Optical bistability in defective photonic multilayers doped by graphene

We study the optical bistability (OB) in photonic multilayers doped by graphene sheets, stacking two Bragg reflectors with a defect layer between the reflectors. OB stems from the nonlinear effect of graphene, so the local field of defect mode (DM) could enhance the nonlinearity and reduce the thresholds of bistability. The structure achieves the tunability of bistability due to that the DM frequency and transmittance could be modulated by the chemical potential. Bistability thresholds and interval of the two stable states could be remarkably reduced by decreasing the chemical potential. A lager Bragg periodic number could increase the localizing of field, but the graphene loss may decrease the intensity of transmission light. We have concluded an appropriate periodic number to achieve OB. The study suggests that the tunable bistability of the structure could be used for all-optical switches in optical communication systems.     

Kerr缺陷一维耦合腔光波导的双稳态方向性

本文提出一种只在一层高折射率介质层中掺杂Kerr介质的一维耦合腔光波导.利用一维传输矩阵理论和非线性传输矩阵方法研究了此结构的光学双稳态.根据一维传输矩阵理论分析了此结构的线性特性,包括低频带边模的偏移及场分布的特点,讨论了此结构实现双稳态的原理.研究发现:由于缺陷层中场分布与入射光方向密切相关,而缺陷层光场的局域,将激发Kerr介质的三阶非线性效应,从而改变了缺陷层的折射率,所以不同方向的入射光具有不同的双稳态阈值.利用非线性传输矩阵方法研究了光学双稳态特性.结果表明:由于缺陷层的位置导致缺陷模正方向（由左到右）入射的场分布大于反方向（由右到左）入射的场分布,正方向的阈值低于反方向的阈值,相差一倍.     

Achieving optical bistability through ultra-compact metal-dielectric structure

The transmission spectra of two-period metal-dielectric structure are studied through the transfer matrix method. When the dielectric is nonlinear material, an optical bistability has been found. The upper threshold value is insensitive to incident frequency, while the lower threshold value increases with the incident frequency decreasing. The effect of loss from the metal layers on the optical bistability is also considered.     

Nonlinear properties of a graded-index photonic heterostructure

The optical properties of a one-dimensional (1D) photonic heterostructure with graded-index nonlinear materials are demonstrated theoretically. The influence of the gradation profile of the graded-index nonlinear layers on the linear and nonlinear responses of the structure are analysed. It is shown that the Q-factor of the defect mode and the threshold input intensity to achieve the optical bistability in the used photonic heterostructure depend on the gradation profile of the graded-index nonlinear layers.     

Properties of defect modes in one-dimensional photonic crystals containing two nonlinear defects

Transmission properties of one-dimensional photonic crystal with two nonlinear defects were investigated based on the nonlinear transfer matrix method. From the inspection of the optical bistabilities around different defect modes, it was found that the threshold of bistability for the bonding mode is always lower than that for the anti-bonding mode. When intensity of the incident wave increases bistability could happen at any wavelength larger than the resonance wavelength of the linear anti-bonding mode in the gap. The threshold of bistability increases initially with the wavelength, then decreases sharply in reaching the resonance wavelength of the linear bonding mode. The coupling behavior of the two defects was also discussed, and it was found that the threshold of bistability increases with the distance between the two defects. A flat spectrum similar to that formed in the photonic crystal molecules was obtained under certain incident intensity.     

介质层厚对含负折射率介质Bragg微腔的影响

研究了介质层厚对含负折射率介质一维光子晶体Bragg微腔的缺陷模和双稳态的影响.在中心频率附近将传输矩阵各矩阵元采用泰勒级数展开并取一级近似,得到了缺陷模频率与介质层厚的关系式及品质因子公式.研究结果表明：一级近似法能很好地解释中心频率附近介质层厚对缺陷模频率的影响.理想Bragg微腔结构的缺陷模品质因子最大；递增正折射率介质层厚和增大缺陷层介质层厚、递减负折射率介质层厚及同时等量递减正和负折射率介质层厚,均可使缺陷模红移,双稳态阈值降低.     

含负折射率介质非线性Bragg腔的双稳态特性

研究了含负折射率介质一维光子晶体非线性Bragg腔的透射特性、光学增强和双稳态特性.对负折射率介质无色散和有色散非线性Bragg腔及由两种正折射率介质构成的非线性Bragg腔的透射谱、光学增强、缺陷模的线宽、入射光的红移量、双稳态开关阈值进行了比较.含负折射率介质的非线性Bragg腔可显著增大腔内光学增强效应,降低缺陷模的线宽、入射光的红移量和双稳态开关阈值.     

