Origami with negative refractive index to generate super-lenses

Fanny Guenneau,Sebastien Guenneau,Sangeeta Chakrabarti,S Anantha Ramakrishna

doi:10.1088/0953-8984/26/40/405303

Abstract

Negative refractive index materials (NRIM) enable unique effects including superlenses with a high degree of sub-wavelength image resolution, a capability that stems from the ability of NRIM to support a host of surface plasmon states. Using a generalized lens theorem and the powerful tools of transformational optics, a variety of focusing configurations involving complementary positive and negative refractive index media can be generated. A paradigm of such complementary media are checkerboards that consist of alternating cells of positive and negative refractive index, and are associated with very singular electromagnetics. We present here a variety of multi-scale checkerboard lenses that we call origami lenses and investigate their electromagnetic properties both theoretically and computationally. Some of these meta-structures in the plane display thin bridges of complementary media, and this highly enhances their plasmonic response. We demonstrate the design of three-dimensional checkerboard meta-structures of complementary media using transformational optics to map the checkerboard onto three-dimensional corner lenses, the only restriction being that the corresponding unfolded structures in the plane are constrained by the four color-map theorem.

Highlights

Materials with simultaneously negative dielectric permittivity (ε) and magnetic permeability (μ) can be said to have negative refractive index [1,2,3]
The case of a checkerboard lens with embedded cylinders as in figure 6 is drastically affected by dissipation: even a small level of absorption leads to a dramatic drop in the transmittance, with less than 2% of light passing through such a silver lens
We examine the response of a Negative refractive index materials (NRIM) checkerboard lattice lens with finite transverse size, when its unit cells exhibit a four-fold geometry with complex patterns

Summary

Introduction

Materials with simultaneously negative dielectric permittivity (ε) and magnetic permeability (μ) can be said to have negative refractive index [1,2,3]. A complementary layer pair composed of triangular cells arranged in checkerboard fashion [13] exemplifies situations whereby the ray picture can predict zero transmittance while the above theorem assures us of perfect transmittance These are examples of extraordinary transmission mediated by excitation and scattering of surface plasmon waves via the corners. In the absence of dissipation, infinite lattices of such checkerboard systems are very singular, and only the idea of complementary media can be used to deduce anything useful Apart from such theoretically esoteric properties, checkerboards potentially have many useful properties: for example, a finite checkerboard of triangular cells with adjacent triangles having refractive index, n = ±1, has been suggested to strongly confine light [13], while plasmonic nano-checkerboards of gold have been shown to support broadband extraordinary transmission of light [17]. The paper is organized into sections elaborating upon the above points

Origami lenses

Four color-map theorem applied to 3-D checkerboards of complementary media

Numerical analysis of checkerboard structures

Transfer matrix method calculations

Findings

Conclusions