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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 20, Iss. 14 — Jul. 2, 2012
  • pp: 15263–15274

Synthesis of spatially variant lattices

Raymond C. Rumpf and Javier Pazos  »View Author Affiliations

Optics Express, Vol. 20, Issue 14, pp. 15263-15274 (2012)

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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 OSA

OCIS Codes
(050.0050) Diffraction and gratings : Diffraction and gratings
(130.0130) Integrated optics : Integrated optics
(230.0230) Optical devices : Optical devices
(160.3918) Materials : Metamaterials
(160.5298) Materials : Photonic crystals

ToC Category:
Photonic Crystals

Original Manuscript: April 13, 2012
Revised Manuscript: May 18, 2012
Manuscript Accepted: June 10, 2012
Published: June 22, 2012

Raymond C. Rumpf and Javier Pazos, "Synthesis of spatially variant lattices," Opt. Express 20, 15263-15274 (2012)

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