Splitting rules of electronic miniband in Fibonacci superlattices: a gap map approach

The splitting rules of fragmental miniband in Fibonacci superlattices (FSLs) with arbitrary basis and generation orders are presented through a gap map diagram. Based on the gap map, we find the invariant conditions of the band structure splitting in the FSL for arbitrary generation orders. Moreover, the band structure splitting can be divided to form many regions, each having a similar pattern. In each region, the widths of most gap bands except two major gaps will decrease for increasing the generation order. It is interesting that the center and gap width of the major gaps will converge to constant values for increasing the generation order of the FSL. Based on the splitting rules displayed in the gap map, it is convenient to predict the fragmental band structure in the FSL for arbitrary generation orders and bases.     

Omnidirectional Single-negative Gap and in Fibonacci Sequences Composed of Single-negative Materials

The band structures of Fibonacci sequence composed of single-negative materials are studied with a transfer matrix method. A new type of omnidirectional single-negative gaps is found in the Fibonacci sequence. In contrast to the Bragg gaps, such an omnidirectional single-negative gap is insensitive to the incident angles and polarization, and is invariant upon the change of the ratio of the thicknesses of two media. It is found that omnidirectional single-negative gap exists in the other Fibonacci sequence, and it is rather stable and independence of the structure sequence.     

色散SiO2/TiO2薄膜组成的Fibonacci序列一维光子晶体在可见光波段的传输特性

用特征矩阵法研究了由正常色散SiO₂/TiO₂薄膜组成的Fibonacci序列一维光子晶体在可见光波段的传输特性,并与无色散时的传输特性做了对比。结果表明,随序列项数的增加,相应的前一序列的透射谱中透射率较低的凹带逐渐变成禁带,禁带数增加;初始介质是低折射率的SiO₂薄膜时比高折射率的TiO₂薄膜时各序列的透射谱中的禁带数多,各禁带的宽度和中心波长基本相同;在总厚度一定的条件下,随SiO₂薄膜的厚度增大（TiO₂薄膜的厚度减小）,禁带的宽度减小,禁带的中心波长基本不变;随入射角增大,禁带的中心波长向短波方向移动,禁带宽度变小。在其它相同条件下,无色散时的最宽禁带和最宽禁带的中心波长比有色散时的最宽禁带和最宽禁带的中心波长都有增加。     

Multi-wavelength photonic band gaps based on quasi-periodically poled lithium niobate ordered in Fibonacci sequences

We demonstrate a quasi-periodic structure exhibiting multiple photonic band gaps （PBGs） based on sub- micron-period poled lithium niobate （LN）. The structure consists of two building blocks, each containing a pair of antiparallel poled domains, arranged as a Fibonacci sequence. The gap wavelengths are analyzed with the Fibonacci sequence parameters such as the quasiperiodic indices and the average lattice parameter. The transmission properties are investigated by a traditional 4×4 matrix method. It has also been proved that the gap depth can be tuned by the lengths of poled domains.     

Design of an omnidirectional mirror using one dimensional photonic crystal with graded geometric layers thicknesses

We propose a flexible design for one-dimensional photonic crystals (1D-PCs) with a controllable omnidirectional band gap covering the optical telecommunication wavelengths which are 0.85 μm, 1.3 μm and 1.55 μm. We used for this design the chirped grating. Chirping is applied to geometric thicknesses of layers. It takes two forms, one is linear and the other is exponential. We exploit this technique to have the suitable omnidirectional band gap covering the maximum of optical telecommunication wavelengths. With a quarter wave structure, we can have an omnidirectional band gap generating only one of these wavelengths. With graded structure, we obtain, as is reported in this paper, an omnidirectional band gap which covers the wavelengths 1.3 μm and 1.55 μm at the same time with a large bandwidth. We also achieve an omnidirectional band gap containing the wavelength 0.85 μm and which is obviously larger than that of the quarter wave stack.     

