On the Limits of Invisibility: From Cloaking to Computation

When: Thursday, October 06, 2011 at 4:00 pm
Where: DA 114
Speaker: Steven G. Johnson
Organization: MIT, Applied Mathematics
Sponsor: Physics Colloquium

The idea of invisibility cloaks, from Harry Potter to Star Trek, has long captured the public imagination, and this excitement has recently spilled into the scientific arena with intriguing mathematical proposals by Pendry and others of theoretical conditions for true “cloaking” materials. However, despite the progress in this area, it has been increasingly recognized that hopes of true invisibility suffer from inherent challenges that rapidly worsen as more and more realism is introduced. By reviewing both the existing invisibility proposals and the limitations that have been identified, we will try to identify the windows of opportunity that still remain for cloaking research.

In computer simulations, many of the limitations of real materials are lifted, and a form of invisibility known as “perfectly matched layers” (PML) has become a dominant technique in modeling wave equations over the past 15 years. The goal of PML is to make the computational boundaries invisible, for simulating infinite space, and PML turns out to be mathematically very closely related to Pendry invisibility. PML has been so successful, in fact, that it is often forgotten that it too has inherent limitations. By reviewing PML’s mathematical roots, we will see how these limitations are revealed and what alternatives remain when PML fails.