title: Synthesis of spatially variant lattices.
abstract: It is often desired to functionally grade and/or spatially vary a periodic structure like a photonic crystal or metamaterial, yet no general method for doing this has been offered in the literature. A straightforward procedure is described here that allows many properties of the lattice to be spatially varied at the same time while producing a final lattice that is still smooth and continuous. Properties include unit cell orientation, lattice spacing, fill fraction, and more. This adds many degrees of freedom to a design such as spatially varying the orientation to exploit directional phenomena. The method is not a coordinate transformation technique so it can more easily produce complicated and arbitrary spatial variance. To demonstrate, the algorithm is used to synthesize a spatially variant self-collimating photonic crystal to flow a Gaussian beam around a 90° bend. The performance of the structure was confirmed through simulation and it showed virtually no scattering around the bend that would have arisen if the lattice had defects or discontinuities.
authors: EM Lab, W. M. Keck Center for 3D Innovation, University of Texas at El Paso, 500 West University Avenue, El Paso, Texas 79968, USA. rcrumpf@utep.edu
authors: Raymond C
authors: RC
authors: Rumpf
authors: Javier
authors: J
authors: Pazos