Design of thin–film photonic metamaterial Lüneburg lens using analytical approach
Johnson, Steven G.
Date of Issue2012
School of Physical and Mathematical Sciences
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.
DRNTU::Science::Physics::Optics and light
© 2012 OSA. This paper was published in Optics Express and is made available as an electronic reprint (preprint) with permission of Optical Society of America. The paper can be found at: [DOI: http://dx.doi.org/10.1364/OE.20.001617]. One print or electronic copy may be made for personal use only. Systematic or multiple reproduction, distribution to multiple locations via electronic or other means, duplication of any material in this paper for a fee or for commercial purposes, or modification of the content of the paper is prohibited and is subject to penalties under law.