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Here, the frequency degree of freedom is introduced into valley photonic crystals with dual band gaps. Based on the high-order plane wave expansion model, we derive an effective Hamiltonian which characterizes dual band gaps. Metallic valley photonic crystals are demonstrated as examples in which all four topological phases are found. At the domain walls between topologically distinct valley photonic crystals, frequency-dependent edge states are demonstrated and a broadband photonic detouring is proposed. Our findings provide the guidance for designing the frequency-dependent property of topological structures and show its potential applications in wavelength division multiplexers., Comment: 12 pages, 4 figures

The recent research of topological photonics has not only proposed and realized novel topological phenomena such as one-way broadband propagation and robust transport of light, but also designed and fabricated photonic devices with high-performance indexes which are immune to fabrication errors such as defects or disorders. Photonic crystals, which are periodic optical structures with the advantages of good light field confinement and multiple adjusting degrees of freedom, provide a powerful platform to control the flow of light. With the topology defined in the reciprocal space, photonic crystals have been widely used to reveal different topological phases of light and demonstrate topological photonic functionalities. In this review, we present the physics of topological photonic crystals with different dimensions, models and topological phases. The design methods of topological photonic crystals are introduced. Furthermore, we review the applications of topological photonic crystals in passive and active photonics. These researches pave the way of applying topological photonic crystals in practical photonic devices.

Beads are a widespread technology for reinforcing sheet metal structures, because they can be applied without any additional manufacturing effort and without significant weight increase. The two main applications of bead technology are to increase the stiffness for static loading conditions and to reduce the noise and vibrations for dynamic loadings. However, it is difficult to design the bead patterns of sheet metal structures due to effect of the bead configuration. A wrong bead pattern layout can even weaken the properties of the structure. In the past, the designs were predominantly determined empirically or by the use of so called bead catalogues. In this paper, parametric modeling was used to build the bead model of an rigid metal container cover. The finite element model was used to simulate the performance of rigid metal container cover. The effects of design parameters on the structure performance of beads were discussed. A hierarchical design optimization method was developed based on the Response Surface Method, Sequential Quadratic Programming and parametric bead model. The proposed method can be used to optimize the other sheet metal structural