Passive nonlinear reshaping towards parabolic pulses in the steady-state regime in optical fibers

The passive nonlinear reshaping in normally dispersive optical fibers in the steady-state regime is studied numerically. It is found that normal dispersion and self-phase modulation are able to provide pulse reshaping towards a parabolic pulse profile at the distances exceeding the optical wave breaking length. However, as compared to the similariton formation in active fibers the resulted pulse shape in passive fibers is strongly depended on the initial pulse parameters and nonlinear and dispersive fiber properties as well. The influence of initial pulse shape, initial chirp, third-order dispersion and loss on the parabolic pulse formation is studied consistently, and estimation of practical conditions which are needed for parabolic pulses formation in a passive fiber is provided.     

Semiclassical trajectory-coherent states of the nonlinear Schrödinger equation with unitary nonlinearity

Semiclassically concentrated states of the nonlinear Schrödinger equation (NLSE) with unitary nonlinearity, representing multidimensional localized wave packets, are constructed on the basis of the Maslov complex germ theory. A system of ordinary differential equations of Hamilton-Ehrenfest (HE) type, describing the motion of the wave packet centroid, is derived. The structure of the HE system is strongly influenced by the initial conditions of the Cauchy problem for the NLSE. Wave packets of Gaussian type are constructed in an explicit form. Possible use of the solutions constructed in the problem of optical pulse propagation in a nonlinear medium with nonstationary dispersion is discussed.     

Modulation instability in systems of coupled waves with nonlinearity dispersion

Conditions for the appearance of modulation instability of an optical wave packet formed by one or two unidirectional strongly interacting waves are studied taking into account the influence of the temporal dispersion of a nonlinear response of the medium on this process. The regions of values of the frequency, input radiation intensity, and dispersion parameters in which the wave perturbations are increased are found. It is shown that the initial conditions for excitation of optical fibers of this type significantly affect the dynamics of the modulation instability.     

Pulse dynamics in inhomogeneous optically coupled amplifying optical fibers with high-order dispersion effects taken into account

The evolution of the envelope of a two-mode wave packet in an inhomogeneous-over-length amplifying optical fiber is analyzed with the third-order dispersion effects taken into account, the presence of which leads to modulations of one or both edges of the wave packet. High degrees of compression of the pulse and the complete suppression of oscillations of its time envelope can be attained by an appropriate choice of the type of inhomogeneity of the dispersion parameters.     

Parametric interaction and compression of optical pulses in field of high-power pump wave

It is shown that, in the undepleted pump approximation, the nonlinear problem of the three-wave parametric interaction under the conditions of phase mismatch can be reduced to a problem of linear interaction of the signal and idle waves with a strong low-frequency pump wave. The whole wave packet formed by the two waves breaks down to partial pulses whose dynamics is controlled by effective dispersion parameters. This can be accompanied by the compression of either one of the pulses that comprises the wave packet or the whole wave packet.     

Short optical solitons in fibers

The dynamics of short (of the order of a few wave periods) intense optical pulses and interaction of short optical solitons in fibers are considered within the framework of the third-order nonlinear Schrodinger equation. It is shown that an initial pulse tends to one or a few short solitons plus a linear quasiperiodic wave when the third-order linear dispersion and nonlinear dispersion have parameters of the same sign. The number and parameters of the solitons depend on the magnitudes of initial pulse parameters. Interaction of short optical solitons having different amplitudes is accompanied by radiation of part of the wave field from the area of interaction, by an increase of the soliton with larger amplitude, and a decrease of the soliton with a smaller one. (c) 2000 American Institute of Physics.     

