Tian-Xue Ma

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.

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.

Investigation of complete bandgaps in a piezoelectric slab covered with periodically structured coatings.

The propagation of elastic waves in a piezoelectric slab covered with periodically structured coatings or the so-called stubbed phononic crystal slab is investigated. Four different models are selected and the effects of distribution forms and geometrical parameters of the structured coatings on complete bandgaps are discussed. The phononic crystal slab with symmetric coatings can generate wider complete bandgaps while that with asymmetric coatings is favorable for the generation of multi-bandgaps. The complete bandgaps, which are induced by locally resonant effects, change significantly as the geometry of the coatings changes. Moreover, the piezoelectric effects benefit the opening of the complete bandgaps.

An improvement of the filter diagonalization-based post-processing method applied to finite difference time domain calculations of three-dimensional phononic band structures

When three-dimensional (3D) phononic band structures are calculated by using the finite difference time domain (FDTD) method with a relatively small number of iterations, the results can be effectively improved by post-processing the FDTD time series (FDTD-TS) based on the filter diagonalization method (FDM), instead of the classical fast Fourier transform. In this paper, we propose a way to further improve the performance of the FDM-based post-processing method by introducing a relatively large number of observing points to record the FDTD-TS. To this end, the existing scheme of FDTD-TS preprocessing is modified. With the new preprocessing scheme, the processing efficiency of a single FDTD-TS can be improved significantly, and thus the entire post-processing method can have sufficiently high efficiency even when a relatively large number of observing points are used. The feasibility of the proposed method for improvement is verified by the numerical results.

Topology optimization of two-dimensional phononic crystals using FDTD and genetic algorithm

The band gap optimization of the two-dimensional solid PNCs is studied. The finite difference time domain method and the genetic algorithm are used as the forward calculation method and optimization scheme, respectively. Some preliminary numerical results are presented.

Effects of poisson's ratio on the band gaps of three-dimensional solid/solid phononic crystals

Phononic crystals (PCs) are a kind of acoustic composite materials which have periodic structures and exhibit elastic wave (EW) band gaps. Due to their unique properties the phononic crystals have potential applications in acoustic devices and noise control, etc. The effects of both positive and negative Poissons ratios on the phononic band gaps (PBGs) due to either Bragg scattering or locally resonance in three-dimensional (3D) solid/solid phononic crystals with a simple-cubic (SC) lattice are studied. The band structures are obtained by the finite difference time domain (FDTD) method combined with the fast Fourier transform- (FFT-) based postprocessing method. The numerical results show that Poissons ratio of the scatterer plays an important role in tuning the PBGs.