2D layered materials have sparked great interest from the perspective of basic physics and applied science in the past few years. Extraordinarily, many novel stacked structures that bring versatile properties and applications can be artificially assembled, as exemplified by vertical van der Waals (vdW) heterostructures, twisted multilayer 2D materials, hybrid dimensional structures, etc. Compared with the ordinary synthesis process, the stacking technique is a powerful strategy to achieve high‐quality and freely controlled 2D material stacked structures with atomic accuracy. This review highlights the most advanced stacking techniques involving the preparation, transfer, and stacking of high‐quality single crystal 2D materials. Apart from the 2D–2D stacked structures, 2D–0D, 2D–1D, and 2D–3D structures offer a prospective platform for the increasing application of 2D materials. The assembly strategy and physical properties of these stacked structures strongly depend on the factors in the stacking process, including the surface quality, angle control, and sample size. In addition, comparative analysis tables on the techniques involved are also available. The summary of these strategies and techniques will hopefully provide a valuable reference for relevant work.

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An efficient numerical method based on the Dirichlet-to-Neumann (DtN) maps of the unit cells is developed for accurate simulations of two-dimensional photonic crystal (PhC) devices in the frequency domain. The DtN map of a unit cell is an operator that maps the wave field on the boundary of the cell to its normal derivative and it can be approximated by a small matrix. Using the DtN maps of the regular and defect unit cells, we can avoid computations in the interiors of the unit cells and calculate the wave field only on the edges. This gives rise to a significant reduction in the total number of unknowns. Reasonably accurate solutions can be obtained using 10 to 15 unknowns for each unit cell. In contrast, standard finite element, finite difference or plane wave expansion methods may require a few hundreds unknowns for each unit cell at the same level of accuracy. We illustrate our method by a number of examples, including waveguide bends, branches, microcavities coupled with waveguides, waveguides with stubs, etc.

Guided modes of a periodic waveguide usually exist below the light line, if the minimum period of the waveguide is used in the definition, but for some periodic waveguides, there are standing waves with the same period as the waveguide. These non-propagating waves localized around the waveguide core are special guided modes above the light line with a zero wavenumber, and they are related to transmission anomalies and other resonant phenomena. In this paper, we analyze the standing waves on two periodic waveguides: a periodic array of circular dielectric cylinders, and a dielectric slab with a periodic array of circular air-holes. Based on an efficient semi-analytic method, the frequencies of standing waves are calculated as functions of the dielectric constant and the radius of cylinders. Our work provides a basis for further studies on these waves and for realizing their potential applications.

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