Outer synchronization between two hybrid‐coupled delayed dynamical networks via aperiodically adaptive intermittent pinning control

This article is concerned with the problem of pinning outer synchronization between two complex delayed dynamical networks via adaptive intermittent control. At first, a general model of hybrid‐coupled dynamical network with time‐varying internal delay and time‐varying coupling delay is given. Then, an aperiodically adaptive intermittent pinning‐control strategy is introduced to drive two such delayed dynamical networks to achieve outer synchronization. Some sufficient conditions to guarantee global outer‐synchronization are derived by constructing a novel piecewise Lyapunov function and utilizing stability analytical method. Moreover, a simple pinned‐node selection scheme determining what kinds of nodes should be pinned first is provided. It is noted that the adaptive pinning control type is aperiodically intermittent, where both control period and control width are non‐fixed. Finally, a numerical example is given to illustrate the validity of the theoretical results. © 2016 Wiley Periodicals, Inc. Complexity 21: 593–605, 2016     

Some remarks on discrete aperiodic Schrödinger operators

We consider Schrödinger operators onl ²( ) with deterministic aperiodic potential and Schrödinger operators on the l²-space of the set of vertices of Penrose tilings and other aperiodic self-similar tilings. The operators onl ²( ) fit into the formalism of ergodic random Schrödinger operators. Hence, their Lyapunov exponent, integrated density of states, and spectrum are almost-surely constant. We show that they are actually constant: the Lyapunov exponent for one-dimensional Schrödinger operators with potential defined by a primitive substitution, the integrated density of states, and the spectrum in arbitrary dimension if the system is strictly ergodic. We give examples of strictly ergodic Schrödinger operators that include several kinds of almost-periodic operators that have been studied in the literature. For Schrödinger operators on Penrose tilings we prove that the integrated density of states exists and is independent of boundary conditions and the particular Penrose tiling under consideration.     

Locally rigorous electromagnetic analysis of non-periodic gratings with large size and small features in the non-scalar validity domain by the field stitching method

Scalar theory is a simple and rapid method to analyse and conceive diffractive optical element and gratings, in some limited cases. When we want to deflect wave fronts with large angles (for telecommunication devices, for instance) or when the features of the grating are around the order of the wavelength, scalar optics fail to be accurate, then adapted rigorous electromagnetic tools must be used. To correct the increasing cost in memory saving and time consuming with the size of the grating, we present here an original `field stitching' method adapted for aperiodic gratings (FSA). This method, initially developed for periodic gratings is extended here to analyse locally and rigorously aperiodic gratings with large sizes and small features without having some of the above-mentioned inconvenients.     

Highly reflective subtractive color filters capitalizing on a silicon metasurface integrated with nanostructured aluminum mirrors

Metasurface‐based color filters have been recently applied for the creation of imaging devices and color printing in a subwavelength scale. In this work, a highly reflective subtractive color filter featuring an excellent color contrast is conceived and demonstrated, by exploiting a crystalline‐silicon nanopillar (NP)‐based dielectric metasurface integrated with an aluminum disk mirror (DM) and holey mirror (HM) at the top and bottom, respectively. A deep suppression in reflection is acquired through a magnetic dipole (MD) resonance that is supported by the constituent NP, and can be effectively tailored via the control of the NP diameter. The cooperation of the nanostructured DM and HM plays a dual role of dramatically boosting the efficiency and reinforcing the confinement of the MD in the NP, which is primarily accountable for the reduction in the spectral bandwidth. For the manufactured filters, both a high reflection efficiency reaching ∼70% and relatively small bandwidth of ∼55 nm are attained, thus leading to a broad palette of vivid and bright colors. The proposed devices are supposed to exhibit a polarization‐insensitive operation and a relaxed angular tolerance, thereby facilitating the implementation of miniaturized display/imaging devices with a high resolution and excellent color fidelity.

