Bending and sculpting metamaterials and photonic crystals

Electroamagnetic fields cannot be controlled using homogeneous materials. Devices must be composed of interfaces, gradients, curved surfaces, or other inhomogeneities. Why is it that almost all metamaterials in the literature are macroscopically homogeneous? Imagine the potential that could be unlocked by making them inhhomogeneous. The problem is that this must be done while keeping the size and shape the unit cells essentially constant. Imagine grabbing a checkerboard at opposite sides and bending it like an accordion, but without changing the size or shape of the squares. Impossible?

We have recently developed an algorithm to do just this, and more. The tool can be used to spatially vary essentially any attribute of a periodic structure while still rendering the overall lattice smooth and continuous. Attributes include unit cell orientation, lattice spacing, fill fraction, geometry, material composition, and more. In fact, any combination of these can be spatially varied at the same time and in unique patterns. The algorithm has an amazing ability to keep all other attributes constant and uniform.

Our algorithm is discussed here:
http://dx.doi.org/10.1364/OE.20.015263

We demonstrated the algorithm by designing a photonic crystal with spatially variant self-collimation. You can read about that here:
http://www.jpier.org/PIER/pier139/01.13030507.pdf

Both papers are open access and freely available. It would be great to hear your input.