Mathematicians who came up with a way to explain how a new "invisibility cloak" hides objects have now developed a theory that could let the technology hide items that emit light.

The new mathematical theory was developed by Prof. Allan Greenleaf at the University of Rochester in Rochester, N.Y., and colleagues in other countries.

It modifies a theory developed by Greenleaf and colleagues in 2003, when they were investigating the math that underlies the detection of tumours. That theory started the mathematics behind invisibility.

A separate team of U.S. and British scientists announced a breakthrough in the field in October 2006, demonstrating the first working invisibility cloak. The cloak redirects microwave beams so they flow around an object "hidden" inside — in their study, a passive copper disk or rod — with little distortion, acting almost as though nothing were there.

The math didn't address things that emit their own electromagnetic light, however, such as cellphones, computers, and anything else that might generate signals. Greenleaf and an expanded team said Tuesday that they've come up with the mathematics to provide invisibility for the full spectrum of light at all frequencies.

The technology cannot yet make a person or thing truly invisible — it simply eliminates a narrow range of wavelengths of light, as Greenleaf points out in a written statement issued on Tuesday.

"For example, an object could be rendered invisible at just a specific wavelength of red; it would be visible in nearly every other colour," he wrote.

His team's latest work, Greenleaf announced in the statement, predicts behaviour inside the cloak and suggests solutions to several problems.

Their study suggests the invisibility effect could be ruined by a light emitted from within the cloaked region — such as a flashlight. The conclusion arose after studying the mathematical properties of light within the cloaked area and deducing that the invisibility would be wrecked due to the behaviour of polarized electromagnetic waves as described by math known as Maxwell's equations.

Maxwell's equations, named for 19th century mathematician and physicist James Clerk Maxwell, predict the behaviour of electrical and magnetic fields and their interaction with matter.

The newest mathematical theory suggests that lining the inside of the cloak with a special material, or lining both the inside and outside with matched materials, could prevent the invisibility effect from being ruined by a light emitted from within the cloak.

The other problem was that the earlier math suggested that to anyone inside the cloak, it would appear as though a mirror surrounded them: they would see their own reflection in every direction.

The new math and the special materials would correct that problem, Greenleaf wrote.

Before announcing the new math, Greenleaf said he discussed it in December with a member of the team that built the cloak, David Smith, an associate professor of electrical and computer engineering at Duke University in Durham, N.C.

The theorists who developed the new invisibility mathematics with Greenleaf include Prof. Matti Lassas of the Helsinki University of Technology; Prof. Yaroslav Kurylev of Loughborough University in Leicestershire, England; and Prof. Gunther Uhlmann at the University of Washington in Seattle.