Tungsten disulfide-gold nanohole hybrid metasurfaces for nonlinear metalens in the visible region

Recently, nonlinear hybrid metasurface comes into an attractive new concept in the research of nanophotonics and nanotechnology. It is composed of semiconductors with an intrinsically large nonlinear susceptibility and traditional plasmonic metasurfaces, offering opportunities for efficiently generating and manipulating nonlinear optical responses. A high second-harmonic generation (SHG) conversion efficiency has been demonstrated in the mid-infrared region by using multi-quantum-well (MQW) based plasmonic metasurfaces. However, it has yet to be demonstrated in the visible region. Here we present a new type of nonlinear hybrid metasurfaces for the visible region, which consists of a single layer of tungsten disulfide (WS2) and a phased gold nanohole array. The results indicate that a large SHG susceptibility of ~0.1 nm/V at 810 nm is achieved, which is 2~3 orders of magnitude larger than that of typical plasmonic metasurfaces. Nonlinear metalenses with the focal lengths of 30 {\mu}m, 50 {\mu}m and 100 {\mu}m are demonstrated experimentally, providing a direct evidence for both generating and manipulating SH signals based on the nonlinear hybrid metasurfaces. It shows great potential applications in designing of integrated, ultra-thin, compacted and efficient nonlinear optical devices, such as frequency converters, nonlinear holography and generation of nonlinear optical vortex beam

Explaining the cosmic ray spectrum feature of Auger beyond the ankle with dip model plus the galactic propagation effect

The Auger Collaboration has recently published the energy spectrum of cosmic rays above 1 EeV, which exhibits interesting features. These spectrum features provide an opportunity to investigate the propagation of ultra-high-energy cosmic rays (UHECRs). In this study, we have developed a model that incorporates the dip model for UHECRs in the extragalactic propagation, while accounting for the suppression due to diffusion and interactions within the galaxy. Our model demonstrates excellent agreement with the energy spectrum measured by Auger and supports a spectral index of 2 for the diffusion coefficient in the galaxy starting from $5\times10^{18}$eV.Comment: 5 pages, 2 figure

Extremal Tri-Cyclic Graphs with respect to the First and Second Zagreb Indices

In this paper, the first and second maximum values of the first and second Zagreb indices of $n-$vertex tri-cyclic graphs are obtained