三阶非线性聚合物光波导研究

以三阶克尔型非线性波导为例,利用雅可比椭圆函数的特性,定义了一种新颖的雅可比椭圆余切振幅函数,以此建立了类似线性的在非线性条件下的色散关系,使形式简化、物理意义清晰。并利用这一关系分析了该情况下的模式特性和场特性。     

Gap solitons in metamaterials

Electromagnetic localization and the existence of gap solitons in nonlinear metamaterials, which exhibit a stop band in their linear spectral response, is theoretically investigated. For a self-focusing Kerr nonlinearity, the equation for the electric field envelope with carrier frequency in the stop band—where the magnetic permeability µ(?) is positive and the dielectric permittivity ε(?) is negative—is described by a nonlinear Klein-Gordon equation with a dispersive nonlinear term. A family of standing and moving localized waves for both electric and magnetic fields is found, and the role played by the nonlinear dispersive term on solitary wave stability is discussed.     

Localization in the model of contacting media with specific nonlinearity and interface interaction

In this paper, we consider the new model of nonlinear contacting media based on nonlinear Schrodinger equation with point potential and term, which is depended stepwise on field amplitude. Such a model theoretically describes a change in properties of the boundary regions along the interface between a Kerr-type crystal with cubic nonlinearity and a nonlinear medium characterized by abruptly change in dielectric constant depending on field amplitude. The short-range local interaction between wave and interface is taken into account by point potential in nonlinear Schrodinger equation. We obtain two new types of localized states characterized by composite structure consisting of three parts of the field distributions. We find exact and approximate solutions of dispersion equations. We described new properties of the spectrum of localized states arising as a result of the interaction of the wave with the interface and the presence of threshold field of the switching between the medium constants. All results are obtained in an analytical form. The proposed theory can be used to describe the propagation features of intense light beams localized along media interfaces in nonlinear optics, and to describe Bose-Einstein condensates with cubic nonlinearity.     

利用暗态共振之间的相互作用提高Kerr非线性

分析了利用双暗态共振之间的相互作用提高Kerr 非线性的方案,采用微扰理论和密度矩阵方法导出三阶极化率实部随外加相干驱动场失谐量变化的关系.结果表明,随着相干驱动场失谐量的增加,双暗态共振之间干涉使得Kerr非线性的最大值也随之变大且逐渐进入电磁感应透明窗口,并使用缀饰态理论对其产生的机制给予相应的解释.证明了在具有双暗态共振的四能级原子系统中获得无吸收巨Kerr非线性实现的可行性.     

克尔型介质平板波导中的弱非线性横向电场波

对芯子为克尔型非线性介质、覆盖层和衬底为线性介质的平板波导，在弱非线性近似下，导出了这类波导横向电场波满足的色散方程和场分布，其物理意义清晰，且大大降低了数值计算的强度。     

Surface waves at the interface between a dielectric and a topological insulator

Surface waves that propagate along the interface between an isotropic linear or nonlinear (of the Kerr type) dielectric and a topological insulator have been studied theoretically. A dispersion relation for surface waves, which are represented by superpositions of TE and TM waves, has been obtained. This hybridization occurs because, upon passage through the interface, the polarization of a surface wave changes, which is caused by an induced surface current (which is transverse to the electric field vector of the wave). The surface current of this kind is characteristic of topological insulators. Expressions for the energy flux transferred by a surface wave have been given.     

Scattering and Focusing Effect of Stepped Index Luneberg Lens

Focusing effect of the Luneberg lens for wide bandwidth is studied with emphasis on experiment. A model experiment was performed using a stepped index (six-layer) spherical lens. The total electric field amplitude along the propagation axis has the maximum value (focal point) on the surface of the lens. As the size parameter ka (k: wave number, a: radius of the sphere) is larger, the electric field amplitude at the focal point becomes larger. These results correspond with the power of convergence (focusing effect) by the Luneberg lens. The experimental values are in a good agreement with theoretical ones that are calculated using homogeneous multilayered approximate method. They are also in a good agreement with the results using exact solutions for the inhomogeneous dielectric sphere (the ideal Luneberg lens). Therefore, it is found that the six-layer spherical lens has the optimum variation of dielectric constants for the Luneberg lens and maintains focusing effect for wide bandwidth.     

