Phase and group synchronization in second-harmonic generation of ultrashort light pulses in one-dimensional photonic crystals

It is shown, on the basis of an analysis of the dispersion relation for an infinite one-dimensional periodic multilayer structure and direct numerical integration of Maxwell’s equations by the finite-difference method, that structures with photonic band gaps (PBGs) make it possible to provide simultaneously conditions for phase and group synchronizations for second-harmonic generation with participation of extremely short light pulses. The phase and group detunings, which arise as a result of the dispersion of the nonlinear medium, are compensated by the dispersion of the PBG structure. The use of this regime of nonlinearly optical interactions opens up the possibility of attaining high frequency conversion efficiencies irrespective of the synchronization length in the interior volume of a nonlinear material.     

有损耗介质中非线性光导波的数值模拟

发展了一种以有限元法为基础的数值方法，用它分析由损耗任意大小材料构成的平面非线性波导结构所传导的非线性有损耗光波。在这种方法中，从给出的非线性有损耗波导直接得到ＴＥ和ＴＭ波与功率有关的复传播常数和局域电磁场分布。     

Nonlinear pulsed ultrasound beams radiated by rectangular focused diagnostic transducers

A numerical model for simulating nonlinear pulsed beams radiated by rectangular focused transducers, which are typical of diagnostic ultrasound systems, is presented. The model is based on a KZK-type nonlinear evolution equation generalized to an arbitrary frequency-dependent absorption. The method of fractional steps with an operator-splitting procedure is employed in the combined frequency-time domain algorithm. The diffraction is described using the implicit backward finite-difference scheme and the alternate direction implicit method. An analytic solution in the time domain is employed for the nonlinearity operator. The absorption and dispersion of the sound speed are also described using an analytic solution but in the frequency domain. Numerical solutions are obtained for the nonlinear acoustic field in a homogeneous tissue-like medium obeying a linear frequency law of absorption and in a thermoviscous fluid with a quadratic frequency law of absorption. The model is applied to study the spatial distributions of the fundamental and second harmonics for a typical diagnostic ultrasound source. The nonlinear distortion of pulses and their spectra due to the propagation in tissues are presented. A better understanding of nonlinear propagation in tissue may lead to improvements in nonlinear imaging and in specific tissue harmonic imaging. Published in Russian in Akusticheskiĭ Zhurnal, 2006, Vol. 52, No. 4, pp. 560–570. This article was translated by the authors.     

Relativistic effects on the modulational instability of electron plasma waves in quantum plasma

Relativistic effects on the linear and nonlinear properties of electron plasma waves are investigated using the one-dimensional quantum hydrodynamic (QHD) model for a two-component electron?Cion dense quantum plasma. Using standard perturbation technique, a nonlinear Schr?dinger equation (NLSE) containing both relativistic and quantum effects has been derived. This equation has been used to discuss the modulational instability of the wave. Through numerical calculations it is shown that relativistic effects significantly change the linear dispersion character of the wave. Unlike quantum effects, relativistic effects are shown to reduce the instability growth rate of electron plasma waves.     

Nonlinear optical response of a dense two-level atom system embedded in a linear dielectric medium

The nonlinear optical (local) response of a dense collection of two-level atoms embedded in a linear dielectric medium is investigated theoretically. The nonlinear response of absorption and dispersion of two-level atoms associated with a weak probe field in the presence of a strong pump field is calculated in terms of the linear response theory. The numerical results show that the absorption and dispersion spectra are different from those in vacua because of the local-field effect enhancement and the local cooperative effect.     

Novel soliton solutions of the nonlinear Schrodinger equation model

The methodology developed provides for a systematic way to find an infinite number of the novel stable bright and dark "soliton islands" in a "sea of solitary waves" of the nonlinear Schrodinger equation model with varying dispersion, nonlinearity, and gain or absorption. It is shown that solitons exist only under certain conditions and the parameter functions describing dispersion, nonlinearity, and gain or absorption inhomogeneities cannot be chosen independently. Fundamental soliton management regimes are discovered.     

