Calculation of Valence Subband Structures for Strained Quantum-Wells by Plane Wave Expansion Method Within 6×6 Luttinger-Kohn Model

The valence subband energies and wave functions of a tensile strained quantum well are calculated by the plane wave expansion method within the 6×6 Luttinger Kohn model.The effect of the number and period of plane waves used for expansion on the stability of energy eigenvalues is examined.For practical calculation,it should choose the period large sufficiently to ensure the envelope functions vanish at the boundary and the number of plane waves large enough to ensure the energy eigenvalues keep unchanged within a prescribed range.

Investigation of a silicon-based one-dimensional phononic crystal plate via the super-cell plane wave expansion method

The super-cell plane wave expansion method is employed to calculate band structures for the design of a siliconbased one-dimensional phononic crystal plate with large absolute forbidden bands. In this method, a low impedance medium is introduced to replace the free stress boundary, which largely reduces the computational complexity. The dependence of band gaps on structural parameters is investigated in detail. To prove the validity of the super-cell plane wave expansion, the transmitted power spectra of the Lamb wave are calculated by using a finite element method. With the detailed computation, the band-gap of a one-dimensional plate can be designed as required with appropriate structural parameters, which provides a guide to the fabrication of a Lamb wave phononic crystal.

Band structures analysis of one-dimensional photonic crystals using plane wave expansion

A theoretical analysis is made, using plane wave expansion, on how the width of the first three band gaps is influenced by filling ratio, dielectric constant ratio, and periodic width in one-dimensional photonic crystals （PhCs）. From simulation and analysis, there are one, two, and three peak points on the first, second and third band gaps respectively with the changes of filling ratio un- der fixed dielectric constant ratio. When filling ratio is fixed, the bandwidth of the first band gap consistently increases with dielectric constant ratio. However, no similar trend is observed in the second and the third band gaps. Because of scaling properties, varying periodic width does not alter the relative bandwidth.

Electro-mechanical coupling wave propagating in a locally resonant piezoelectric/elastic phononic crystal nanobeam with surface effects

The model of a "spring-mass" resonator periodically attached to a piezoelectric/elastic phononic crystal(PC) nanobeam with surface effects is proposed, and the corresponding calculation method of the band structures is formulized and displayed by introducing the Euler beam theory and the surface piezoelectricity theory to the plane wave expansion(PWE) method. In order to reveal the unique wave propagation characteristics of such a model, the band structures of locally resonant(LR) elastic PC Euler nanobeams with and without resonators, the band structures of LR piezoelectric PC Euler nanobeams with and without resonators, as well as the band structures of LR elastic/piezoelectric PC Euler nanobeams with resonators attached on PZT-4, with resonators attached on epoxy, and without resonators are compared. The results demonstrate that adding resonators indeed plays an active role in opening and widening band gaps. Moreover, the influence rules of different parameters on the band gaps of LR elastic/piezoelectric PC Euler nanobeams with resonators attached on epoxy are discussed, which will play an active role in the further realization of active control of wave propagations.

Effects of orientation and shape of holes on the band gaps in water waves over periodically drilled bottoms

The complete band gaps （CBGs） of shallow water waves propagating over bottoms with periodically drilled holes are investigated numerically by the plane wave expansion method. Four different patterns are considered, containing triangular, square, hexagonal and circular cross-sectioned holes arranged into triangular lattices. Results show that the width of CBGs can be changed by adjusting the orientation of noncircular holes and the effect of hole shape on the width of the maximal CBGs is discussed.

Band Structure of Three-dimensional Phononic Crystals

By using the plane-wave-expansion method, the band structure of three-dimension phononic crystals was calculated, in which the cuboid scatterers were arranged in a host with a face-centered-cubic （FCC） structure.The influences of a few factors such as the component materials, the filling fraction of scatterers and the ratio （RHL） of the scatterer＇s height to its length on the band-gaps of phononic crystals were investigated.It is found that in the three-dimension solid phononic crystals with FCC structure, the optimum case to obtain band-gaps is to embed high-velocity and high-density scatterers in a low-velocity and low-density host. The maximum value of band-gap can be obtained when the filling fraction is in the middle value. It is also found that the symmetry of the scatterers strongly influences the band-gaps. For RHL＞1, the width of the band-gap decreases as RHL increases. On the contrary, the width of the band-gap increases with the increase of RHL when RHL is smaller than 1.

