Recently it has been predicted that materials with exceptionally strong optical activity may also possess a negative refractive index, allowing the realization of superlenses for super-resolution imaging and data storage applications. Here we demonstrate experimentally and numerically that chirality-induced negative refraction is possible. Negative refraction due to 3D chirality is demonstrated for a bilayered metamaterial based on pairs of mutually twisted planar metal patterns in parallel planes, which also shows negative electric and magnetic responses and exceptionally strong optical activity and circular dichroism. Multi-layered forms of the metamaterial are found to be suitable for use as ultra-thin polarization rotators and circular polarizers for practical applications.
Hybridization plays an important role in the evolution of certain groups of organisms, adaptation to their environments, and diversification of their genomes. The evolutionary histories of such groups are reticulate, and methods for reconstructing them are still in their infancy and have limited applicability. We present a maximum likelihood method for inferring reticulate evolutionary histories while accounting simultaneously for incomplete lineage sorting. Additionally, we propose methods for assessing confidence in the amount of reticulation and the topology of the inferred evolutionary history. Our method obtains accurate estimates of reticulate evolutionary histories on simulated datasets. Furthermore, our method provides support for a hypothesis of a reticulate evolutionary history inferred from a set of house mouse (Mus musculus) genomes. As evidence of hybridization in eukaryotic groups accumulates, it is essential to have methods that infer reticulate evolutionary histories. The work we present here allows for such inference and provides a significant step toward putting phylogenetic networks on par with phylogenetic trees as a model of capturing evolutionary relationships. reticulate evolution | incomplete lineage sorting | phylogenetic networks | maximum likelihood P hylogenetic trees have long been a mainstay of biology, providing an interpretive model of the evolution of molecules and characters and a backdrop against which comparative genomics and phenomics are conducted. Nevertheless, some evolutionary events, most notably horizontal gene transfer in prokaryotes and hybridization in eukaryotes, necessitate going beyond trees (1). These events result in reticulate evolutionary histories, which are best modeled by phylogenetic networks (2). The topology of a phylogenetic network is given by a rooted, directed, acyclic graph (rDAG) that is leaf-labeled by a set of taxa ( Fig. 1; more details are provided in Model and SI Appendix). Reticulation events result in genomic regions with local genealogies that are incongruent with the speciation pattern. Several methods and heuristics use this incongruence as a signal for inferring reticulation events and reconstructing phylogenetic networks from local genealogies. These methods, which are surveyed elsewhere (2-4), assume that reticulation events are the sole cause of all incongruence among the gene trees and seek phylogenetic networks to explain all of the incongruence. A serious limitation of these methods is that they would grossly overestimate the amount of reticulation in a dataset when other causes of incongruence are at play. Indeed, several recent studies (5-9) have shown that detecting hybridization in practice can be complicated by the presence of incomplete lineage sorting (ILS) (Fig. 1).Recently, a set of methods was devised to analyze data where reticulation and ILS might both be simultaneously at play (10-15). However, these methods are all applicable to simple scenarios of species evolution and mostly assume a known hypothesis about the topol...
We demonstrate experimentally and numerically that metamaterials based on bilayer cross wires give giant optical activity, circular dichroism, and negative refractive index. The presented chiral design offers a much simpler geometry and more efficient way to realize negative refractive index at any frequency. We also developed a retrieval procedure for chiral materials which works successfully for circularly polarized waves
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