Modeling the propagation of nonlinear three-dimensional acoustic beams in inhomogeneous media

A three-dimensional model of the forward propagation of nonlinear sound beams in inhomogeneous media, a generalized Khokhlov-Zabolotskaya-Kuznetsov equation, is described. The Texas time-domain code (which accounts for paraxial diffraction, nonlinearity, thermoviscous absorption, and absorption and dispersion associated with multiple relaxation processes) was extended to solve for the propagation of nonlinear beams for the case where all medium properties vary in space. The code was validated with measurements of the nonlinear acoustic field generated by a phased array transducer operating at 2.5 MHz in water. A nonuniform layer of gel was employed to create an inhomogeneous medium. There was good agreement between the code and measurements in capturing the shift in the pressure distribution of both the fundamental and second harmonic due to the gel layer. The results indicate that the numerical tool described here is appropriate for propagation of nonlinear sound beams through weakly inhomogeneous media.     

Conditions for the existence of laser bullets

Conditions for the existence of completely localized three-dimensional dissipative laser solitons—“laser bullets” in a medium with nonlinear amplification and absorption and frequency dispersion are studied. Solitons with different profiles are considered and the regions of their stable existence are found. The stability of spherical solitons is studied as a function of frequency mismatch of amplification and absorption lines by the method of direct numerical simulation.     

Nonlinear Absorption and Dispersion Response in Optically Dense Media Driven by a Single-Mode Laser

Taking the density-dependent near dipole-dipole （NDD） interaction into consideration, we theoretically investigate the response of nonlinear absorption and dispersion in optically dense media of three-level atoms driven by a single-mode probe laser. The influence of the NDD effects on the absorption and dispersion spectra of the probe field is predicted via numerical calculations. It is shown that the NDD effects reduce gradually to transient absorption and amplification with the increase of the strengths of the NDD interaction, but do not change the steady-state behavior. Due to the presence of the NDD effects, steady-state absorption spectra exhibit asymmetric double-peak structure and overall shifts when a continuous-wave （cw） probe field is applied. However, frequency dispersion spectra are insensitive to them near the zero detuning.     

微结构固体中的孤立波及其存在条件

根据Mindlin理论,考虑宏观尺度非线性效应、二次和三次微尺度非线性效应以及微尺度频散效应,建立了描述一维微结构固体中纵波传播的一种新模型.用动力系统定性分析理论,分析了微结构固体中孤立波的存在条件及其几何特征,证明了当介质参数和孤立波传播速度满足适当条件时,在二次微尺度非线性效应的影响下微结构固体中可以形成一种非对称孤立波,在三次微尺度非线性效应的影响下微结构固体中可以形成一种对称孤立波.最后,用数值方法进一步验证了上述结论.     

Nonlinear Absorption and Dispersion Response in Optically Dense Media Driven by a Single-Mode Laser

Taking the density-dependent near dipole-dipole (NDD) interaction into consideration, we theoretically investigate the response of nonlinear absorption and dispersion in optically dense media of three-level atoms driven by a single-mode probe laser. The influence of the NDD effects on the absorption and dispersion spectra of the probe field is predicted via numerical calculations. It is shown that the NDD effects reduce gradually to transient absorption and amplification with the increase of the strengths of the NDD interaction, but do not change the steady-state behavior.Due to the presence of the NDD effects, steady-state absorption spectra exhibit asymmetric double-peak structure and overall shifts when a continuous-wave (cw) probe field is applied. However, frequency dispersion spectra are insensitive to them near the zero detuning.     

