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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 18, Iss. 19 — Sep. 13, 2010
  • pp: 20321–20333

Controlling electromagnetic fields with graded photonic crystals in metamaterial regime

Borislav Vasić, Goran Isić, Radoš Gajić, and Kurt Hingerl  »View Author Affiliations

Optics Express, Vol. 18, Issue 19, pp. 20321-20333 (2010)

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Engineering of a refractive index profile is a powerful method for controlling electromagnetic fields. In this paper, we investigate possible realization of isotropic gradient refractive index media at optical frequencies using two-dimensional graded photonic crystals. They consist of dielectric rods with spatially varying radii and can be homogenized in broad frequency range within the lowest band. Here they operate in metamaterial regime, that is, the graded photonic crystals are described with spatially varying effective refractive index so they can be regarded as low-loss and broadband graded dielectric metamaterials. Homogenization of graded photonic crystals is done with Maxwell-Garnett effective medium theory. Based on this theory, the analytical formulas are given for calculations of the rods radii which makes the implementation straightforward. The frequency range where homogenization is valid and where graded photonic crystal based devices work properly is discussed in detail. Numerical simulations of the graded photonic crystal based Luneburg lens and electromagnetic beam bend show that the homogenization based on Maxwell-Garnett theory gives very good results for implementation of devices intended to steer and focus electromagnetic fields.

© 2010 Optical Society of America

OCIS Codes
(160.3918) Materials : Metamaterials
(160.5298) Materials : Photonic crystals

ToC Category:
Photonic Crystals

Original Manuscript: June 30, 2010
Revised Manuscript: August 13, 2010
Manuscript Accepted: August 23, 2010
Published: September 9, 2010

Borislav Vasic, Goran Isic, Rados Gajic, and Kurt Hingerl, "Controlling electromagnetic fields with graded photonic crystals in metamaterial regime," Opt. Express 18, 20321-20333 (2010)

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