Polymeric photorefractive surface waves

We theoretically studied photorefractive surface waves supported by polymers with orientationally enhanced photorefractive effect. We find that the orientational enhancement and the dependency of the quantum efficiency of generating mobile holes on the electric field make the diffusion nonlinearity in photorefractive polymers dependent not on only the variation of light intensity but also on external electric field, which is very different from the external electric field independent diffusion nonlinearity in inorganic photorefractive crystals. Consequently the profile, frequency and especially the penetration depth of polymeric photorefractive surface waves strongly depend on external electric field, which makes it more controllable than that in photorefractive inorganic crystals. The stability of polymeric photorefractive surface waves, the effects of birefringence component and electro-optic component of orientationally enhanced photorefractive nonlinearity on the formation of x or y-polarized polymeric photorefractive surface waves are also discussed.     

Asymptotic analysis of nonlinear nonaxisymmetric waves on the surface of a neutral dielectric jet in a longitudinal electrostatic field

The problem of calculation of finite-amplitude waves on the cylindrical surface of an ideal incompressible dielectric liquid jet in a uniform electrostatic field collinear to the unperturbed jet axis is solved using a second-order asymptotic analytic procedure in ratio of the wave amplitude to the jet radius. Nonlinear corrections to the jet profile, velocity field potential, and electrostatic potentials inside and outside the jet are of resonant nature. The degenerate resonant interaction between the wave determining the initial strain and the waves excited due to nonlinearity of the hydrodynamic equations can take place for waves with different symmetries (different azimuth numbers).     

Diffraction of surface waves in metals and metamaterials

The diffraction of pulsed electromagnetic beams propagating along the interface between a dielectric and a metal or a metamaterial is investigated. The equation for slowly varying amplitudes of confined surface waves with a finite cross section size and duration is derived and solved. The dynamics of the diffractive-dispersive broadening of pulsed beams are examined. The conditions of surface dark soliton existence in media with Kerr nonlinearity are obtained.     

Surface plasmon polariton at the interface of dielectric and graphene medium using Kerr effect

We theoretically investigate the control of surface plasmon polariton(SPP) generated at the interface of dielectric and graphene medium under Kerr nonlinearity. The controlled Kerr nonlinear signal of probe light beam in a dielectric medium is used to generate SPPs at the interface of dielectric and graphene medium. The positive, negative absorption, and dispersion properties of SPPs are modified and controlled by the control and Kerr fields. A large amplification(negative absorption) is noted for SPPs under the Kerr nonlinearity. The normal/anomalous slope of dispersion and propagation length of SPPs is modified and controlled with Kerr nonlinearity. This leads to significant variation in slow and fast SPP propagation. The controlled slow and fast SPP propagation may predict significant applications in nano-photonics, optical tweezers, photovoltaic devices, plasmonster, and sensing technology.     

Peregrine solitons and algebraic soliton pairs in Kerr media considering space–time correction

Exact unified rational solutions describing a family of Peregrine solitons as well as related algebraic soliton pairs in either self-focusing or self-defocusing Kerr media are presented, with distinct defining regimes and an explicit relationship for those of opposite nonlinearity. The active role of the space–time correction effect that plays in these soliton species is highlighted, leading to unique dynamics such as the persistence of Peregrine solitons in a defocusing Kerr medium, the availability of giant peak amplitude for the bright–bright soliton pair, and the existence of so-called bright–dark soliton pair. The evolution dynamics of the algebraic two-soliton state toward a spliced single soliton is also discussed.     

附加克尔介质Jaynes－Cummings模型的场熵演化

研究了附加克尔（Ｋｅｒｒ）介质Ｊａｙｎｅｓ－Ｃｕｍｍｉｎｇｓ（Ｊ－Ｃ）模型场熵演化的动力学特性，讨论了克尔介质非线性相互作用以及失谐量对场熵演化的影响．     

Modelling of optical Kerr effects on the static and dynamic behaviors of quantum cascade laser

The effect of optical Kerr nonlinearity on the static and dynamic behaviors of quantum cascade laser operating in the mid-infrared is theoretically investigated. Our model is based on three-level rate equations including the dependence of the loss on photon number in the cavity. The optical stability domain that allows for the determination of current injection is derived within the premises of our model. The analytical solutions of eigenvalue equation allowing the investigation of stability analysis are obtained. Furthermore, nonlinear effects influence significantly the dynamics of photons in cavity and electrons in the upper laser level.     