Instabilities and quasi-localized states in nonlinear Fano-like systems

We study the dynamical scattering in one-dimensional systems with a nonlinear side-coupled defect. Such structures exhibit the nonlinear Fano resonances, where nothing can propagate through. We developed a numerical model to study dynamical scattering. According to our analysis the scattering waves become dynamically unstable in the vicinity of the nonlinear Fano resonances, due to modulational instability caused by the presence of nonlinearity. It results in a time-growing amplitude of the nonlinear defect. We also demonstrate the existence of the nonlinear quasi-localized state, supported by such structures.     

Nonuniform time-step Runge–Kutta discontinuous Galerkin method for Computational Aeroacoustics

With many superior features, Runge–Kutta discontinuous Galerkin method (RKDG), which adopts Discontinuous Galerkin method (DG) for space discretization and Runge–Kutta method (RK) for time integration, has been an attractive alternative to the finite difference based high-order Computational Aeroacoustics (CAA) approaches. However, when it comes to complex physical problems, especially the ones involving irregular geometries, the time step size of an explicit RK scheme is limited by the smallest grid size in the computational domain, demanding a high computational cost for obtaining time accurate numerical solutions in CAA. For computational efficiency, high-order RK method with nonuniform time step sizes on nonuniform meshes is developed in this paper. In order to ensure correct communication of solutions on the interfaces of grids with different time step sizes, the values at intermediate-stages of the Runge–Kutta time integration on the elements neighboring such interfaces are coupled with minimal dissipation and dispersion errors. Based upon the general form of an explicit p-stage RK scheme, a linear coupling procedure is proposed, with details on the coefficient matrices and execution steps at common time-levels and intermediate time-levels. Applications of the coupling procedures to Runge–Kutta schemes frequently used in simulation of fluid flow and acoustics are given, including the third-order TVD scheme, and low-storage low dissipation and low dispersion (LDDRK) schemes. In addition, an analysis on the stability of coupling procedures on a nonuniform grid is carried out. For validation, numerical experiments on one-dimensional and two-dimensional problems are presented to illustrate the stability and accuracy of proposed nonuniform time-step RKDG scheme, as well as the computational benefits it brings. Application to a one-dimensional nonlinear problem is also investigated.     

大模场面积光子晶体光纤耗散孤子锁模激光器

研制了一种基于掺Yb3+的双包层大模场面积偏振光子晶体光纤的耗散孤子锁模激光器.利用数值模拟分析了光纤激光器中耗散孤子动力学过程,与全正色散锁模激光器相比,脉冲窄化机理更加丰富,半导体可饱和吸收镜(SESAM)的非线性吸收,啁啾脉冲的光谱滤波以及光纤的增益色散同时起作用,这些因素使耗散孤子锁模更加容易实现,并且稳定运行.其中,光谱滤波的耗散过程是稳定锁模机制的主导因素,滤波片能够在频域和时域同时窄化脉冲,并且去除脉冲啁啾,限制脉冲在腔内始终小于1ps.在实验上实现了无色散补偿腔中直接输出脉冲宽度777fs,最高平均功率达到1W,重复频率48·27MHz,对应单脉冲能量20nJ的飞秒激光.     

高声压级时多孔金属板的吸声特性研究

针对高声压级下有限厚度多孔金属板在线性阻抗背衬条件下(背衬表面声压与声质点速度为线性关系)的吸声问题,提出了一个描述不同声压级下材料层法向吸声性能的一维模型,并给出求解材料层内部声质点速度的线化与差分方法,以预测多孔金属板在高声压级下的非线性吸声特性。在阻抗管中对两块多孔金属板进行了声学测试,得到了材料层法向表面阻抗和吸声系数随入射声压级变化的实验结果。研究表明:实验与理论预测符合良好,验证了模型与数值方法的正确性。本文所提原理和方法,可用于一般硬质多孔材料。      

A model for the propagation of nonlinear dispersive strain waves in a solid with defect clusters

