Xiao-Xing Su

Large bandgaps of two-dimensional phononic crystals with cross-like holes

In this paper we study the bandgap properties of two-dimensional phononic crystals with cross-like holes using the finite element method. The influence of the geometry parameters of the holes on the bandgaps is discussed. In contrast to a system of square holes, which does not exhibits bandgaps if the symmetry of the holes is the same as that of the lattice, systems of cross-like holes show large bandgaps at lower frequencies. The bandgaps are significantly dependent upon the geometry (including the size, shape, and rotation) of the cross-like holes. The vibration modes of the bandgap edges are computed and analyzed in order to clarify the mechanism of the generation of the lowest bandgap. It is found that the generation of the lowest bangdap is a result of the local resonance of the periodically arranged lumps connected with narrow connectors. Spring-mass models are developed in order to predict the frequencies of the lower bandgap edges. The study in this paper is relevant to the optimal design of the b...

Multi-objective optimization of two-dimensional porous phononic crystals

In this paper, we show that it is possible to design two-dimensional (2D) porous phononic crystals (PnCs) with a simultaneously maximal bandgap width (BGW) and the minimal mass through multi-objective optimization (MOOP) by using the non-dominated sorting-based genetic algorithm II. Compared with the single-objective optimization, the optimized structures from the MOOP can achieve a balance between the relative BGW and mass of PnCs. For the combined out-of-plane and in-plane wave modes, we present an optimized design with the relatively big BGW, which breaks the record value of 2D porous PnCs.

Three-dimensional dielectric phoxonic crystals with network topology

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.

Effects of Poisson’s ratio on the band gaps and defect states in two-dimensional vacuum/solid porous phononic crystals

The effects of the Poissons ratio of the solid host on the band gaps and point defect states of the mixed elastic wave modes in two-dimensional vacuum/solid porous PNCs are studied by numerical simulations. Four typical systems are considered. The four systems are, respectively, (I) the system with a square lattice and circular pores, (II) the system with a hexagonal lattice and circular pores, (III) the system with a square lattice and square pores and (IV) the system with a hexagonal lattice and regular-hexagonal pores. In the latter two systems, with respect to the outer boundaries of the Wigner-Seitz unit cell, the pores rotate 45° and 30°, respectively. Some observable effects of the Poissons ratio are found in the numerical results. Especially, the variations of the band gap boundaries with the Poissons ratio exhibit relatively consistent behaviors. With the increase of the Poissons ratio, the normalized frequency of a band gap boundary generally increases, except that in system (III) the normalized frequency of the upper boundary of the first band gap remains almost unchanged. Detailed interpretations on this phenomenon are given.

Topology optimization of simultaneous photonic and phononic bandgaps and highly effective phoxonic cavity

By using the nondominated sorting-based genetic algorithm II, we study the topology optimization of 2D phoxonic crystals (PxC) with simultaneously maximal and complete photonic and phononic bandgaps. Our results show that the optimized structures are composed of 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 PxC 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 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 similar properties to the optimized structure, i.e., simultaneous wide phononic and photonic bandgaps and a highly effective phononic/photonic cavity.

Acousto-optical interaction of surface acoustic and optical waves in a two-dimensional phoxonic crystal hetero-structure cavity.

Phoxonic crystal is a promising material for manipulating sound and light simultaneously. In this paper, we theoretically demonstrate the propagation of acoustic and optical waves along the truncated surface of a two-dimensional square-latticed phoxonic crystal. Further, a phoxonic crystal hetero-structure cavity is proposed, which can simultaneously confine surface acoustic and optical waves. The interface motion and photoelastic effects are taken into account in the acousto-optical coupling. The results show obvious shifts in eigenfrequencies of the photonic cavity modes induced by different phononic cavity modes. The symmetry of the phononic cavity modes plays a more important role in the single-phonon exchange process than in the case of the multi-phonon exchange. Under the same deformation, the frequency shift of the photonic transverse electric mode is larger than that of the transverse magnetic mode.

Effects of material parameters on elastic band gaps of three-dimensional solid phononic crystals

In this paper, we study the influences of material parameters on the phononic band gaps of three-dimensional (3D) solid phononic crystals (PCs) based on the finite difference time domain (FDTD) method. We begin with the basic wave equations and the FDTD formulation to derive the material parameters directly determining the band gaps of the 3D solid PCs. The parameters include the transverse velocity ratio, the acoustic impedance ratio and the Poisson ratios (or equivalently, the mass density ratio, the shear modulus ratio and the Poisson ratios) of the scatterers and host materials. The negative Poisson ratio is also considered in our investigation. The effects of these material parameters on band gap width are discussed based on detailed numerical calculations for systems with three typical lattices. The generation mechanism of band gaps (Bragg scattering or local resonance) which is determined by the material parameters is also discussed. The analysis is expected to be applied to the artificial design of 3D phononic band gap materials.

Simultaneous guiding of slow elastic and light waves in three-dimensional topology-type phoxonic crystals with a line defect

Phoxonic crystals (PXCs) which exhibit simultaneous phononic and photonic bandgaps are promising artificial materials for optomechanical and acousto-optical devices. In this paper, we theoretically investigate the phononic and photonic guided modes in the three-dimensional topology-type PXCs with a line defect. By varying the geometrical parameters, simultaneous guidance of the slow elastic and light (electromagnetic) waves can be realized. Both elastic and optical energies can be highly confined in and near the defect region. Small elastic and optical group velocities with small group velocity dispersions can be achieved. The group velocities are about 10 and 20 times smaller than the transverse velocity of the elastic waves in silicon and the speed of light in vacuum, respectively.

Finite difference time domain calculation of three-dimensional phononic band structures using a postprocessing method based on the filter diagonalization

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.

A matrix-exponential decomposition based time-domain method for calculating the defect states of scalar waves in two-dimensional periodic structures

A time-domain method for calculating the defect states of scalar waves in two-dimensional (2D) periodic structures is proposed. In the time-stepping process of the proposed method, the column vector containing the spatially sampled field values is updated by multiplying it with an iteration matrix, which is written in a matrix-exponential form. The matrix-exponential is first computed by using the Suzukis decomposition based technique of the fourth order, in which the FloquetBloch boundary conditions are incorporated. The obtained iteration matrix is then squared to enlarge the time-step that can be used in the time-stepping process (namely, the squaring technique), and the small nonzero elements in the iteration matrix is finally pruned to improve the sparse structure of the matrix (namely, the pruning technique). The numerical examples of the super-cell calculations for 2D defect-containing phononic crystal structures show that, the fourth order decomposition based technique for the matrix-exponential computation is much more efficient than the frequently used precise integration technique (PIT) if the PIT is of an order greater than 2. Although it is not unconditionally stable, the proposed time-domain method is particularly efficient for the super-cell calculations of the defect states in a 2D periodic structure containing a defect with a wave speed much higher than those of the background materials. For this kind of defect-containing structures, the time-stepping process can run stably for a sufficiently large number of the time-steps with a time-step much larger than the CourantFriedrichsLewy (CFL) upper limit, and consequently the overall efficiency of the proposed time-domain method can be significantly higher than that of the conventional finite-difference time-domain (FDTD) method. Some physical interpretations on the properties of the band structures and the defect states of the calculated periodic structures are also presented.