Dark-in-the-Bright solitary wave solution of higher-order nonlinear Schrödinger equation with non-Kerr terms

We present new type of Dark-in-the-Bright solution also called dipole soliton for the higher order nonlinear Schrödinger (HNLS) equation with non-Kerr nonlinearity under some parametric conditions and subject to constraint relation among the parameters in optical context. This equation could be a model equation of pulse propagation beyond ultrashort range in optical communication systems. The solitary wave solution is composed of the product of bright and dark solitary waves. This type of pulse shape to be formed both the group velocity dispersion and third-order dispersion must be compensated. We also investigated the stability of the solitary wave solution under some initial perturbation on the parametric conditions. We have shown that the shape of pulse remains unchanged up to 20 normalized lengths even under some very small violation in parametric conditions.     

On the propagation of a light pulse in the “transparency window” of a medium with population inversion

The propagation of a light pulse through a layer of a substance with population inversion and, correspondingly, with an anomalous dispersion in the transparency range is considered. It is shown that, when the wave packet approaches the layer of the substance with a strong anomalous dispersion, two additional wave packets arise at the rear boundary of the layer. One of these packets has a negative energy and moves in the layer from its rear to the front boundary, while the other packet moves away from the rear boundary of the layer into a vacuum. As the initial wave packet comes into contact with the front boundary of the layer of the substance, it meets the packet of the negative energy. As a result, the two packets annihilate one another, after which only one packet remains, which moves away from the layer.     

Dynamics of a two-wave packet in a nonlinear optical fiber at detuning from phase matching

The effect of detuning from phase matching on the dynamics of a wave packet consisting of two unidirectional strongly interacting modes in a fiber with Kerr nonlinearity is considered. The effective parameters of dispersion and nonlinearity are analyzed for a wave packet that can be represented by a single partial pulse.     

Linear approximation in pulse propagation problems in nonlinear media

It seems obvious that the manifestation of nonlinear effects (such as shock wave and soliton formation) is possible only at comparatively high levels of nonlinearity. Nevertheless, there are well-known examples where a disturbance which is as small as one pleases ceases in time to be linear, and must be described in nonlinear terms. This, e.g., is the situation for the well-known Korteweg-de Vries (KdV) equations, which for an impulsive initial condition of definite sign has an asymptotic solution described by a set of solitons and by a rapidly oscillating wave packet. There will in fact always be at least one soliton asymptotically, no matter how small the initial pulse amplitude [1]. Another example is shock wave (triangular pulse) attenuation at large distances (or times) within the framework of the Burgers equation; the wave remains a shock wave even though its amplitude decreases to zero [1]. It is thus necessary to indicate a criterion which might be used to establish the nature of the asymptotic solution. The aim of the present note is the definition of such a criterion; that is, a relation between nonlinearity and dispersion (dissipation) in which nonlinear effects are manifested only above some threshold level.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 21, No. 11, pp. 1706–1708, November, 1978.     

Self-focusing of wave packets and envelope shock formation in nonlinear dispersive media

The self-action of three-dimensional wave packets is analyzed analytically and numerically under the conditions of competing diffraction, cubic nonlinearity, and nonlinear dispersion (dependence of group velocity on wave amplitude). A qualitative analysis of pulse evolution is performed by the moment method to find a sufficient condition for self-focusing. Self-action effects in an electromagnetically induced transparency medium (without cubic nonlinearity) are analyzed numerically. It is shown that the self-focusing of a wave packet is accompanied by self-steepening of the longitudinal profile and envelope shock formation. The possibility of envelope shock formation is also demonstrated for self-focusing wave packets propagating in a normally dispersive medium.     

Nonlinear dynamics of a pulse in an anisotropic medium with birefringence

The dynamics of a wave packet propagating in an anisotropic nonlinear optical fiber with strong linear coupling of the orthogonal components of the pulse is studied. The regimes of modulation instability and formation of soliton-like pulses are analyzed for different polarization angles of the incident light with allowance made for the first-and second-order dispersion effects and the nonlinear effects of self-and cross-modulation.     

