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

Abstract

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.

On-chip transformation optics for multimode waveguide bends

“…Although in principle anisotropic materials, such as SiC, can be used in silicon photonics, TO requires in general a gradient anisotropy, which is much more complex to achieve. Note that one could also use photonic crystals [9][10][11][12] or grooves 13,14 to tailor the index and anisotropy, however these discrete structures result in additional field scattering and inter-mode coupling due to the finite wavelength/period ratio (typically around 10:1). Instead, we use a grayscale-lithography technique described below that produces smooth gradients but is limited to mostly isotropic effective indices.…”

Luneburg and flat lens based on graded photonic crystal

“…As we all know, the broad range of photonic crystal (PC) applications enables the design of various cavities, waveguides, switches, mirrors and filters [3]. While they were also shown that the potential applications ranges from invisibility cloaks [4,5] and optical black holes [6], to planar devices such as Luneburg [7,8]. The graded photonic crystals (GPCs) consist of unit cells with spatially varying geometrical or material properties [9].…”

Negative refraction and self-collimation in the far infrared with aligned carbon nanotube films

“…The optical anisotropy in such nanowire arrays was identified as a mechanism for negative refraction [18,19]. As the permittivity for electric field along the nanowire axis approaches infinity, a "canalization" or collimation effect can be observed in aligned nanowire arrays [20,21]. This phenomenon is called "selfcollimation" and Kosaka et al [22] were the first to notice the self-collimation effect in photonic crystals.…”