一种基于光子晶体结构的坦克涂层设计

为减少坦克在实战中的红外辐射, 分析了坦克炮慢射后的辐射特征, 针对其炮管所辐射的特征波长在8-12 μm的电磁波,选用常见的SiO₂和Si为介质, 并在考虑各自色散关系的基础上, 设计了具有光子晶体结构的防辐射涂层. 数值计算表明: 当两介质各取4层, 其几何厚度分别取1330和825 nm时,在8-12 μm 的范围内有一个严格的带隙. 当两介质的几何厚度增加, 带隙红移, 宽度增加, 反之亦然. 只要两介质的几何厚度变化不同时超过10%, 原带隙总是存在. 当介质层数取7-8时, 涂层在上述波长范围内的严格带隙已形成, 介质层数再增加, 带隙没有实质性的变化. 带隙结构对入射角的变化并不敏感.     

基于像素法用模拟退火-遗传算法搜索一维宽带隙光子晶体

将一维光子晶体用像素填充法进行二进制编码,把模拟退火、遗传算法、模拟退火-遗传混合算法与传输矩阵法结合,搜索、计算了一维光子晶体结构和能带,找到了全方位相对禁带宽度高达43.53%的四层结构和43.76%的两层结构,并给出了一维四层结构光子晶体的能带图及其4个原胞的反射率和透射率的频谱图;发现一维两层结构光子晶体的全方位禁带宽度对每层厚度的变化不敏感,但随着两种介质折射率差的增加而增大.     

Tunable photonic band-gaps in one-dimensional photonic crystals containing linear graded index material

We have demonstrated control of the photonic band gaps (PBGs) in 1-D photonic crystals using linear graded index material. The analysis of PBG has been done in THz region by considering photonic crystals in the form of ten periods of second, third and fourth generation of the Fibonacci sequence as unit cell. The unit cells are constituted of two kinds of layers; one is taken of linear graded index material and other of normal dielectric material. For this investigation, we used a theoretical model based on transfer matrix method. We have obtained a large number of PBGs and their bandwidths can be tuned by changing the grading profile and thicknesses of linear graded index layers. The number of PBGs increases with increase in the thicknesses of layers and their bandwidths can be controlled by the contrast of initial and final refractive index of the graded layers. In this way, we provide more design freedom for photonic devices such as reflectors, filters, optical sensors, couplers, etc.     

Optical fields in a multilayered microsphere with a quasiperiodic spherical stack

We studied the frequency spectrum of photons in a multilayered microsphere coated by a quasiperiodic (Fibonacci) dielectric stack numerically. We found that the transmittancy spectrum of such a stack consists of quasiband gaps and narrow resonances caused by re-reflection of optical waves. When the number (Fibonacci order) of layers increases, the band gaps and resonances split, and the structure of the frequency spectrum acquires a fractal form. We found the self-similarity of the frequency spectrum and evaluated the fractal dimension both for lossless and dissipative cases. The influence of a weak random deviation of spherical layers width is also discussed.     

Optical properties of structures composed of periodic,quasi-periodic,and aperiodic sequences of particulate monolayers

The spectra of the coherent transmission and reflection coefficients of multilayers consisting of the periodic, Fibonacci (quasi-periodic), and Thue–Morse (aperiodic) sequences of plane-parallel monolayers of monodisperse spherical alumina and silica particles are investigated using the quasi-crystalline approximation (QCA) and the transfer matrix method (TMM). The additional opportunities for the transmission and reflection spectra manipulation in comparison with the periodic sequence of monolayers are demonstrated. Photonic band gaps in the spectra of the particulate structures are shifted to the short-wavelength range in comparison with those for systems of homogeneous layers. The shift is larger for the Thue–Morse sequence. The widths of the photonic band gaps for particulate systems are narrower than the ones for multilayers consisting of homogeneous layers of an equivalent volume of matter. The results can be used to create optical, optoelectronics, and photonics devices—for example, multispectral filters, light emitting diodes, solar cells, displays.     

