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

Details Design of thin-film photonic metamaterial Lüneburg lens using analytical approach Design of thin-film photonic metamaterial Lüneburg lens using analytical approach

2011-11-17

arxiv.org/abs/1111.4001v1

Physics

Optics

11 pages, 8 figures, uses opex3.sty

Scientific paper

We design an all-dielectric L\"uneburg 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 L\"uneburg lens is quite different than the estimates obtained assuming infinite height.

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