Nonlinear pulse propagation in periodic media with and without defects

The influence of single defects within a periodic structure on the nonlinear transmission of optical pulses through the structure is investigated numerically. A stack of alternating linear and cubically nonlinear layers of submicron thicknesses is considered. The simulations are based on a modified equation for the pulse envelope. Diffraction of the pulse has been taken into account, too. The results of simulations have been demonstrated as an essential influence of defects within the periodic structure on the nonlinear propagation of optical pulses, when the carrier frequency is chosen within the stop band of the structure with the defect.     

Optical bistability in one-dimensional photonic band gap structures with coupled nonlinear defects

Using the transfer matrix method, we study the transmission property of one-dimensional photonic band gap structure with two coupled nonlinear defects separated by a linear middle layer and find that such composite structure exhibits a bistability that’s strongly dependent of the linear middle layer. The switching threshold values can be greatly reduced just by choosing the proper parameters of the linear middle layer.     

球几何中子输运保正线性间断有限元格式

针对球几何中子输运方程线性间断有限元方法计算的负中子通量问题,构造了保正线性间断有限元格式,该格式保持中子角通量0阶矩和1阶矩。现有方法计算中子角通量非负时,采用传统的线性间断有限元方法,求解线性方程组;原方法计算出现负通量,则采用构造的保正格式,求解非线性方程组。编制了球几何中子输运问题保正格式程序模块,并集成到应用程序。数值算例表明构造的保正格式计算的中子通量非负,有效降低数值误差,提高数值计算的精度。     

Controllable optical bistability and multistability in asymmetric double quantum wells via spontaneously generated coherence

We investigate the nonlinear optical phenomena of the optical bistability and multistability via spontaneously generated coherence in an asymmetric double quantum well structure coupled by a weak probe field and a controlling field. It is shown that the threshold and hysteresis cycle of the optical bistability can be conveniently controlled only by adjusting the intensity of the SGC or the controlling field. Moreover, switching between optical bistability and multistability can be achieved. These studies may have practical significance for the preparation of optical bistable switching device.     

Interpolation-free monotone finite volume method for diffusion equations on polygonal meshes

We developed a new monotone finite volume method for diffusion equations. The second-order linear methods, such as the multipoint flux approximation, mixed finite element and mimetic finite difference methods, are not monotone on strongly anisotropic meshes or for diffusion problems with strongly anisotropic coefficients. The finite volume (FV) method with linear two-point flux approximation is monotone but not even first-order accurate in these cases. The developed monotone method is based on a nonlinear two-point flux approximation. It does not require any interpolation scheme and thus differs from other nonlinear finite volume methods based on a two-point flux approximation. The second-order convergence rate is verified with numerical experiments.     

Transmission property for a one-dimensional photonic crystal containing a subwavelength layer and a nonlinear layer

Using the transfer matrix method, we investigate the transmission property of a one-dimensional photonic crystal doped with a linear subwavelength layer and a Kerr-type nonlinear layer. We find that a thin film of subwavelength layer can significantly modify the characteristic of optical bistability. We also find that the sequence of the thin film and the nonlinear layer has a major impact on the hysteretic behavior. With the investigations to the linear defect mode and the electric field distribution in the nonlinear material, we explain these phenomena. PACS 42.65.Pc; 42.25.Bs; 42.70.Qs; 42.65.-k; 78.66.-w     

Tunable optical bistability at microwave frequency based on 1D sandwich photonic structure consisting of a nonlinear dielectric slab and two magnetized cold plasma layers

In this paper, tunable optical bistability that denotes the relationship between input intensity and output intensity is numerically investigated in the microwave frequency region based on the one-dimensional (1D) sandwich photonic structure consisting of a Kerr-type nonlinear material slab and two magnetized cold plasma layers. Results show that, in the case of TM-polarized electromagnetic wave, width and switching thresholds of the bistability loops are dependent on the working frequency, initial incidence angle, layer thickness, plasma density, and external magnetic field, which should be judiciously selected to obtain a required bistability behavior. Compared to the case of switch-down threshold, the switch-up threshold in the bistability loop is more sensitive to the changes of parameters. Through this study, the suggested 1D sandwich photonic structure is beneficial to the all-optical signal processing.     

