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.

©2012 Optical Society of America

Tight control of light beams in photonic crystals with spatially-variant lattice orientation Jennefir L. Digaum, Javier J. Pazos, Jeffrey Chiles, Jeffrey D’Archangel, Gabriel Padilla, Adrian Tatulian, Raymond C. Rumpf, Sasan Fathpour, Glenn D. Boreman, and Stephen M. Kuebler

Opt. Express 22(21) 25788-25804 (2014)

Independent control of phase and power in spatially variant self-collimating photonic crystals Jesus J. Gutierrez, Noel P. Martinez, and Raymond C. Rumpf

J. Opt. Soc. Am. A 36(9) 1534-1539 (2019)