INFLUENCES OF ANISOTROPY ON BAND GAPS OF 2D PHONONIC CRYSTAL

Band gaps of 2D phononic crystal with orthotropic cylindrical fillers embedded in the isotropic host are studied in this paper. Two kinds of periodic structures, namely, the square lattice and the triangle lattice, are considered. For anisotropic phononic crystal, band gaps not only depend on the periodic lattice but also the angle between the symmetry axis of orthotropic material and that of the periodic structure. Rotating these cylindrical fillers makes the angle changing continuously; as a result, pass bands and forbidden bands of the phononic crystal are changed. The plane wave expansion method is used to reduce the band gap problem to an eigenvalue problem. The numerical example is given for YBCO/Epoxy composites. The location and the width of band gaps are estimated for different rotating angles. The influence of anisotropy on band gaps is discussed based on numerical results.

A new patch antenna with metamaterial cover

A metamaterial was introduced into the cover of a patch antenna and its band structure was analyzed. The metama- terial cover with correct selection of the working frequency increases by 9.14 dB the patch antenna’s directivity. The mechanism of metamaterial cover is completely different from that of a photonic bandgap cover. The mechanism of the metamaterial cover, the number of the cover’s layers, and the distance between the layers, were analyzed in detail. The results showed that the metamaterial cover, which works like a lens, could effectively improve the patch antenna’s directivity. The physical reasons for the improvement are also given.

Main Factors for Affecting Photonic Bandgap of Photonic Crystals

The factors affecting one dimensional （1D） and two dimensional （2D） photonic crystals （PhCs） are systemically analyzed in this paper by numerical simulation. Transfer matrix method （TMM） is employed for 1D PCs, both finite difference time domain method （FDTD） and plane wave expansion method （PWE） are employed for 2D PCs. The result shows that the photonic bandgaps （PBG） are directly affected by crystal type, crystal lattice constant, modulation of refractive index and periodicity, and it is should be useful for design of different type photonic crystals with the required PBG and functional devices. Finally, as an example, a near-IR 1D PCs narrow filter was designed.

The Photonic Band Gaps in the Two-Dimensional Plasma Photonic Crystals with Rhombus Lattice

In this paper,under two different electromagnetic modes,the photonic band gaps（PBGs） in the two-dimensional plasma photonic crystals（PPCs） are theoretically investigated based on the plane wave expansion method.The proposed PPCs are arranged in rhombus lattices,in which the homogeneous unmagnetized plasma rods are immersed in the isotropic dielectric background.The computed results showed that PBGs can be easily tuned by the angle of rhombus lattices,and a cutoff frequency and a flatbands region can be observed under the TM and TE polarized waves,respectively.The relationships between the relative bandwidths of first PBGs and the parameters of PPCs in two such cases also are discussed.The numerical simulations showed that the PBGs can be manipulated obviously by the parameters as mentioned above.The proposed results can be used to design the waveguide and filter based on the PPCs.

The features of band structures for woodpile three-dimensional photonic crystals with plasma and function dielectric constituents

The features of the band structures of woodpile three-dimensional （3D） photonic crystals composed of plasma and function dielectric constituents, referred to as function plasma photonic crystals （FPPCs）, are theoretically studied by a modified plane wave expansion method, and the formulas for computing the band structures are derived. The arrangement for the proposed FPPCs is that the function dielectric columns are surrounded by plasma, and the embedded dielectric columns are stacked according to the woodpile lattices, which are arrayed with facecentered-tetragonal symmetry. The relative permittivity of function dielectric rods depends on the function coefficient and space coordinates. The relationships between the parameters for inserted function dielectric rods and plasma and the band structures are also investigated. The computed results illustrate that the obtained PBG can be tuned by those parameters as mentioned above. Compared to dielectric-air PCs, function dielectric PCs and plasma dielectric PCs with the same topology, a wider bandwidth of the photonic band gap can be observed in the proposed FPPCs. The calculated results also show us another alternative way to realize reconfigurable applications with 3D FPPCs.

