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Keywords: P -symmetric compact convex hypersurfaces; P -cyclic closed characteristics; Hamiltonian systems; Maslov P -index iteration; stability.GraphBy Xiaorui Li; Zhenxiong Li and Hui LiuReported by Author; Author; Author [Extracted from the article]

We consider ground states of the nonlinear fractional Schrödinger equation with potentials

With the rapid development of modern technology and information systems, optical anti-counterfeiting and encryption have recently attracted considerable attention. The demand for optical materials is also constantly increasing, with new requirements proposed for performance and application fields. Currently, rare earth ion doped materials possess a unique electronic layer structure, underfilled 4f5d electronic configuration, rich electronic energy level, and long-life excited state, which can produce a variety of radiation absorption and emission. The distinctive properties of rare earth are beneficial for using in diverse optical output anti-counterfeiting. Design is essential for rare earth ion doped materials with multiple responsiveness and multi-channel optical information anti-counterfeiting in the field of information security. Therefore, this mini review summarizes the luminescent mechanisms, preparation methods, performance characteristics and anti-counterfeiting application of rare earth doped materials. In addition, we discuss some critical challenges in this field, and potential solutions that have been or are being developed to overcome these challenges. [ABSTRACT FROM AUTHOR]

After decades of development, LIDAR and visual SLAM technology has relatively matured and been widely used in the military and civil fields. SLAM technology enables the mobile robot to have the abilities of autonomous positioning and mapping, which allows the robot to move in indoor and outdoor scenes where GPS signals are scarce. However, SLAM technology relying only on a single sensor has its limitations. For example, LIDAR SLAM is not suitable for scenes with highly dynamic or sparse features, and visual SLAM has poor robustness in low-texture or dark scenes. However, through the fusion of the two technologies, they have great potential to learn from each other. Therefore, this paper predicts that SLAM technology combining LIDAR and visual sensors, as well as various other sensors, will be the mainstream direction in the future. This paper reviews the development history of SLAM technology, deeply analyzes the hardware information of LIDAR and cameras, and presents some classical open source algorithms and datasets. According to the algorithm adopted by the fusion sensor, the traditional multi-sensor fusion methods based on uncertainty, features, and novel deep learning are introduced in detail. The excellent performance of the multi-sensor fusion method in complex scenes is summarized, and the future development of multi-sensor fusion method is prospected. [ABSTRACT FROM AUTHOR]

Visual SLAM (VSLAM) has been developing rapidly due to its advantages of low-cost sensors, the easy fusion of other sensors, and richer environmental information. Traditional visionbased SLAM research has made many achievements, but it may fail to achieve wished results in challenging environments. Deep learning has promoted the development of computer vision, and the combination of deep learning and SLAM has attracted more and more attention. Semantic information, as high-level environmental information, can enable robots to better understand the surrounding environment. This paper introduces the development of VSLAM technology from two aspects: traditional VSLAM and semantic VSLAM combined with deep learning. For traditional VSLAM, we summarize the advantages and disadvantages of indirect and direct methods in detail and give some classical VSLAM open-source algorithms. In addition, we focus on the development of semantic VSLAM based on deep learning. Starting with typical neural networks CNN and RNN, we summarize the improvement of neural networks for the VSLAM system in detail. Later, we focus on the help of target detection and semantic segmentation for VSLAM semantic information introduction. We believe that the development of the future intelligent era cannot be without the help of semantic technology. Introducing deep learning into the VSLAM system to provide semantic information can help robots better perceive the surrounding environment and provide people with higher-level help. [ABSTRACT FROM AUTHOR]

The unidirectional reflectionless (UR) light propagation is investigated in the waveguide coupled to gain and loss resonators by using a developed coupled mode-scattering matrix theory. The results show that there is almost no reflection in the case of the backward incidence, but total reflection in the case of the forward incidence under the condition of balancing gain and loss in the gain resonator for the proposed waveguide when the indirect coupling phase θ ranges from 0.8 rad to 2.3 rad and from 4 rad to 5.5 rad. Moreover, the coherent perfect absorption (CPA) can be observed at the same time. Especially, the UR light propagation appears when the absolute value of detuning δ is smaller than 1 × 1013 rad s−1. Based on the findings above, we propose a metal–insulator–metal non-parity-time symmetric plasmonic waveguide and obtain the UR plasmonic propagation and CPA. The theoretical results are in excellent agreement with the finite-difference time-domain simulations. These results will provide a new pathway for the realization of unidirectional propagation and absorption of light at the nanoscale. [ABSTRACT FROM AUTHOR]

