ZnSe－ZnS量子阱的光学非线性

半导体量子阱及超晶格材料具有室温激子效应以及强的光学非线性从而得到人们广泛的重视。利用半导体量子阱和超晶格可以制备出高速度、低闭值、小尺寸及室温工作的半导体激光器、光双稳器件等一系列光电子器件.     

Two-dimensional nonlinear beam shaping

We develop a technique for two-dimensional arbitrary wavefront shaping in quadratic nonlinear crystals by using binary nonlinear computer generated holograms. The method is based on transverse illumination of a binary modulated nonlinear photonic crystal, where the phase matching is partially satisfied through the nonlinear Raman-Nath process. We demonstrate the method experimentally showing a conversion of a fundamental Gaussian beam pump light into three Hermite-Gaussian and three Laguerre-Gaussian beams in the second harmonic. Two-dimensional binary nonlinear computer generated holograms open wide possibilities in the field of nonlinear beam shaping and mode conversion.     

Impact of Viscosity on DNA Dynamics

We study the influence of viscosity on DNA dynamics. By employing the nonlinear Peyrard-Bishop-Dauxois （PBD） model, it is shown that the DNA dynamics can be explained by a solution of a complex nonlinear Schrǒdinger equation （CNLSE）. This is the nonlinear Schrǒdinger equation （NLSE） with a nonlinear parameter being a complex number. We compare real and imaginary parts of this nonlinear parameter and show that the latter one should not be negligible, which means that the CNLSE should be solved numerically,     

Phase-matched nonlinear diffraction

We report on a new (to our knowledge) configuration incorporating both birefringence and quasi-phase-matching, enabling efficient phase-matched nonlinear diffraction in one-dimensional periodically poled nonlinear crystals. We demonstrate the method experimentally, showing an efficient nonlinear diffraction to the first few orders in two types of crystals, MgO doped congruent lithium niobate and congruent lithium niobate, and characterize its efficiency dependence on the fundamental power, the propagation angle, and the crystal temperature. This configuration can increase efficiencies observed in nonlinear diffraction experiments, enables ferroelectric domain characterization by nonlinear microscopy, and can be used to determine the duty cycles of periodically poled nonlinear crystals.     

A Nonlinear Landau-Zener Formula

We consider a system of two coupled ordinary differential equations which appears as an envelope equation in Bose–Einstein Condensation. This system can be viewed as a nonlinear extension of the celebrated model introduced by Landau and Zener. We show how the nonlinear system may appear from different physical models. We focus our attention on the large time behavior of the solution. We show the existence of a nonlinear scattering operator, which is reminiscent of long range scattering for the nonlinear Schrödinger equation, and which can be compared with its linear counterpart.     

New optical soliton solutions for nonlinear complex fractional Schrödinger equation via new auxiliary equation method and novel $$({G'}/{G})$$-expansion method

In this research, we apply two different techniques on nonlinear complex fractional nonlinear Schrödinger equation which is a very important model in fractional quantum mechanics. Nonlinear Schrödinger equation is one of the basic models in fibre optics and many other branches of science. We use the conformable fractional derivative to transfer the nonlinear real integer-order nonlinear Schrödinger equation to nonlinear complex fractional nonlinear Schrödinger equation. We apply new auxiliary equation method and novel \(\left( {G'}/{G}\right) \)-expansion method on nonlinear complex fractional Schrödinger equation to obtain new optical forms of solitary travelling wave solutions. We find many new optical solitary travelling wave solutions for this model. These solutions are obtained precisely and efficiency of the method can be demonstrated.     

Nonlinear photonics with metallic nanostructures on top of dielectrics and waveguides

We review recent experimental and theoretical studies of the ultrafast and nonlinear optical response of metallic nanostructures on top of dielectric substrates and slab waveguides where plasmon hybridization is a key ingredient. In a first three-pulse all-optical control experiment a hybrid plasmonic mode is turned on or off only a few tens of femtoseconds after its excitation. A second experiment concentrates on the origin of the nonlinear response in a metallo-dielectric photonic crystal structure. We show that the shape of the nonlinear optical spectra provides unambiguous information about the nonlinear optical contribution of the metallic as well as the dielectric part of the structure. Furthermore, we discuss the influence of slow-light on the nonlinear response. All experimental results agree perfectly with numerical scattering matrix calculations as well as simulations based on a classical harmonic oscillator model.     

