In 1929, Hermann Weyl derived the massless solutions from the Dirac equation - the relativistic wave equation for electrons. Neutrinos were thought, for decades, to be Weyl fermions until the discovery of the neutrino mass. Moreover, it has been suggested that low energy excitations in condensed matter can be the solutions to the Weyl Hamiltonian. Recently, photons have also been proposed to emerge as Weyl particles inside photonic crystals. In all cases, two linear dispersion bands in the three-dimensional (3D) momentum space intersect at a single degenerate point - the Weyl point. Remarkably, these Weyl points are monopoles of Berry flux with topological charges defined by the Chern numbers. These topological invariants enable materials containing Weyl points to exhibit a wide variety of novel phenomena including surface Fermi arcs, chiral anomaly, negative magnetoresistance, nonlocal transport, quantum anomalous Hall effect, unconventional superconductivity[15] and others [16, 17]. Nevertheless, Weyl points are yet to be experimentally observed in nature. In this work, we report on precisely such an observation in an inversion-breaking 3D double-gyroid photonic crystal without breaking time-reversal symmetry.
We demonstrate how broadband angular selectivity can be achieved with stacks of one-dimensionally periodic photonic crystals, each consisting of alternating isotropic layers and effective anisotropic layers, where each effective anisotropic layer is constructed from a multilayered metamaterial. We show that by simply changing the structure of the metamaterials, the selective angle can be tuned to a broad range of angles; and, by increasing the number of stacks, the angular transmission window can be made as narrow as desired. As a proof of principle, we realize the idea experimentally in the microwave regime. The angular selectivity and tunability we report here can have various applications such as in directional control of electromagnetic emitters and detectors.
The dynamics of collisionless galaxy can be described by the Vlasov-Poisson system. By the Jeans theorem, all the spherically symmetric steady galaxy models are given by a distribution of {Phi}(E,L), where E is the particle energy and L the angular momentum. In a celebrated Doremus-Feix-Baumann Theorem, the galaxy model {Phi}(E,L) is stable if the distribution {Phi} is monotonically decreasing with respect to the particle energy E. On the other hand, the stability of {Phi}(E,L) remains largely open otherwise. Based on a recent abstract instability criterion of Guo-Lin, we constuct examples of unstable galaxy models of f(E,L) and f(E) in which f fails to be monotone in E.
In this paper, we show by experiment that by covering a thin flat nonlinear lens on the sources, the sub-diffraction-limit observation can be achieved by measuring either the near-field distribution or the far-field radiation of the sources at the harmonic frequencies and calculating the inverse Fourier transformation to obtain the sub-wavelength imaging. Especially, the sub-wavelength image calculated from measured far-field data demonstrates very clear resolution. Since metamaterials included with active elements can easily behave strong nonlinearity under very weak incident electromagnetic powers, the application of the nonlinear lens proposed in this paper would have important potential in improving the sub-wavelength resolution in the near future.
