchers from the Cockrell School of Engineering at UT Austin have quantified the physical limitations of the performance of cloaking devices. From an article on phys.org [phys.org]:
The researchers' theory confirms that it is possible to use cloaks to perfectly hide an object for a specific wavelength, but hiding an object from an illumination containing different wavelengths becomes more challenging as the size of the object increases.
[Researchers Alu and Monticone] created a quantitative framework that now establishes boundaries on the bandwidth capabilities of electromagnetic cloaks for objects of different sizes and composition. As a result, researchers can calculate the expected optimal performance of invisibility devices before designing and developing a specific cloak for an object of interest. Alu and Monticone describe their work in the journal Optica.
Cloaks are made from artificial materials, called metamaterials, that have special properties enabling a better control of the incoming wave, and can make an object invisible or transparent. The newly established boundaries apply to cloaks made of passive metamaterials -- those that do not draw energy from an external power source.
[...] The researchers' framework shows that the performance of a passive cloak is largely determined by the size of the object to be hidden compared with the wavelength of the incoming wave, and it quantifies how, for shorter wavelengths, cloaking gets drastically more difficult.