Shock waves in a long-period optical fiber

The possibility of forming a shock wave of the pulse envelope has been investigated in a long-period or Bragg optical fiber with a system of two unidirectional linearly coupled waves. It has been demonstrated that, in principle, the possibility exists of forming a shock wave in a nonlinear optical fiber not only at the trailing edge but also at the leading edge of the wave packet. The origin of the formation of a shock wave depends substantially on the initial conditions providing excitation of the optical fiber.     

光子晶体光纤非线性光谱特性的理论与实验研究

光子晶体光纤具有特殊的导光机制和结构可调性,可以产生奇异的色散特性及高非线性,为非线性光纤光学领域的研究提供了新的条件。受多种非线性光学效应的共同作用,在不同泵浦光脉冲参数条件下,不同结构参数及传输特性的光子晶体光纤能产生丰富的非线性光谱。利用分步傅里叶方法求解非线性薛定谔方程,模拟飞秒激光脉冲在光子晶体光纤中的传输过程,获得输出光谱与入射光脉冲参数(泵浦光峰值功率P、泵浦光波长λ、光脉冲形状、光脉冲宽度T_FWHM)、光纤结构参数(孔间距Λ、空气填充比d/Λ、光纤长度z)、传输特性(色散、非线性系数)的关系,分析拉曼孤子、色散波、自相位调制等非线性效应产生的光谱特性。利用光子晶体光纤包层节区进行非线性光学实验研究,获得了孤子波和色散波的宽带光谱输出。理论分析与实验测量的光谱中都包括了波长0.5 μm附近可见光波段的蓝移色散波、0.82 μm波段的剩余泵浦光、1.1 μm波段的孤子波、2 μm附近的红移宽带色散波。理论分析与实验测量结果一致,阐明光子晶体光纤中非线性光谱产生的物理原理,实现了对宽带光谱的可控输出,为高非线性光子晶体光纤的结构设计、制备及非线性光谱的应用研究奠定基础。     

The structural features of wave collapse in medium with normal group velocity dispersion

The dynamic characteristics of self-action in three-dimensional wave packets described by the nonlinear Schrödinger equation with a hyperbolic space operator were studied analytically and numerically. The class of the initial wave field distributions for which self-focusing effects predominated over dispersion spreading and caused the arising of wave collapses was considered. The collapse of tubular wave packets was shown to be accompanied by packet shape changes during its contraction to the axis of the system. The nonlinear stabilization of collapses resulted in wave field fragmentation in the longitudinal direction followed by the expansion of the bunches thus formed along the axis. The dynamics of collapses was numerically studied taking into account medium nonlinearity saturation and nonlinear dissipation.     

Electronic wave packets in vacuum photodetectors and the possibility of observing them

The motion of an electronic wave packet in the interelectrode space of a vacuum photodetector is investigated. It is shown that the dimensions of such a packet are of the order of 1 micron and are comparable to the optical wavelength. On interacting with a powerful laser pulse the packet scatters a large number of photons and is deflected from its initial trajectory. Both effects can be used to determine the parameters of an electronic wave packet. Pis’ma Zh. éksp. Teor. Fiz. 63, No. 6, 408–411 (25 March 1996)     

高阶效应对超短艾里-高斯脉冲相互作用的影响

本文运用分步傅里叶变换,对满足高阶耦合非线性薛定谔方程的超短艾里脉冲与超短高斯脉冲,利用MATLAB数值模拟了在高阶效应下两脉冲相互作用后的演化过程以及时域上的强度变化。结果表明：负三阶色散效应使超短脉冲相互作用能传输更远距离;正三阶色散效应会减慢超短脉冲相互作用的传输。自陡峭效应通过孤子分裂现象的形式使超短脉冲相互作用产生时域位移,内拉曼效应可以将超短脉冲相互作用的能量由前沿处转移到后沿处。     

Soliton-like pulses in nonlinear lightguides with strong birefringence and realizable intermode coupling

The dynamics of a wave packet formed by two unidirectional waves propagating in a nonlinear birefringence lightguide with and without linear coupling between the orthogonal pulse components is investigated. