Propagation of a soliton-like pulse in a weakly nonlinear medium

Numerical methods are used to study the decay dynamics of a soliton-like signal in a medium with a cubic nonlinearity (using the nonlinear Shrödinger equation). We consider the influence of the initial pulse area, shape, and random modulations in its amplitude and phase on the decay process, as well as the effects of absorption and pumping in the medium.V. D. Kuznetsov Physico-Technical Institute, Tomsk State University, Siberia. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 4, pp. 36–40, April, 1995.     

Optical limiting and pulse reshaping of picosecond pulse trains by fullerene C60

We present a dynamical theory of nonlinear absorption and propagation of a laser pulse train that contains 20 subpulses with an individual pulse width of 100 ps. It is shown that the accumulative nonlinearity and the reverse saturation absorption play important roles in the optical limiting performance and pulse shaping. When the incident field is not too strong, the population transfer reveals a slow response process, and the periodic sequence of short light pulses can be regarded as a continuous long pulse. The general theory is applied to fullerence C₆₀, which is a popular reverse saturable absorption material and a good limiter because of its larger excited-state absorption cross-section compared with that of the ground state. The propagation of the front subpulses is mainly affected by the linear transition between the ground state and the first excited singlet state, while the latter subpulses are attenuated by the excited-state absorption. Moreover, these two different kinds of absorption mechanisms result in different radial distributions for different subpulses. The pulse propagation is studied by solving numerically the coupled rate equations and the propagation equation of the optical pulse intensity, using experimental parameters as input. We suggest a new method to measure the lifetime of the triplet state.     

Third-Order Nonlinear Optical Properties of a Series of Polythiophenes

The third-order nonlinear optical properties of a series of polythiophenes are investigated with the Z-scan method under picosecond pulse laser irradiation at 532nm. The copolymers exhibit a good nonlinear response： large nonlinear refraction coefficients without nonlinear absorption. The signs of nonlinear refraction coefficients are positive, which are opposite to the negative signs of the polythiophene reported before. The mechanism accounting for the process of nonlinear refraction under pulse laser excitation is analyzed from the viewpoint of the electrondonor/acceptor units of polythiophenes. Moreover, changes of nonlinearity according to the lengths of main chains in polythiophene molecules are discussed.     

Simulation of nanosecond square pulse fiber laser based on nonlinear amplifying loop mirror

A nanosecond square pulse fiber laser based on the nonlinear amplifying loop mirror(NALM) is numeri-cally analyzed by the nonlinear Schrdinger equation. The fiber cavity with a NALM has a tendency to provide pulse shaping effect with nonlinearity increasing in the NALM,and the nanosecond square pulse is generated by the pulse shaping effect. The numerical results show that the stable square pulse can be obtained when the parameters of the NALM are chosen appropriately. The generated square pulses have flat top and no internal structure.     

五阶非线性作用下光纤中类明孤子运动方程的变分研究

当考虑到五阶非线性对光脉冲传输的影响时, 光纤中类明孤子的传输服从含五阶非线性修正项的非线性Schrdinger方程。利用何氏半反推法建立该类明孤子运动方程的变分形式, 然后应用何氏变分法导出该方程基态孤子解的双曲正割表达式。同时, 受何氏指数函数方法的启发, 建立了一种新的高斯表达式。一方面, 基于得到的显式表达式相关学者可进一步研究五阶非线性对光脉冲传输的影响。另一方面, 该求解过程也进一步显示了用何氏变分法求解数学物理中非线性发展方程的简洁有效性。     

Pulse Propagation with Self-Phase Modulation in Nonlinear Chiral Fiber and Its Applications

From Maxwell's equations and Post's formalism,a generalized chiral nonlinear Schrodinger equation(CNLSE) is obtained for the nonlinear chiral fiber.This equation governs light transmission through a dispersive nonlinear chiral fiber with joint action of chirality in linear and nonlinear ways.The generalized CNLSE shows a modulation of chirality to the effect of attenuation and nonlinearity compared with the case for a conventional fiber.Simulations based on the split-step beam propagation method reveal the role of nonlinearity with cooperation to chirality playing in the pulse evolution.By adjusting its strength the role of chirality in forming solitons is demonstrated for a given circularly polarized component.The application of nonlinear optical rotation is also discussed in an all-optical switch.     

