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1.
We carry out a careful study of operator algebras associated with Delone dynamical systems. A von Neumann algebra is defined using noncommutative integration theory. Features of these algebras and the operators they contain are discussed. We restrict our attention to a certain C
*-subalgebra to discuss a Shubin trace formula. 相似文献
2.
Thomas Höche Wolfgang NeumannSaeid Esmaeilzadeh Reinhard UeckerMarkus Lentzen Christian Rüssel 《Journal of solid state chemistry》2002,166(1):15-23
Sr2TiSi2O8 single crystals were grown by Czochralski pulling and from a high-temperature solution. X-ray diffractometry revealed the modulated crystal structure of Sr2TiSi2O8 to belong to the 5D superspace group P4bm (−α, α, 1/2; α, α, 1/2) with α=0.3. Atomic positions, anisotropic displacement factors and positional modulation parameters for Sr2TiSi2O8 are determined and discussed. The positional modulation is further investigated by electron diffraction and high-resolution transmission electron microscopy. In the latter experiments, the 2D modulation appears to be superimposed by some 1D modulation waves. This effect is discussed in terms of growth conditions. 相似文献
3.
Dongliang Tang Changtao Wang Zeyu Zhao Yanqin Wang Mingbo Pu Xiong Li Ping Gao Xiangang Luo 《Laser \u0026amp; Photonics Reviews》2015,9(6):713-719
Conventional optics is diffraction limited due to the cutoff of spatial frequency components, and evanescent waves allow subdiffraction optics at the cost of complex near‐field manipulation. Recently, optical superoscillatory phenomena were employed to realize superresolution lenses in the far field, but suffering from very narrow working wavelength band due to the fragility of the superoscillatory light field. Here, an ultrabroadband superoscillatory lens (UBSOL) is proposed and realized by utilizing the metasurface‐assisted law of refraction and reflection in arrayed nanorectangular apertures with variant orientations. The ultrabroadband feature mainly arises from the nearly dispersionless phase profile of transmitted light through the UBSOL for opposite circulation polarization with respect to the incident light. It is demonstrated in experiments that subdiffraction light focusing behavior holds well with nearly unchanged focal patterns for wavelengths spanning across visible and near‐infrared light. This method is believed to find promising applications in superresolution microscopes or telescopes, high‐density optical data storage, etc.
4.
针对相位梯度超表面在灵活操控电磁波与提高天线增益中的潜在应用,提出一种新型的宽带超表面单元,实现了在较宽频带范围内操控电磁波波前与提高天线增益.本文首先设计了一种圆环十字形对称单元来控制反射波的相移量,单元厚度为1 mm,尺寸为0.3λ_0(λ_0=20 mm),工作频段15—18 GHz,而后验证了由该单元组成的相位梯度超表面在15—18 GHz范围内对电磁波的奇异反射与聚焦特性.最后将设计的反射聚焦超表面应用于提高天线增益中,仿真与测试结果均表明,天线最高增益在15—18 GHz内平均增加了11 d B且-1 dB增益带宽为15—18 GHz(相对带宽为18.2%).由于厚度薄、重量轻、频带宽,设计的该单元拓展了相位梯度超表面在微波领域的应用,有望为高增益天线的实现提供新的方法. 相似文献
5.
A 3‐phase Barker array is a matrix of third roots of unity for which all out‐of‐phase aperiodic autocorrelations have magnitude 0 or 1. The only known truly two‐dimensional 3‐phase Barker arrays have size 2 × 2 or 3 × 3. We use a mixture of combinatorial arguments and algebraic number theory to establish severe restrictions on the size of a 3‐phase Barker array when at least one of its dimensions is divisible by 3. In particular, there exists a double‐exponentially growing arithmetic function T such that no 3‐phase Barker array of size with exists for all . For example, , , and . When both dimensions are divisible by 3, the existence problem is settled completely: if a 3‐phase Barker array of size exists, then . 相似文献
6.
We derive a homeomorphism invariant for those tiling spaces which are made by rather general substitution rules on polygonal tiles, including those tilings, like the pinwheel, which contain tiles in infinitely many orientations. The invariant is a quotient of ech cohomology, is easily computed directly from the substitution rule, and distinguishes many examples, including most pinwheel-like tiling spaces. We also introduce a module structure on cohomology which is very convenient as well as of intuitive value. 相似文献
7.
We consider tiling models of round quasicrystals which would have diffraction patterns which are fully rotation invariant—rings instead of Bragg peaks. They can be distinguished from glasses by self-similarity of the pattern of radii of the rings. 相似文献
8.
Seyedeh Mahsa Kamali Ehsan Arbabi Amir Arbabi Yu Horie Andrei Faraon 《Laser \u0026amp; Photonics Reviews》2016,10(6):1002-1008
Dielectric metasurfaces are two‐dimensional structures composed of nano‐scatterers that manipulate the phase and polarization of optical waves with subwavelength spatial resolution, thus enabling ultra‐thin components for free‐space optics. While high performance devices with various functionalities, including some that are difficult to achieve using conventional optical setups have been shown, most demonstrated components have fixed parameters. Here, we demonstrate highly tunable dielectric metasurface devices based on subwavelength thick silicon nano‐posts encapsulated in a thin transparent elastic polymer. As proof of concept, we demonstrate a metasurface microlens operating at 915 nm, with focal distance tuning from 600 μm to 1400 μm (over 952 diopters change in optical power) through radial strain, while maintaining a diffraction limited focus and a focusing efficiency above 50%. The demonstrated tunable metasurface concept is highly versatile for developing ultra‐slim, multi‐functional and tunable optical devices with widespread applications ranging from consumer electronics to medical devices and optical communications.
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