Comment on “Band gaps structure and semi-Dirac point of two-dimensional function photonic crystals” by Si-Qi Zhang et al.

Recently, Zhang et al. （Chin. Phys. B 26 024208 （2017）） investigated the band gap structures and semi-Dirac point of two-dimensional function photonic crystals, and the equations for the plane wave expansion method were induced to obtain the band structures. That report shows the band diagrams with the effects of function coefficient k and medium column ra under TE and TM waves. The proposed results look correct at first glance, but the authors made some mistakes in their report. Thus, the calculated results in their paper are incorrect. According to our calculations, the errors in their report are corrected, and the correct band structures also are presented in this paper.

PHONONIC BAND GAPS IN TWO-DIMENSIONAL HYBRID TRIANGULAR LATTICE

Absolute phononic band gaps can be substantially improved in two-dimensional lattices by using a symmetry reduction approach. In this paper, the propagation of elastic waves in a two-dirnensional hybrid triangular lattice structure consisting of stainless steel cylinders in air is investigated theoretically. The band structure is calculated with the plane wave expansion （PWE） method. The hybrid triangular Bravais lattice is formed by two kinds of triangular lattices. Different from ordinary triangular lattices, the band gap opens at low frequency （between the first and the second bands） regime because of lifting the bands degeneracy at high symmetry points of the Brillouin zone. The location and width of the band gaps can be tuned by the position of the additional rods.

Photonic band gap of 2D complex lattice photonic crystal

It is of great significance to present a photonic crystal lattice structure with a wide photonic bandgap. A two-dimension complex lattice photonic crystal is proposed. The photonic crystal is composed of complex lattices with triangular structure, and each single cell is surrounded by six scatterers in an hexagon. The photonic band gaps are calculated based on the plane wave expansion (PWE) method. The results indicate that the photonic crystal has tunable large TM polarization band gap, and a gap-midgap ra...

The Brillouin zones and band gaps of a two-dimensional phononic crystal with parallelogram lattice structure

We present a detailed theoretical study on the acoustic band structure of two-dimensional （2D） phononic crystal. The 2D pho- nonic crystal with parallelogram lattice structure is considered to be formed by rigid solid rods embedded in air. For the circu- lar rods, some of the extrema of the acoustic bands appear in the usual high-symmetry points and, in contrast, we find that some of them are located in other specific lines. For the case of elliptic rods, our results indicate that it is necessary to study the whole first Brillouin zone to obtain rightly the band structure and corresponding band gaps. Furthermore, we evaluate the first and second band gaps using the plane wave expansion method and find that these gaps can be tuned by adjusting the side lengths ratio R, inclined angle 0 and filling fraction F of the parallelogram lattice with circular rods. The results show that the largest value of the first band gap appears at θ=90° and F--0.7854. In contrast, the largest value of the second band gap is at θ=60° and F=0.9068. Our results indicate that the improvement of matching degree between scatterers and lattice pattern, ra- ther than the reduction of structural symmetry, is mainly responsible for the enhancement of the band gaps in the 2D phononic crystal.

Modelling overall transmitted efficiency at 1550 nm for polymer grating Silicon-on-insulator structure with defect

The overall transmitted efficiency at 1550 nm for Nylon-Teflon/Teflon-Nylon （N-T/T-N） grating Silicon- on-insulator （SOI） structure with defect in even and odd position was investigated in this paper. Different types of losses, such as absorption, reflection and diffraction, were considered to find out the overall transmitted efficiency. The absorption loss of both Nylon-Teflon （N-T） and Teflon-Nylon （T-N） structure is zero at the wavelength of 1550 nm. Reflectance of these structures was analyzed by using plane wave expansion （PWE） method. Simulation result showed that reflectance as well as transmittance was varied linearly with respect to defect at odd and even positions. Simulation is also done for the diffraction efficiency at 1550nm with respect to detuning from Bragg＇s angle, which was ranged from -0.4 rad to ＋ 0.4 rad. Finally, it was found that overall transmitted efficiency increased as even defect position varied from 2nd to 10th for both N-T/T-N grating SOI structure. Similarly, the overall transmitted efficiency decreased as odd defect position changed from 3rd to l lth for both N-T/T-N grating SOI structure.