     

New frontiers in metamaterials research: Novel electronic materials and inhomogeneous metasurfaces

In reviewing some recent work in metamaterials, we highlight two exciting new frontiers just emerging in this field — metamaterials made by new electronic materials (particularly graphene) and inhomogeneous metasurfaces to control light wave-fronts.     

Role of the Radiation‐Reaction Electric Field in the Optical Response of Two‐Dimensional Crystals

A classical theory of a radiating two‐dimensional crystal is proposed and an expression for the radiation‐reaction electric field is derived. This field plays an essential role in connecting the microscopic electromagnetic fields acting on each dipole of the crystal to the macroscopic one, via the boundary conditions for the system. The expression of the radiative‐reaction electric field coincides with the macroscopic electric field radiating from the crystal and, summed to the incident electric field, generates the total macroscopic electric field.     

Triples of Prototiles (With Prescribed Properties) in Space (A quasiperiodic triple in space)

For every set of cubic dominoes there is a set of three prototiles which exhibits essentially the same tiling properties. In particular, there is an one-to-one correspondence between the tilings admitted by the two sets.     

Optimal Design of Multilayer Mirrors for Water-Window Microscope Optics

A small bandwidth of periodic multilayers at wavelengths 2.4–4.4 nm presents problems for the spectral matching of mirrors. This leads to low throughput of a Schwarzschild microscope and its sensitivity to technological errors in layer thickness. We consider two cures for these difficulties: aperiodic coatings and a lateral gradient of layer thickness. Our design of aperiodic multilayers maximizes the throughput of a microscope made at a fixed level of technology. The method includes a new merit function, fast procedure for its minimization, linkage between multilayers and an equation for a lateral gradient of layer thickness. Computation is performed for Sc/Cr coatings at 398 eV. It shows that the aperiodicity makes optics stable to technological errors, while the lateral gradient increases throughput, but enhances sensitivity to the errors. The best results are obtained for aperiodic mirrors with a lateral gradient of thickness, which assure both high microscope throughput and stability to the errors.     

基于导波驱动相变材料超构表面的基波及二次谐波聚焦

利用超构表面优异的波前调控能力将片上光子集成电路对光场的操控拓展至自由空间是当前一项重要课题.本文采用传输相位方法设计了一种基于波导模式激发的内嵌式超构表面,其相位分布同时满足导模的基频以及二倍频的聚焦.在此基础上,将内嵌式材料限定为相变材料,结合其在不同相态时的折射率差异,通过仿真手段实现了两种相态下分别针对于基波和二次谐波的聚焦.在基波(或二次谐波)实现高质量聚焦时,焦点处二次谐波(或基波)的成分得到了很大程度上的抑制,更有利于后续完全滤波.进一步地,通过在波导层底面嵌入与顶面完全相同的超构表面,并横向错开半个周期,最终将关于基波聚焦和二次谐波聚焦的器件效率提升为原先单阵列情形的2.2倍和3.7倍.本文的研究为导波驱动(或激发)超构表面的线性及非线性多功能复合调控提供了一种新的可能途径.     

THz wave generation by repeated and continuous frequency conversions from pump wave to high-order Stokes waves

We propose a novel scheme for THz wave generation by repeated and continuous frequency conversions from pump wave to high-order Stokes waves (HSWs). The repeated frequency conversions are accomplished by oscillations of Stoke waves in resonant cavity (RC) where low-order Stokes waves (LSWs) are converted to high-order Stokes waves again and again. The continuous frequency conversions are accomplished by optimized cascaded difference frequency generation (OCDFG) where the poling periods of the optical crystal are aperiodic leading to the frequency conversions from low-order Stokes waves to high-order Stokes waves uninterruptedly and unidirectionally. Combined with the repeated and continuous frequency conversions, the optical-to-THz energy conversion efficiency (OTECE) exceeds 26% at 300 K and 43% at 100 K with pump intensities of 300 MW/cm².