Mathematics of a Novel Type of Active Cloaking

August 25, 2009

Numerical computations have revealed a new cloaking method that might someday shield submarines from sonar, planes from radar, and buildings from earthquakes.

"We have shown that it is . . . possible to cloak objects of any shape that lie outside the cloaking devices," said mathematician Graeme W. Milton (University of Utah). "It's a brand-new method of cloaking."

Milton, Fernando Guevara Vasquez, and Daniel Onofrei have written two theoretical papers to show how the cloaking method might work in two dimensions at a single frequency of electromagnetic waves and at a wide range of frequencies. Video.

In "Active Exterior Cloaking for the 2D Laplace and Helmholtz Equations," which appeared in Physical Review Letters (Aug. 11, 2009), the researchers proved, for two-dimensional Laplace equations, that a single active exterior cloaking device could shield an object from surrounding fields, yet produce only small scattered fields. For the two-dimensional Helmholtz equation, they showed that three cloaking devices placed around an object made the object hard to identify or locate. They then extended the approach other linear wave equations.

In "Broadband Exterior Cloaking," which appeared in Optics Express (Aug. 5, 2009), the mathematicians showed that their method of cloaking for a broad range of frequencies involves at least three devices. Within any "quiet zone" between the devices, where the wave amplitude is small, objects become nearly impossible to detect.

"We proved mathematically that this method works when the wavelength of incoming electromagnetic radiation is large compared with the objects being cloaked, meaning it can cloak very small objects," Milton said. So, for the tiny wavelengths of visible light, only microscopic objects would disappear from view.

"It's a fascinating subject," Milton said, "and there is beautiful mathematics behind it."

Source: University of Utah, Aug. 17, 2009.