A model for the propagation of nonlinear dispersive one-dimensional longitudinal strain waves in an isotropic solid with quadratic nonlinearity of elastic continuum is developed with taking into account the interaction with atomic defect clusters. The governing nonlinear dispersive-dissipative equation describing the evolution of longitudinal strain waves is derived. An approximate solution of the model equation was derived which describes asymmetrical distortion of geometry of the solitary strain wave due to the interaction between the strain field and the field of clusters. The contributions of the finiteness of the relaxation times of cluster-induced atomic defects to the linear elastic modulus and the lattice dissipation and dispersion parameters are determined. The amplitudes and width of the nonlinear waves depend on the elastic constants and on the properties of the defect subsystem (atomic defects, clusters) in the medium. The explicit expression is received for the sound velocity dependence upon the fractional cluster volume, which is in good agreement with experiment. The critical value of cluster volume fraction for the influence on the strain wave propagation is determined.     

Properties of plasmon-polariton modes in one-dimensional photonic superlattices made of Rudin-Shapiro bases

Theoretical investigations on the features of the plasmon-polariton frequency spectrum in one-dimensional photonic superlattices with Rudin-Shapiro dielectric layered unit cell are preformed. The plasmon polariton dispersion relations as well as the dependence on the angle of incidence of the Bragg and plasmon-polariton photonic bandgaps are reported. Results show that plasmon-polariton modes are robust even in the presence of rather large absorption. The outcome of the study shows that the reduced plasmon-polariton dispersion relation obtained within a Drude-like dielectric model points at a multifractal character under lossless conditions.     

Vortex rings and solitary waves in trapped Bose–Einstein condensates

We discuss nonlinear excitations in an atomic Bose–Einstein condensate which is trapped in a harmonic potential. We focus on axially symmetric solitary waves propagating along a cylindrical condensate. A quasi one-dimensional dark soliton is the only nonlinear mode for a condensate with weak interactions. For sufficiently strong interactions of experimental interest solitary waves are hybrids of one-dimensional dark solitons and three-dimensional vortex rings. The energy-momentum dispersion of these solitary waves exhibits characteristics similar to a mode proposed sometime ago by Lieb in a strictly 1D model, as well as some rotonlike features. We subsequently discuss interactions between solitary waves. Head-on collisions between dark solitons are elastic. Slow vortex rings collide elastically but faster ones form intermediate structures during collisions before they lose energy to the background fluid. Solitary waves and their interactions have been observed in experiments. However, some of their intriguing features still remain to be experimentally identified.     

Influence of the group-velocity on the pulse propagation in 1D silicon photonic crystal waveguides

We present a detailed analysis of the influence of the group velocity (GV) on the dynamics of optical pulses upon their propagation in one-dimensional photonic crystal waveguides (PhCW). The theoretical model used in our analysis incorporates the linear optical properties of the PhCW (GV dispersion and optical losses), free-carrier (FC) effects (FC dispersion and FC-induced optical losses) and nonlinear optical effects (Kerr nonlinearity and two-photon absorption). Our analysis shows that, unlike the case of uniform waveguides, the GV of the pulse, dispersion coefficients, and the waveguide nonlinear coefficient are periodic functions with respect to the propagation distance. We also demonstrate that linear and nonlinear effects depend on the group velocity, v _g , as v_g^-1v_{g}^{-1} and v_g^-2v_{g}^{-2}, respectively.     

Dynamic response of one-dimensional interacting fermions

We evaluate the dynamic structure factor S(q, omega) of interacting one-dimensional spinless fermions with a nonlinear dispersion relation. The combined effect of the nonlinear dispersion and of the interactions leads to new universal features of S(q, omega). The sharp peak S(q, omega) approximately q(delta(omega -uq), characteristic for the Tomonaga-Luttinger model, broadens up; for a fixed becomes finite at arbitrarily large . The main spectral weight, however, is confined to a narrow frequency interval of the width deltaomega approximately q(2)/m. At the boundaries of this interval the structure factor exhibits power-law singularities with exponents depending on the interaction strength and on the wave number q.