The cloak works on the principal of light as an electromagnetic wave, with a longer wavelength than X-rays and ultraviolet and shorter wavelength than infrared, microwaves and radio waves. The electromagnetic waves follow four mathematical formulas established nearly 150 years ago by James Clerk Maxwell.
Light that transmits through the fabric is made indistinguishable from light that passes through free space. "Using Negative dialectic constant materials is likely in principle, as we are discovering things in small scale that are possible in laborites," said B. Sriram Shastry, physics professor at the University of California at Santa Cruz.
Just one more of those things first seen in Star Trek that most people thought was "impossible". This is something that wasn't in "How Star Trek Changed the World". You might want to check out the link under "Metamaterials" before that whole site is classified.