Tunable optical properties in engineered one-dimensional coupled resonator optical waveguides

In this paper, the optical properties in finite size tilted and engineered one dimensional coupled resonator optical waveguide have been investigated. The large dependence of the optical transmittance, dispersion parameter and its higher order slope such as transmittance group delay, third order dispersion and intrinsic waveguide induced loss on the oblique incidence and fraction factor, as the ratio of the optical thicknesses of two adjacent layers, have been studied. Our results showed that as a consequence of changing the fraction factor, at normal incidence, photonic band gap zone, flat portion of third order dispersion curve and maximum magnitude of the transmission group delay can be tuned in long range of wavelength (red shift) slightly. Despite of slight tuning the optical properties in one dimensional coupled resonator optical waveguide by changing the fraction factor, incidence angle has a significant large magnitude of tunability in the overall region of operational wavelength. This fact yields us by changing the incidence from 30 to 60, the operational wavelength can be tuned between two main optical communication windows, while by changing the fraction factor, dispersion and its higher order can be fine tuned in each of optical communication windows which are very useful in wavelength division multiplexing systems and planar lightwave circuits.     

Influence of the thickness of matching layers on narrow band transmitter ultrasonic airborne transducers with frequencies <100 kHz: Application of a genetic algorithm

The acoustic impedances of matching layers and their thicknesses are the most important and influential parameters in the performance of airborne ultrasonic transducers. In this paper, the optimum thicknesses of the matching layers of the narrow band transmitter ultrasonic transducer regarding transmission coefficient were determined by individual calculations using a genetic algorithm. The genetic algorithm was chosen because it is a powerful tool in the optimization domain. The results show that the permitted thickness variation is 0.0005% for one matching layer, and this value can be increased to 0.0031%, which corresponds to the permitted thickness variation for five matching layers. Approximately 55% enhancement in the transmission coefficient is theoretically possible, and 42% enhancement was observed experimentally when the genetic algorithm was applied to calculate the matching layer thicknesses in place of the quarter wavelength equation that is conventionally used for the determination of layer thickness. To verify our approach, the effect of the thickness variation on the transmission coefficient has been investigated experimentally for three, four and five matching layers. The experimental results displayed good agreement with the theoretical predictions.     

Linear periodic and quasiperiodic anisotropic layered media with arbitrary orientation of optic axis—A numerical study

We study numerically the linear properties of periodic and quasiperiodic anisotropic layered media. Each anisotropic slab can have arbitrary orientation of optic axis. We apply the general numerical code to recover the known results for solc filters. We propose novel periodic structures where the location and width of the gaps can be controlled easily. We also study the transmission properties of a Fibonacci sequence of anisotropic layers and show the interesting features like self-similarity and scaling.     

Three channel GHz-ranged demultiplexer in solid-solid phononic crystals

We present the design procedure for the elastic GHz-ranged demultiplexer based on a solid-solid phononic crystal platform. It consists of a T-shaped waveguide with three arms. The PnC platform consists of a square array of infinitely long rods of Tungsten embedded in PMMA background. In order to have a wide band gap, it is essential that constituent materials have large contrast in physical properties. These materials have large contrast in their physical properties and it gives us the possibility of having complete band gaps with low filling fractions. To calculate the band diagram and transmission field map, the finite element method (FEM) has been employed. The main waveguides are made by removing one row or one column of rods. For each arm, the radius of rods is modified to have three different defects. Therefore, the designed demultiplexer can separate three frequencies in the range of GHz. To the best of our knowledge, it is for the first time.     

Bound states in the continuum in quasiperiodic systems

We first propose the existence of bound states in the continuums (BICs) in quasiperiodic systems. Owing to long-range correlation, destructive interference may occur in quasiperiodic systems with higher generation order. Occurrences of BICs in Fibonacci quantum wells studied by localization analysis and gap map method are proposed.     

