Two-dimensional (2D) nanomaterials (sheet-like materials with few-atoms thickness and lateral size above 100 nm) have always aroused scientists' interests since 2004 when Novoselov et al successfully exfoliated graphene from graphite using Scotch tape. It is some unique characters of 2D nanomaterials such as the confinement of electrons in two dimensions in the ultrathin region, strong in-plane covalent bond and atomic thickness, ultra-high specific surface area and exposed atoms that enable 2D nanomaterials to show excellent properties in electrics, catalysis and mechanics. Recently, amorphous materials (varied from crystal materials by atomic arrangement) have demonstrated high performance in mechanics, catalysis and magnetic owing to their unique long-range atomic disorder arrangements. Thus, the 2D amorphous nanomaterials inspire a new path to the study of high performance 2D materials. Herein, we summarize the recent progress in 2D amorphous nanomaterials, whose synthetic methods and potential applications in fields of catalysis, energy storage and mechanics discussed in details. The vital blocking mechanisms for synthesis of 2D amorphous nanomaterials and their performance-structure relationship are focused on. Finally, we conclude the review with our personal insights and provide a critical outlook for the development of 2D amorphous nanomaterials.

One kind of optical element combining Fresnel lens with microlens array is designed simply for LED lighting based on geometrical optics and nonimaging optics. This design method imposes no restriction on the source intensity pattern. The designed element has compact construction and can produce multiple shapes of illumination distribution. Taking square lighting as an example, tolerance analysis is carried out to determine tolerance limits for applying the element in the assembly process. This element can produce on-axis lighting and off-axis lighting.

A collimating lens for a light-emitting-diode (LED) light source is an essential device widely used in lighting engineering. Lens surfaces are calculated by geometrical optics and nonimaging optics. This design progress does not rely on any software optimization and any complex iterative process. This method can be used for any type of light source not only Lambertian. The theoretical model is based on point source. But the practical LED source has a certain size. So in the simulation, an LED chip whose size is 1 mm*1 mm is used to verify the feasibility of the model. The mean results show that the lenses have a very compact structure and good collimating performance. Efficiency is defined as the ratio of the flux in the illuminated plane to the flux from LED source without considering the lens material transmission. Just investigating the loss in the designed lens surfaces, the two types of lenses have high efficiencies of more than 90% and 99%, respectively. Most lighting area (possessing 80% flux) radii are no more than 5 m when the illuminated plane is 200 m away from the light source.

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A secondary optical lens was designed and investigated in three-dimensional (3D) space, which was far more accurate than a two-dimensional space in far-field lighting. The shape of the lens surface was from numerical solutions to a group of equations based on source-target mapping; calculating time was only 1.6 s. Neglecting absorption and scattering loss, the main results show that, for circular lighting, light efficiency can reach as high as 95%, and uniformity, which is the ratio of the minimum illuminance to average illuminance, is 92.2%. For rectangular lighting, light efficiency can reach 83.6% and uniformity can reach 66.7%. Performance of lenses under different parameters was studied to provide direct references for production and application.

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