Fiber laser mode locked by a Sagnac interferometer with nonlinear polarization rotation

We describe a new fiber laser configuration based on a nonlinear optical loop mirror with a symmetrical coupler, a quarter-wave retarder, and highly twisted, birefringent fiber in the loop. The nonlinear optical loop mirror configuration operates by nonlinear polarization rotation. We have achieved stable generation of subpicosecond pulses with milliwatts of average output power.     

Propagation of ultrashort pulses in a nonlinear long-period fiber grating

By solving a pair of normalized nonlinear coupled-mode equations, we analyze in detail the propagation of ultrashort optical pulses in a nonlinear long-period fiber grating and investigate the conditions for the grating to function as an optical limiter or a saturable absorber. We show that the function of the grating depends on whether the nonlinear effect counteracts or enhances the detuning effect, and the nonlinear effect can be weakened significantly by the group-delay difference between the core mode and the coupled cladding mode. We present simulation results to illustrate these effects and discuss the physical conditions required for an effective operation of a nonlinear long-period grating.     

非线性系数对超晶格透射的影响

研究了非线性系数对超晶格中波透射的影响.把非线性薛定谔方程转化成二阶差分方程，通过迭代此差分方程得到透射谱.透射谱显示非线性系数对波的透射有明显的调制作用. 关键词： 透射 非线性Kronig-Penny模型 非线性系数     

Nonlinear computer-generated holograms

We propose a novel technique for arbitrary wavefront shaping in quadratic nonlinear crystals by introducing the concept of computer-generated holograms (CGHs) into the nonlinear optical regime. We demonstrate the method experimentally showing a conversion of a fundamental Gaussian beam pump light into the first three Hermite-Gaussian beams at the second harmonic in a stoichiometric lithium tantalate nonlinear crystal, and we characterize its efficiency dependence on the fundamental power and the crystal temperature. Nonlinear CGHs open new possibilities in the fields of nonlinear beam shaping, mode conversion, and beam steering.     

Two-Grid Discretization Scheme for Nonlinear Reaction Diffusion Equation by Mixed Finite Element Methods

In this paper, we study an efficient scheme for nonlinear reaction-diffusion equations discretized by mixed finite element methods. We mainly concern the case when pressure coefficients and source terms are nonlinear. To linearize the nonlinear mixed equations, we use the two-grid algorithm. We first solve the nonlinear equations on the coarse grid, then, on the fine mesh, we solve a linearized problem using Newton iteration once. It is shown that the algorithm can achieve asymptotically optimal approximation as long as the mesh sizes satisfy $H =\mathcal{O}(h^{\frac{1}{2}})$. As a result, solving such a large class of nonlinear equations will not be much more difficult than getting solutions of one linearized system.     

Third-order nonlinear optical response of Au:SiO 2 thin films: Influence of gold nanoparticle concentration and morphologic parameters

We report a study on the third-order nonlinear optical properties of nanocomposite thin films composed of gold particles embedded in a silica host matrix. Samples of various metal volume fractions, ranging from 8 to 35%, are synthesized by the sputtering technique. Some of them are annealed. Nonlinear optical measurements, which are performed by using the z-scan technique, reveal both a very large nonlinear absorption and a weak nonlinear refraction close to the surface plasmon resonance frequency of the particles. We especially study the effect of the metal concentration and the influence of thermal treatment on the real and imaginary components of the third-order nonlinear susceptibility. Our results reveal that, as the metal concentration reaches a few percent, the mutual electromagnetic interactions between particles greatly enlarge the nonlinear optical response of the material and can not be neglected in the theoretical analysis. Moreover, the thermal treatment leads, for a given concentration, to a significant increase of the nonlinear response, which is ascribed to a modification of the material morphology. We finally point out that the material nonlinear properties are very sensitive to the incident wavelength through the local field enhancement phenomenon. Received 12 December 2001     

Comparison of Solutions of the General Nonlinear Amplitude Equation and a Modified Schrӧdinger Equation

We review the dynamics of narrow and broad-band optical pulses in nonlinear dispersive media. A major problem that arises during the development of theoretical models, which describe accurately and correctly the behavior of these pulses, is the limited application of the nonlinear Schr?dinger equation. It describes very well the evolution of nanosecond and picosecond laser pulses. However, when we investigate the propagation of femtosecond and attosecond light pulses, it is necessary to use the more general nonlinear amplitude equation. We show that in this equation two additional terms are included and they have a significant impact on the phase of the pulse. We perform numerical simulations and show the temporal shift of the position of fundamental solitons. This effect depends on the initial duration of the laser pulses. To clarify the influence of the additional terms on the parameters of the optical pulses, we consider the nonlinear amplitude equation, which is a modified nonlinear Schr?dinger equation.     

