Non-Fourier heat conduction models assume wave-like behavior does exist in the heat conduction process. Based on this wave-like behavior, thermal conduction controlled in a one-dimensional periodical structure, named thermal wave crystal, has been demonstrated through both theoretical analysis and numerical simulation based on the Cattaneo-Vernotte (CV) heat-conduction model. The transfer matrix method and Bloch analysis have been applied to calculate the band structure of thermal wave propagating in thermal wave crystals. And the temperature responses are obtained by using the FDTD method, which is also used to verify the correctness of the band structure. The results show that band gaps do exist due to the Bragg scattering. Then, a calculation method to predict the mid-gap frequency of band gaps for the thermal wave crystal has been introduced in this Letter. And key parameters determining the band gaps have been discussed. This study shows the potential applications of this novel mechanism, such as thermal imagining, thermal diodes and thermal waveguides.

We theoretically demonstrate the existence of simultaneous large complete photonic and phononic bandgaps in three-dimensional dielectric phoxonic crystals with a simple cubic lattice. These phoxonic crystals consist of dielectric spheres on the cubic lattice sites connected by thin dielectric cylinders. The simultaneous photonic and phononic bandgaps can exist over a wide range of geometry parameters. The vibration modes corresponding to the phononic bandgap edges are the local torsional resonances of the dielectric spheres and rods. Detailed discussion is presented on the variation of the photonic and phononic bandgaps with the geometry of the structure. Optimal geometry which generates large phoxonic bandgaps is suggested.

By using the non-dominated sorting-based genetic algorithm II, we study the topology optimization of the twodimensional phoxonic crystals (PxCs) with simultaneously maximal and complete photonic and phononic bandgaps. Our results show that the optimized structures are composed of the solid lumps with narrow connections, and their Pareto-optimal solution set can keep a balance between photonic and phononic bandgap widths. Moreover, we investigate the localized states of PxCs based on the optimized structure and obtain structures with more effectively multimodal photon and phonon localization. The presented structures with highly focused energy are good choices for the PxC sensors. For practical application, we design a simple structure with smooth edges based on the optimized structure. It is shown that the designed simple structure has the similar properties with the optimized structure, i.e. simultaneous wide phononic and photonic bandgaps and a highly effective phononic/photonic cavity, see Figures 8(b) and 8(c).

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The topology concept in the condensed physics and acoustics is introduced into the elastic wave metamaterial plate, which can show the topological property of the flexural wave. The elastic wave metamaterial plate consists of the hexagonal array which is connected by the piezoelectric shunting circuits. The Dirac point is found by adjusting the size of the unit cell and numerical simulations are illustrated to show the topological immunity. Then the closing and breaking of the Dirac point can be generated by the negative capacitance circuits. These investigations denote that the topological immunity can be achieved for flexural wave in mechanical metamaterial plate. The experiments with the active control action are finally carried out to support the numerical design.

If the band structure of a three-dimensional (3D) phononic crystal (PNC) is calculated by using the finite difference time domain (FDTD) method combined with the fast Fourier transform (FFT)-based postprocessing method, good results can only be ensured by a sufficiently large number of FDTD iterations. On a common computer platform, the total computation time will be very long. To overcome this difficulty, an excellent harmonic inversion algorithm called the filter diagonalization method (FDM) can be used in the postprocessing to reduce the number of FDTD iterations. However, the low efficiency of the FDM, which occurs when a relatively long time series is given, does not necessarily ensure an effective reduction of the total computation time. In this paper, a postprocessing method based on the FDM is proposed. The main procedure of the method is designed considering the aim to make the time spent on the method itself far less than the corresponding time spent on the FDTD iterations. To this end, the FDTD time series is preprocessed to be shortened significantly before the FDM frequency extraction. The preprocessing procedure is performed with the filter and decimation operations, which are widely used in narrow-band signal processing. Numerical results for a typical 3D solid PNC system show that the proposed postprocessing method can be used to effectively reduce the total computation time of the FDTD calculation of 3D phononic band structures.

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