Amplitude degradation of time-reversed pulses in nonlinear absorbing thermoviscous fluids

The linear wave equation in a lossless medium is time reversible, i.e., every solution p(x, t) has a temporal mirror solution p(x, -t). Analysis shows that time reversal also holds for the lossless nonlinear wave equation. In both cases, time-reversal invariance is violated when losses are present. For nonlinear propagation loses cannot normally be ignored; they are necessary to prevent the occurrence of multivalued waveforms. Further analysis of the nonlinear wave equation shows that amplification of a time-reversed pulse at the array elements also leads to a violation of time reversal even for lossless nonlinear acoustics. Numerical simulations are used to illustrate the effect of nonlinearity on the ability of a time-reversal system to effectively focus on a target in an absorbing fluid medium. We consider both the amplitude and arrival time of retrodirected pulses. The numerical results confirm that both shock generation (with the accompanying absorption) and amplification at the array, adversely affect the ability of a time-reversal system to form strong retrodirective sound fields.     

Modulational instability in the cubic-quintic nonlinear Schrödinger equation through the variational approach

The dynamics of nonlinear pulse propagation in an average dispersion-managed soliton system is governed by a constant coefficient nonlinear Schrödinger (NLS) equation. For a special set of parameters the constant coefficient NLS equation is completely integrable. The same constant coefficient NLS equation is also applicable to optical fiber systems with phase modulation or pulse compression. We also investigate MI arising in the cubic-quintic nonlinear Schrödinger equation for ultrashort pulse propagation. Within this framework, we derive ordinary differential equations (ODE’s) for the time evolution of the amplitude and phase of modulation perturbations. Analyzing the ensuing ODE’s, we derive the classical modulational instability criterion and identify it numerically. We show that the quintic nonlinearity can be essential for the stability of solutions. The evolutions of modulational instability are numerically investigated and the effects of the quintic nonlinearity on the evolutions are examined. Numerical simulations demonstrate the validity of the analytical predictions.     

Diffuse X-ray scattering near a two-dimensional solid–liquid phase transition at the <Emphasis Type="Italic">n</Emphasis>-hexane–water interface

Spatial profiles of single-shot microcraters produced by tightly focused femtosecond laser pulses with variable pulse energies are measured by means of a laser confocal microscope. Dependences of crater depth on laser intensity at different pulse energies appear as overlapping saturating curves with the same threshold, indicating the presence of nonlinear absorption and absence of nonlocal ablation effects. A monotonic twofold increase in absorption nonlinearity is related to the transition from minor defect-band absorption to fundamental band-to-band absorption.     

Line narrowing and hole burning within the homogeneous linewidth: a new wave-mixing effect in two-level systems

The interaction of strong low-area pulses with two-level systems shows absorption line narrowing and hole burning within the homogeneous linewidth as a result of nonlinear wave mixing. The wave mixing results from the two-level electronic saturation nonlinearity and occurs, depending on the sign of the pulse area, as a strong absorption enhancement or gain at the transition frequency of the two-level system for resonant excitation.     

Nonlinear laser amplifier with a suppressed level of quantum noise on the basis of a Bose condensate for 23Na atoms

Based on advanced quantum theory for the Λ-scheme nonlinear interaction of optical fields in atomic Bose-Einstein condensate, the regimes of giant negative nonlinearity and absorption coefficients have been obtained for a probe light pulse. The nonlinear laser amplifier setup (under the Λ-scheme realization) for generation of the quadrature-squeezed light is presented The text was submitted by the authors in English.     

Investigation of self-focusing a Gaussian laser pulse in a weakly relativistic and ponderomotive regime inside a collisionless warm quantum plasma

This article investigates nonlinear self-focusing of an intense right hand circularly polarized Gaussian profile laser pulse in a weakly relativistic and ponderomotive regime inside a collisionless and unmagnetized warm quantum plasma. The nonlinear propagation equation for laser pulse in plasma has been derived. Then, the evolution differential equation for laser spot-size was obtained with considering the parabolic equation approach under the Wentzel-Kramers-Brillouin and paraxial ray approximations. This differential equation was solved numerically by fourth-order Runge-Kutta method. It is shown that our solution confirms the results of the self-focusing of the laser pulse in a weakly relativistic ponderomotive regime in cold quantum plasma in extreme conditions. Numerical results indicate that self-focusing of the laser pulse in the presence of relativistic and ponderomotive nonlinearity inside warm quantum plasma is improved in comparison with relativistic and ponderomotive cold quantum plasma.     

Control of laser pulse parameters in a cavity with a thermal-nonlinearity shutter

The light pulse generation by a laser controlled by shutter from a finite-thickness absorbing layer with thermal nonlinearity has been studied theoretically. The layer placed in the cavity is oriented with respect to the mirror so that conditions for nonlinear total internal reflection of generated radiation are created. In the plane-wave approximation, a self-consistent system of nonlinear truncated equations for the field amplitudes together with constitutive equations has been obtained. Numerical simulation with the use of the obtained system has shown that it is possible to control the form and duration of the generated pulse by varying the absorption coefficient of the nonlinear medium and the angle of incidence on the absorbing layer, as well as the layer thickness.Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 71, No. 6, pp. 771–777, November–December, 2004.This revised version was published online in April 2005 with a corrected cover date.     