A nodal discontinuous Galerkin finite element method for nonlinear elastic wave propagation

A nodal discontinuous Galerkin finite element method (DG-FEM) to solve the linear and nonlinear elastic wave equation in heterogeneous media with arbitrary high order accuracy in space on unstructured triangular or quadrilateral meshes is presented. This DG-FEM method combines the geometrical flexibility of the finite element method, and the high parallelization potentiality and strongly nonlinear wave phenomena simulation capability of the finite volume method, required for nonlinear elastodynamics simulations. In order to facilitate the implementation based on a numerical scheme developed for electromagnetic applications, the equations of nonlinear elastodynamics have been written in a conservative form. The adopted formalism allows the introduction of different kinds of elastic nonlinearities, such as the classical quadratic and cubic nonlinearities, or the quadratic hysteretic nonlinearities. Absorbing layers perfectly matched to the calculation domain of the nearly perfectly matched layers type have been introduced to simulate, when needed, semi-infinite or infinite media. The developed DG-FEM scheme has been verified by means of a comparison with analytical solutions and numerical results already published in the literature for simple geometrical configurations: Lamb's problem and plane wave nonlinear propagation.     

分数阶对流扩散方程的特征有限元方法

讨论非线性分数阶对流扩散方程的特征有限元方法.利用特征线法和分数阶有限元框架,构建一种基于特征方向的全离散有限元格式.模拟物理问题,并在数值上与常规有限元格式进行比较,计算结果表明：该方法能准确地捕捉到控制方程的精确解,即使是在对流效应占优时,也具有稳定性好和逼近精度高等特征.     

Analysis of Transient Optical Bistability and Stability in a Nonlinear Fiber Fabry-Perot Resonator Based on an Iterative Method

We perform a transient analysis, steady-state analysis, and linear stability analysis of a nonlinear Fabry-Perot resonator in order to examine the possibility of a fiber bistable device. We here develop two iterative methods for calculating the dynamics of the Fabry-Perot resonator containing a nonlinear medium with an instantaneous response time. The treatment of the counter-propagating field within the cavity is very important in estimating the nonlinear phase shift due to propagation. A trapezoid rule and midpoint rule are used here for the numerical integration. The iterative method using the trapezoid rule gives excellent agreement with the multiple-beam method developed by Bischofberger and Shen (Phys. Rev. A 19 (1979) 1169), which is more complicated than the proposed procedure. Unfortunately it is found that the midpoint approximation is numerically unstable. Assuming a conventional optical fiber, the switching power for optical bistability is less than 1 kW for a resonator length of 1-2 cm. On the basis of the iterative method, we perform a linear stability analysis to examine whether Ikeda instability affects bistable device application or not. The stability analysis shows that the instability threshold is two orders of magnitude larger than the switching power for optical bistability.     

Comparison of 1D transfer matrix method and finite element method with tests for acoustic performance of multi-chamber perforated resonator

Multi-chamber perforated resonator (MCPR) is a kind of typical silencer element which can both attenuate broadband noise and satisfy specific installation requirements. The one-dimensional transfer matrix method (TMM) and finite element method (FEM) are widely used to predict the transmission loss of the resonators. This paper mainly focuses on the comparison between 1D TMM and FEM in which detailed perforation modeling is applied for the acoustic modeling of MCPRs. Five resonators with different acoustic attenuation frequency ranges are built for simulation and test. In order to verify the results of the above methods, a transmission loss test facility is designed based on two-load method. Through adjusting the distance between microphones, the facility’s effective measurement frequency can be changed. The results show that despite of the complex modeling and calculation, FEM with detailed perforation modeling shows good consistency with test results in both frequency and amplitude within entire frequency range. In comparison, TMM is limited by the cut-off frequency when calculating transmission losses. Besides, accuracy of TMM in low frequency range is also affected by perforation conditions. However, TMM is time-saving in calculation and structure optimization. In MCPRs’ development process, TMM can be used to quickly design and optimize structure parameters while FEM can be used to verify the acoustic performance before prototyping.     

Low-threshold bistable reflection assisted by oscillating wave interaction with Kerr nonlinear medium

Owing to the enormously enhanced oscillating wave, a minute variation of the incident light intensity will give rise to a change in the dielectric constant of the Kerr nonlinear medium and lead to a bistable reflection with an ultra-low threshold intensity, which is closely related to the angle of incidence and the thickness of the Kerr nonlinear medium. The criterion for the existence of optical bistability is derived. Our bistability scheme is simple and not limited to the TM-polarization.     

具有非线性缺陷的光子晶体的局域模

采用传输矩阵的方法，严格导出一维具有克尔非线性缺陷的光子晶体的局域模频率方程。局域模频率依赖于局域光强。取负克尔系数时，随着局域光强的增加，局域模频率从下带边出现，在带隙间上升，最后消失在上带边。在给定人射光频率下，随着人射光强的变化，系统呈现出双稳态。这种光学稳态性质则由局域模频率的移动引起的。