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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 20, Iss. 2 — Jan. 16, 2012
  • pp: 1617–1628

Design of thin–film photonic metamaterial Lüneburg lens using analytical approach

Hanhong Gao, Baile Zhang, Steven G. Johnson, and George Barbastathis  »View Author Affiliations

Optics Express, Vol. 20, Issue 2, pp. 1617-1628 (2012)

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We design an all–dielectric Lüneburg lens as an adiabatic space–variant lattice explicitly accounting for finite film thickness. We describe an all–analytical approach to compensate for the finite height of subwavelength dielectric structures in the pass–band regime. This method calculates the effective refractive index of the infinite–height lattice from effective medium theory, then embeds a medium of the same effective index into a slab waveguide of finite height and uses the waveguide dispersion diagram to calculate a new effective index. The results are compared with the conventional numerical treatment – a direct band diagram calculation, using a modified three–dimensional lattice with the superstrate and substrate included in the cell geometry. We show that the analytical results are in good agreement with the numerical ones, and the performance of the thin–film Lüneburg lens is quite different than the estimates obtained assuming infinite height.

© 2012 OSA

OCIS Codes
(110.2760) Imaging systems : Gradient-index lenses
(230.7400) Optical devices : Waveguides, slab
(310.0310) Thin films : Thin films
(050.6624) Diffraction and gratings : Subwavelength structures

ToC Category:

Original Manuscript: November 21, 2011
Revised Manuscript: December 16, 2011
Manuscript Accepted: December 18, 2011
Published: January 10, 2012

Hanhong Gao, Baile Zhang, Steven G. Johnson, and George Barbastathis, "Design of thin–film photonic metamaterial Lüneburg lens using analytical approach," Opt. Express 20, 1617-1628 (2012)

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