Improved semiconductor lattice parameters and band gaps from a middle-range screened hybrid exchange functional

We show that the middle-range exchange-correlation hybrid of Henderson, Izmaylov, Scuseria and Savin (HISS) performs extremely well for elemental and binary semiconductors with narrow or visible spectrum band gaps, as well as some wider gap or more ionic systems used in devices. The lattice parameters are superior to those predicted by the screened hybrid functional of Heyd, Scuseria and Ernzerhof (HSE), and provide a significant improvement over the geometries predicted by typical semilocal functionals, yielding results competitive with PBEsol, which was specially tuned for solids. HISS also yields band gaps superior to those produced by functionals developed specifically for the solid state. Timings indicate that HISS is more computationally efficient than HSE, implying that the high quality lattice constants coupled with improved optical band gap predictions render HISS a useful adjunct to HSE in the modeling of geometry-sensitive semiconductors.     

Enhancement of phononic band gaps in ternary/binary structure

Based on the transfer matrix method (TMM) and Bloch theory, the interaction of elastic waves (normal incidence) with 1D phononic crystal had been studied. The transfer matrix method was obtained for both longitudinal and transverse waves by applying the continuity conditions between the consecutive unit cells. Dispersion relations are calculated and plotted for both binary and ternary structures. Also we have investigated the corresponding effects on the band gaps values for the two types of phononic crystals. Furthermore, it can be observed that the complete band gaps are located in the common frequency stop-band regions. Numerical simulations are performed to investigate the effect of different thickness ratios inside each unit cell on the band gap values, as well as unit cells thickness on the central band gap frequency. These phononic band gap materials can be used as a filter for elastic waves at different frequencies values.     

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在理想条件下,为了研究等离子体参数、填充率、入射角度和介质层相对介电常数对一维三元磁化等离子体光子晶体的禁带特性的影响,用由传输矩阵法计算得到的TE波任意角度入射时的左旋极化波(LCP)和右旋极化波(RCP)的透射系数来研究其禁带特性。结果表明,仅增加等离子体碰撞频率不能实现禁带宽度的拓展,改变等离子体频率、填充率和介质层的相对介电常数能实现对禁带宽度和数目的调谐。改变等离子体回旋频率能实现对右旋极化波的禁带的调谐,但对左旋极化波的禁带几乎无影响。入射角度的增大使得禁带低频区域带宽变大,而高频区域带宽则是将先减小再增大。     

Transmission properties of Fibonacci quasi-periodic one-dimensional superconducting photonic crystals

The transmission properties of Fibonacci quasi-periodic one-dimensional photonic crystals (1DPCs) containing superconducting material are theoretically investigated based on the transfer matrix method. It is shown that the 1DPCs can possess a same photonic band gap property as the periodic structure superconducting PC. The results of transmittance spectra show that the cutoff frequency can be manipulated through the thicknesses of the superconductor and dielectric layers as well as the ambient temperature of the system. It is observed that the shift of cutoff frequency becomes more noticeable by adjusting the thickness of the superconductor layer than that of the dielectric one. Furthermore, the cutoff frequency becomes very sensitive when the system temperature is tuned to close vicinity of the critical temperature of the superconductor.     

Ultrarelativistic electron-hole pairing in graphene bilayer

We consider the ground state of an electron-hole graphene bilayer composed of two independently-doped graphene layers when a condensate of spatially separated electron-hole pairs is formed. In the weak coupling regime the pairing affects only the conduction band of the electron-doped layer and the valence band of the hole-doped layer, thus the ground state is similar to an ordinary BCS condensate. At strong coupling, an ultrarelativistic character of the electron dynamics reveals itself and the bands which are remote from Fermi surfaces (valence band of electron-doped layer and conduction band of hole-doped layer) are also affected by the pairing. Analysis of the instability of the unpaired state shows that s-wave pairing with band-diagonal condensate structure, described by two gaps, is preferable. The relative phase of the gaps is fixed, however at weak coupling this fixation diminishes allowing gapped and soliton-like excitations. The coupled self-consistent gap equations for these two gaps are solved at zero temperature in the constant-gap approximation and in the approximation of a separable potential. It is shown that, if the characteristic width of the pairing region is of the order of magnitude of the chemical potential, then the value of the gap in the spectrum is not much different from the BCS estimation. However if the pairing region is wider, then the gap value can be much larger and depends exponentially on its energy width.