We develop a novel nonlinear radiation oscillator theory, which can describe nonlinear optical responses in symmetric and anti-symmetric damping graphene coupled metamaterials. An ultra-high quality factor of induced transparency can be realized in the proposed model. The results show that the spectral response and quality factor can be effectively tuned by the resonant detuning, the phase difference, the damping factor as well as the field intensity of the pump light. Moreover, the quality factor of induced transparency is increased by more than 60 times when the field intensity of the pump light and the damping factor are changed. Especially, the single induced transparency window splits into double induced transparency windows as the damping factors of dark mode and bright mode show anti-symmetric damping case. These results may pave the way for designing the high performance of nano-optical devices in terahertz. [ABSTRACT FROM AUTHOR]

This paper examines the fractional cointegration between downside (upside) components of realized and implied variances. A positive association is found between the strength of their cofractional relation and the return predictability of their differences. That association is established via the common long‐memory component of the variances that are fractionally cointegrated, which represents the volatility‐of‐volatility factor that determines the variance premium. Our results indicate that market fears play a critical role not only in driving the long‐run equilibrium relationship between implied‐realized variances but also in understanding the return predictability. A simulation study further verifies these claims. [ABSTRACT FROM AUTHOR]

We investigate Fano resonances and sensing enhancements in a simple Au/TiO2 hybrid metasurface through the finite-different time-domain (FDTD) simulation and coupled mode theory (CMT) analysis. The results show that the Fano resonance in the proposed simple metasurface is caused by the destructive interaction between the surface plasmon polaritons (SPPs) and the local surface plasmon resonances (LSPRs), the quality factor and dephasing time for the Fano resonance can be effectively tuned by the thickness of Au and TiO2 structures, the length of each unit in x and y directions, as well as the structural defect. In particular, single Fano resonance splits into multiple Fano resonances caused by a stub-shaped defect, and multiple Fano resonances can be tuned by the size and position of the stub-shaped defect. Moreover, we also find that the sensitivity in the Au/TiO2 hybrid metasurface with the stub-shaped defect can reach up to 330 nm/RIU and 535 nm/RIU at the Fano resonance 1 and Fano resonance 2, which is more than three times as sensitive in the Au/TiO2 hybrid metasurface without the stub-shaped defect, and also higher than that in the TiO2 metasurface reported before. These results may provide further understanding of Fano resonances and guidance for designing ultra-high sensitive refractive index sensors. [ABSTRACT FROM AUTHOR]

Silicon (Si), germanium (Ge), and gallium arsenide (GaAs) are familiar semiconductors that always act in the role of optical dielectrics. However, these semiconductors also have plasmonic behaviors in ultraviolet (UV) ranges due to the strong interband transitions or valence electrons. And few studies are aimed at investigating plasmonic properties in the semiconductor at the nanoscale. In this work, we discuss UV plasmonics and sensing properties in single and dimer Si, Ge, and GaAs triangular prism meta-antenna systems. The results show that obvious local surface plasmon resonances (LSPRs) can be realized in the proposed triangular prism meta-antennas, and the resonant wavelength, electromagnetic field distribution, surface charge distribution, and surface current density can be effectively tuned by structural and material parameters. In addition, we also find that the Si triangular prism meta-antenna shows more intense plasmonic responses in UV ranges than that in the Ge or GaAs triangular prism nanostructures. Especially, the phase difference between the triangular prism nanostructure and light source can effectively regulate the symbol and value of the surface charge. Moreover, the great enhancement of electric field can be seen in the dimer triangular prism meta-antennas when the distance of the gap is g<5 nm, especially g=1 nm. The most interesting result is that the maximum of refractive index sensitivity s and figure of merit (FoM) are greatly enlarged in dimer triangular prism meta-antennas. Particularly, the sensitivity can reach up to 215 nm/RIU in the dimer GaAs triangular prism meta-antennas, which is improved more than one order of magnitude. These research results may play important roles in applications of the photo detecting, plasmonic sensing and disinfecting in UV ranges.

We investigate Fano resonances and sensing enhancements in a simple Au/TiO 2 hybrid metasurface through the finite-different time-domain (FDTD) simulation and coupled mode theory (CMT) analysis. The results show that the Fano resonance in the proposed simple metasurface is caused by the destructive interaction between the surface plasmon polaritons (SPPs) and the local surface plasmon resonances (LSPRs), the quality factor and dephasing time for the Fano resonance can be effectively tuned by the thickness of Au and TiO 2 structures, the length of each unit in x and y directions, as well as the structural defect. In particular, single Fano resonance splits into multiple Fano resonances caused by a stub-shaped defect, and multiple Fano resonances can be tuned by the size and position of the stub-shaped defect. Moreover, we also find that the sensitivity in the Au/TiO 2 hybrid metasurface with the stub-shaped defect can reach up to 330 nm/RIU and 535 nm/RIU at the Fano resonance 1 and Fano resonance 2, which is more than three times as sensitive in the Au/TiO 2 hybrid metasurface without the stub-shaped defect, and also higher than that in the TiO 2 metasurface reported before. These results may provide further understanding of Fano resonances and guidance for designing ultra-high sensitive refractive index sensors., Competing Interests: The authors declare no conflicts of interest.