Convective amplification of parametrically generated acoustic wave in a piezoelectric semiconductor plasma

Using hydrodynamic model of semiconductor plasmas and coupled-mode theory of interacting waves, we have analytically investigated parametric interaction in a magnetised piezoelectric semiconductor plasma in non-relativistic domain. The temperature dependence of momentum transfer collision frequency of electrons due to their heating by the pump is assumed to induce nonlinearity in the medium. We have derived a dispersion relation which finally gives four unstable acoustic modes; two forward amplifying modes and two backscattered attenuating modes. We have also obtained an expression for the critical pump amplitude ( ) at and around which gains and phase velocities of amplifying acoustic modes become least dependent on the pump amplitude and static magnetic field . The required can be readily obtained from a pulsed 10.6 μm CO₂ laser. The magnetic field is found to shift the critical point towards lower pump amplitudes. Received 5 September 2000 and Received in final form 5 March 2001     

非线性Jaynes-Cummings模型的动力学特性

运用密度算符间的距离研究了附加克尔介质依赖强度耦合Jaynes-Cummings模型中原子，场及整个量子系统态的演化规律。在与附加克尔介质单光子Jaynes-Cummings模型相比较的基础上。详细讨论了克尔介质非线性相互作用及初始相干光场的强弱对该模型动力学行为的影响。     

Spatiotemporal instability in dispersive nonlinear Kerr medium with a finite response time

We investigated the spatiotemporal modulation instability (MI) in a medium with a non-instantaneous Kerr response in which the nonlinear contribution to the refractive index is governed by a relaxing Debye type equation. The expression for the MI gain spectrum in non-instantaneous Kerr medium is obtained, which clearly reveals the influence of the finite time of the nonlinear response (relaxation effect) on the spatiotemporal MI. It is shown that, due to the relaxation effect, the spatiotemporal MI can appear for the case of anomalous dispersion and defocusing nonlinearity, while it cannot appear in instantaneous Kerr medium for the same case, and a new MI gain spectrum appears, adding to the conventional MI gain spectrum similar to that in an instantaneous Ker medium. In addition, the bandwidth of MI gain spectrum is extended and the maximum MI gain is reduced with increasing of the relaxation time. Interestingly, spatiotemporal MI can appear for any spatial frequencies in non-instantaneous Kerr medium for any combination of dispersion and nonlinearity. We have performed an experiment of MI in carbon disulfide (CS₂), a typical non-instantaneous Kerr medium, which shows quantitative agreement with the theoretical analyses.     

Exact periodic and explicit solutions of the conformable time fractional Ginzburg Landau equation

The Ginzburg–Landau (GL) equation is one of the most important nonlinear equation in physics. It is used to model a vast variety of phenomena in physics like nonlinear waves, second order phase transitions, Bose–Einstein condensation, superfluidity, superconductivity, liquid crystals and strings in field theory. In this work, new exact, periodic and explicit solutions of a time fractional GL equation involving conformable fractional derivatives with Kerr law nonlinearity have been found. The Kerr law nonlinearity is due to the non-harmonic motion of electrons under the influence of an applied field. To determine the solution of the model, we have employed a couple of integration algorithms, solitary wave ansatz and \(\exp (-\varphi ({\chi }\))) methods. New periodic and hyperbolic soliton solutions are found as well as the constraint condition for the existence of the solution.     

A waveguide amplifier based on a counterdirectional coupler

The propagation of continuous-wave radiation in tunnel-coupled waveguides, one of which is characterized by a negative refraction and linear losses while the other is made of an ordinary dielectric and represents a linear amplifier, is analyzed theoretically. We found that, in the case of linear waveguides, the losses can be compensated at certain values of the pump-wave amplitude depending on values of the gain and loss coefficients in the corresponding waveguides, resulting in the amplification of radiation at the output of the waveguide with the negative refraction. The Kerr nonlinearity of the amplifying waveguide prevents the compensation of losses due to the violation of the phase-matching condition between the coupled waves in a counterdirectional coupler.     

Interaction of strongly nonlinear waves on the free surface of a dielectric liquid in a horizontal electric field

The nonlinear dynamics of the free surface of an ideal dielectric liquid with a large relative permittivity in a strong horizontal electric field has been considered. It has been demonstrated that the interaction between oppositely propagating solitary waves in arbitrary geometry is elastic: they conserve their energy and momentum. The interaction between waves has been numerically simulated with the use of conformal variables. It has been shown that the interaction deforms the waves; this effect is weak for waves with a relatively small amplitude: deformation for oppositely propagating waves with the identical shape is determined by the fourth power of their amplitude. At multiple collisions of strongly nonlinear waves, a tendency to the formation of singularities, i.e., points with a high energy density of the field, is observed.