Two separate teams, including Professor Pendry's, have outlined ways to cloak objects in the journal Science and their research papers present the maths required to verify that the concept could work although developing an invisibility cloak is likely to present serious challenges.
Both research groups propose methods using the unusual properties of so-called "metamaterials" to build a workable cloaking device.
These metamaterials can be designed to induce a desired change in the direction of electromagnetic waves, such as light, and this is achieved by tinkering with the nano-scale structure of the metamaterial, not by altering its chemistry.
John Pendry's team say that by enveloping an object in a metamaterial cloak, light waves can be made to flow around the object just like water would do.
John Pendry, along with colleagues David Smith and David Schurig at Duke University in North Carolina, US, have been researching suitable metamaterials for the device their planned invention.
Sir John explained that it would consist of a sphere or cylinder wrapped in a sheath of metamaterial, which would cloak it from electromagnetic waves such as radar.
And Professor Ulf Leonhardt, author of another cloaking paper in Science, described the effect for light as a "mirage".
The work could be used in military stealth technology although engineers have not yet created the materials that could be used to cloak an aircraft or a tank.