One-dimensional EM solitons in ultrashort intense laser pulse-partially stripped plasmas

The one-dimensional electromagnetic (EM) envelope solitons in ultrashort intense laser pulse-partially stripped plasmas were discussed based on the wave equation of intense laser pulse propagating in partially stripped plasmas. Under the weakly relativistic assumption, a modified nonlinear Schrödinger (NLS) equation describing the evolution of the EM field was derived. The analytical analysis shows that in the ultra-short broad beam limits, the relativistic nonlinearity and striction nonlinearity cancel each other, and a one-dimensional laser pulse envelope soliton can be formed only due to the polarization nonlinearity. The relationship between the characteristics of soliton and the parameters of laser pulse and partially stripped plasmas was discussed by numerical analysis.     

Nonlinear wave processes in porous waterlike media containing a system of capillaries partially filled with a viscous liquid

A nonlinear dynamic state equation of waterlike porous material that contains a system of cylindrical capillaries partially filled with viscous liquid was received. It is shown that an acoustic nonlinearity of such media contains the relaxation elastic and inelastic components due to the nonlinear dependence of the capillary and viscous pressure in fluid on the capillary diameter. For the medium, theoretical study of such nonlinear phenomena as generation of the second harmonic and a difference frequency wave, self-demodulation of high-frequency pulses as well as the change in the propagation velocity and absorption coefficient of a test wave being under an action of static loading have been carried out. The frequency dependences of medium nonlinearity parameters for these processes were determined.     

五阶非线性光纤中连续谱相位扰动下的光传输与脉冲串产生

根据包含五阶非线性的扩展非线性薛定谔方程,数值研究了高斯型连续谱相位扰动而不是传统单色扰动下基于调制不稳定性的高重复率脉冲串产生.结果表明:脉冲串也能像传统情形那样形成,但却呈现出不同的特性.如脉冲数目有限,且各脉冲的高度、强度及间距不等.脉冲数目随传输距离增加而增加.而五阶非线性能使脉冲宽度和间距变小因而有利于高重复率脉冲串产生,负五阶非线性则相反.对脉冲串形成过程中演变啁啾的数值计算表明,啁啾及其随距离的变化都是高度非单调的,五阶非线性将改变啁啾的范围和量值.     

Self-action of short pulses in nonhomogeneous graded-index light guides

The weak nonlinear process of propagation of short pulses in graded-index light guides that are weakly inhomogeneous in the longitudinal direction and slightly bent is investigated by means of a consistent asymptotic method. The process as a whole is proved to be three-scale in respect to a small parameter related to the magnitude of nonlinearity. The phase of the most rapid process and transverse distribution of the wave field are expressed explicitly in terms of a certain Sturm-Liouville problem. For a pulse envelope the nonlinear Schrödinger equation is derived, its coefficients depending on the longitudinal coordinate. The existence of a guaranteed interval of conservation of concentration of the pulse envelope is ascertained. For a class of very smooth inhomogeneities formulae are obtained describing the variation of the amplitude and width of the pulse during propagation.     

Analytic study on solitons in the nonlinear fibers with time-modulated parabolic law nonlinearity and Raman effect

In this paper, the nonlinear optical transmission equation with time-modulated cubic–quintic nonlinearity and Raman effect term, describing the ultrashort optical pulse propagate along the nonlinear media, has been studied by using the non-auto-Bäcklund transformation (NATB) and subsidiary ordinary differential equation (sub-ODE) expansion method. As a result, analytical solution expressions to that equation are obtained. Finally, two simple examples, including systems with the external potential in exponential form and periodic form, are provided to show the solution steps.     

Self distortion of a Gaussian electromagnetic pulse in a plasma

On the basis of perturbation theory, the phenomenon of nonlinear self distortion of an electromagnetic pulse (Gaussian in time) in a collisional plasma has been studied. The nonlinearity appears through the modulation of electron collision frequency by the power absorption from the wave. At moderate energies of the pulse, considerable distortion in the amplitude envelope has been predicted.     

Nonlinear Schrödinger equations under random nonlinearity management

We consider effects of random time modulation of the nonlinearity coefficient on the dynamics of one- and two-dimensional (1D and 2D) solitary waves in the nonlinear Schrödinger equation (NLSE). In particular, the cases of a single Gaussian random variable, and a temporally correlated Gaussian process are considered. In the 1D case, we demonstrate the robustness of solitons against the random nonlinearity management. In the 2D case, the share (percentage) of realizations that lead to collapse of a localized pulse is computed, in order to quantify the effect of the randomness in preventing the collapse. Dependences of this share on the mean value, standard deviation, and correlation length of the random process are obtained, and, whenever possible, compared to analytical predictions.