Three-dimensionally isotropic negative refractive index materials from block copolymer self-assembled chiral gyroid networks.

In 1999, Pendry et al. predicted that specifically engineered artificial materials, that is, metamaterials, would have unusual magnetic responses, for example, negative permeability. Following this work, much effort has been devoted to the design and fabrication of metamaterials with negative refractive index. 3] Such negative index metamaterials have the potential, for example, in the form of superlenses, to overcome the diffraction limit in imaging or to enable novel optical effects, including cloaking. Today most metamaterial fabrication relies on top-down approaches such as lithography techniques, making efficient access to three-dimensionally (3D) isotropic metamaterials challenging thus hindering their practical applications. Recent progress in bottom-up type self-assembly offers promise to overcome some of these limitations. In particular block copolymer (BCP) selfassembly has emerged as a useful designer tool to create nanostructures including 3D continuous morphologies of disparate materials like ceramics and metals. The present paper makes clear theoretical predictions for how to design 3D isotropic materials with negative refraction and circularly polarized light propagation from a class of block copolymer based self-assembled materials not yet rigorously studied in the context of metamaterials. Through theoretical understanding and guidance on materials choices, characteristic length and frequency scales, which are determined by calculations and described in detail here, a “recipe” is provided for the synthesis, fabrication and characterization of these materials. We present calculations of the photonic properties of 3D periodic metallic nanomaterials with co-continuous cubic morphologies as illustrated in Figure 1. Such structures are experimentally accessible through self-assembly of AB diblock copolymers and ABC triblock terpolymers and are referred to as double gyroid (D-GYR) and alternating gyroid (A-GYR). Both of these structures have two 3D continuous cubic and interwoven minority networks separated by a matrix majority network. In the A-GYR the two minority networks are distinguishable leading to chirality while in the D-GYR they are not. We predict for the resulting metallic nanomaterials that the coupled surface plasmon resonance of the two minority networks of the D-GYR induces low frequency light propagation with a negative index of refraction. Due to their cubic symmetry, these materials are 3D isotropic (see Figure 1e). They also show circularly polarized light propagation originating from the chirality of the gyroid networks. We further predict that by tailoring BCP synthesis one can design materials with varying refractive index and frequency at which negative refraction occurs. Finally, in contrast to D-GYR metallic nanomaterials, chiral A-GYR metallic nanomaterials are expected to exhibit a surprising metallic band gap despite their smaller metallic fraction. We Figure 1. Schematic routes to 3-dimensionally co-continuous metamaterials with cubic symmetry and expected optical behavior. a) D-GYR; b) hollow D-GYR; and c) A-GYR metamaterials. For clarity of presentation, specific blocks are represented to be transparent. d) D-GYR metamaterial formed from many unit cells. The two chiral gyroid struts are depicted in different color for clarity. e) Projected images of a DGYR metamaterial unit cell with unit cell length a onto three orthogonal axes. Two struts are cut in different planes for showing full loops. Surface plasmon polaritons f) oscillate on the closed loop of gyroid networks and g) on a 1-dimensional metal/insulator/metal wave-guide.