Tunable Bandgaps in Phononic Crystal Microbeams Based on Microstructure, Piezo and Temperature Effects

A new model of non-classical phononic crystal (PC) microbeam for the elastic wave bandgap generation is provided, incorporating microstructure, piezomagnetism, piezoelectricity and temperature effects. The wave equation of a general magneto–electro–elastic (MEE) phononic crystal microbeam is derived, which recovers piezoelectric- and piezomagnetic-based counterparts as special cases. The piezomagnetic and piezoelectric materials are periodically combined to construct the PC microbeam and corresponding bandgaps are obtained by using the plane wave expansion (PWE) method. The effects of the piezomagnetism, piezoelectricity, microstructure, geometrical parameters and applied multi-fields (e.g., external electric potential, external magnetic potential, temperature change) on the bandgaps are discussed. The numerical results reveal that the bandgap frequency is raised with the presence of piezo and microstructure effects. In addition, the geometry parameters play an important role on the bandgap. Furthermore, large bandgaps can be realized by adjusting the external electric and magnetic potentials at micron scale, and lower bandgap frequency can be realized through the temperature rise at all length scales.

Realization of 3D reflectors by using metal-air and semiconductor-air based photonic structures at three communication windows

This study is based on analysis of 3D photonic crystal structure (PCS) for realization of photonic reflector pertaining to suitable optical communication wavelengths of 850, 1310 and 1550 nm. The said photonic reflector application is envisaged separately by two 3D PCSs, which comprise semiconductor (germanium) and metal (iron) based circular rods respectively, arranged on a square lattice having air as the background material. The plane wave expansion (PWE) technique is employed to investigate the photonic band gap (PBG) vis-à-vis all the aforementioned wavelengths. PBG is meticulously controlled by suitably selected various structure parameters, such as lattice spacing, diameter of the circular rods and nature of their material. Simulation outcomes explored that semiconductor based PCS reflects wavelengths of 850, 1310 and 1550 nm, when selecting the diameter of the circular rods as 282, 608 and 771 nm, respectively, whereas metal based PCS reflects the aforementioned wavelengths for diameters of the circular rods close to 335, 1070 and 871 nm, respectively. Further, we assayed the variation in reflected wavelength with respect to different diameters of circular rods for both proposed structures. Thus, the proposed optical reflectors can find a wide range of applications vis-à-vis three communication windows.

Broadband Vibration Attenuation Achieved by 2D Elasto-Acoustic Metamaterial Plates with Rainbow Stepped Resonators

This paper investigates the influences of nonperiodic rainbow resonators on the vibration attenuation of two-dimensional metamaterial plates. Rainbow metamaterial plates composed of thin host plates and nonperiodic stepped resonators are considered and compared with periodic metamaterial plates. The metamaterial plates are modelled with the finite element modelling method and verified by the plane wave expansion method. It was found that the rainbow metamaterial plates with spatially varying resonators possess broader vibration attenuation bands than the periodic metamaterial plate with the same host plates and total mass. The extension of attenuation bands was found not to be attributed to the extended bandgaps for the two-dimensional metamaterial plates, as is generally believed for a one-dimensional metamaterial beam. The complete local resonance bandgap of the metamaterial plates is separated to discrete bandgaps by the modes of nonperiodic resonators. Although the additional modes stop the formation of integrated bandgaps, the vibration of the plate is much smaller than that of resonators at these modal frequencies, the rainbow metamaterial plates could have a distinct vibration attenuation at these modal frequencies and achieve broader integrated attenuation bands as a result. The present paper could offer a new idea for the development of plate structures with broadband vibration attenuation by introducing non-periodicity.

Binary-Like Topology Optimization of Piezoelectric Metamaterial Plate with Interface Circuits Using Extended Plane Wave Expansion Method

Piezoelectric metamaterial plate (PMP) is being investigated for structural vibration energy harvesting (SVEH), in which an interface circuit is often used. Thus, it is a challenge to perform bandgap optimization of such an elastic–electro–mechanical coupling system. This paper presents a binary-like topology optimization scheme by dividing the unit cell into identical pieces, where a {0, 1} matrix is optimized to indicate material distribution. Firstly, a unified motion equation is derived for the elastic plate and the piezoelectric patch, and an electromechanical coupling model is built for a self-powered synchronized charge extraction circuit. Then, an extended plane wave expansion method is presented to model the bandgap character of the PMP with interface circuits (PMPICs), and the numerical solution of the dispersion curves is derived based on the Bloch theorem. Next, an extended genetic algorithm is applied for the topology optimization of the PMPIC. In the end, numerical and finite element simulations are performed to validate the proposed method. The results demonstrate that both the structure and the circuit can be optimized simultaneously to obtain the maximum first-order bandgap at a given central frequency. Therefore, the proposed method should provide an effective solution for the topology optimization of a PMPIC for broadband SVEH.

Studies of a New-style Resonator on Electro-mechanical Coupling Bandgap Control of a Locally Resonant Piezoelectric/elastic Phononic Crystal Double-layer Nonlocal Nanobeam

The paper proposed a model of a locally resonant (LR) piezoelectric/elastic phononic crystal (PC) nanobeam with periodically attached “spring-mass” resonator and additional spring between upper and lower nanobeams, as well as horizontal spring between mass and foundation. Euler beam theory and nonlocal piezoelectricity theory are coupled and introduced to plane wave expansion (PWE) method to calculate the band structures of such a model with different parameters. Numerical results and further analysis demonstrate that all the bands of double-layer nanobeam can be divided into symmetric and antisymmetric ones. Adding additional and horizontal springs play a role in control the symmetric and antisymmetric bands respectively, which make wider band gaps be opened than corresponding single-layer nanobeam. Moreover, the change of parameters of electro-mechanical coupling fields and resonator can be applied to effectively control the starting frequencies and widths of band gaps, which can provide a theoretical basis for active control of vibration. Effects of geometric and non-dimensional nonlocal parameters on band gaps are also discussed. All the studies are expected to be applied to actively control vibration propagation in the field of nano electro-mechanical system (NEMS).

Compact and ultrafast all optical 1-bit comparator based on wave interference and threshold switching methods

In this study, we are going to design all optical 1-bit comparator by combining wave interference and threshold switching methods. The final structure composed of two nonlinear ring resonators and seven waveguides. The functionality of the suggested logical structure is analyzed and simulated by using plane wave expansion (PWE) and finite difference time domain (FDTD) methods. According to results, the proposed all optical 1-bit comparator has faster response and smaller footprint than all previous works. The maximum ON-OFF contrast ratio, delay time and area of the suggested optical comparator are about 16.67 dB, 1.8 ps, and 513 µm2, respectively.

Stochastic Modeling of 2D Photonic Crystals

Due to the fabrication processes, inaccurate manufacturing of the photonic crystals (PCs) might occur which affect their performance. In this paper, we examine the effects of tolerance variations of the radii of the rods and the permittivity of the material of the two-dimensional PCs on their performance. The presented stochastic analysis relies on plane wave expansion method and Mote Carlo simulations. We focus on two structures, namely Si-Rods PCs and Air-Holes PCs. Numerical results show – for both structures – that uncertainties in the dimensions of the PCs have higher impact on its photonic gap than do the uncertainties in the permittivity of the Si material. In addition, Air-Holes PCs could be a good candidate with least alteration in the photonic gap considering deviations that might occur in the permittivity of Si due to impurities up to 5%.