Compensation of phase-to-amplitude modulation conversion in a complete frequency conversion system with an all-fiber system

We report on an experimental demonstration of linear precompensation of nonlinear phase and amplitude transfer functions. We show the effective compensation with a linear all-fiber system of phase-to-amplitude modulation conversion due to a complete frequency conversion system including plane gratings and a nonlinear crystal.     

BDF-like methods for nonlinear dynamic analysis

We present several time integration algorithms of second-order accuracy that are numerically simple and effective for nonlinear elastodynamic problems. These algorithms are based on a general four-step scheme that has a resemblance to the backward differentiation formulas. We also present an extension to the composite strategy of the Bathe method. Appropriate values for the algorithmic parameters are determined based on considerations of stability and dissipativity, and less dissipative members of each algorithm have been identified. We demonstrate the convergence characteristics of the proposed algorithms with a nonlinear dynamic problem having analytic solutions, and test these algorithms with several three-dimensional nonlinear elastodynamic problems involving large deformations and rotations, employing St. Venant-Kirchhoff and compressible Neo-Hookean hyperelastic material models. These tests show that stable computations are obtained with the proposed algorithms in nonlinear situations where the trapezoidal rule encounters a well-known instability.     

Enhancement of nonlinear susceptibility in a four-level tripod scheme

We propose a scheme for the enhancement of nonlinear susceptibility in a four-level tripod-type atomic system in the presence of a microwave field. With a microwave field, nonlinear susceptibility can be enhanced. Nonlinearity can also be ulteriorly enhanced by controlling the coupling field under the optimal intensity of the microwave field. The physical mechanism of the obtained giant nonlinear susceptibility is mainly based on interactions between microwave field and coupling fields. We present a physical understanding of our numerical results using a dressed-state approach and an analytical explanation.     

Testing Born-Infeld electrodynamics in waveguides

Waveguides can be employed to test nonlinear effects in electrodynamics. We solve Born-Infeld equations for TE waves in a rectangular waveguide. We show that the energy velocity acquires a dependence on the amplitude, and harmonic components appear as a consequence of the nonlinear behavior.     

Strongly nonlinear shear perturbations in discrete and continuous cubic nonlinear systems

Systems with constraints, the masses in which move only along guides, can execute strongly nonlinear vibrations. This means that nonlinear phenomena manifest themselves at arbitrary small deviations from equilibrium. The form of vibrations of a single mass is described by elliptical Jacobi functions. The spectrum of these vibrations is found. With an increase in amplitude, the period of vibrations decreases. We deduce equations of strongly nonlinear vibrations of a chain of connected masses. In the continuum limit, we obtain a new nonlinear equation in partial derivatives. We devise transformation of variables leading to linearization of this equation. We implemented a factorization procedure that decreases the order of the equation in partial derivatives from second to first. Exact solutions to the first-order equation describe the slow evolution of the displacement profile in a distributed system. In the absence of preliminary tension of elastic elements in the continued model, traveling waves cannot be achieved; however, time-oscillating solutions like standing waves are possible. We obtain an equation for a field of strongly nonlinear deformations. Its exact solution describes periodic movement in time and space. As well, the period of time oscillations decreases with an increase in amplitude, and the spatial period, in contrast, increases. The product of the vibration frequency multiplied by the spatial period is a constant that depends on the deformation energy. We propose a scheme of the mechanical system producing strongly nonlinear torsional vibrations. We experimentally measured the period of torsional vibrations of a single disc. We show that with an increase in amplitude in the process of vibration attenuation, an increase in the period occurs, which agrees with calculations. We measure the shapes of nonlinear vibrations of a chain of connected discs. A strongly nonlinear behavior of the chain is observed.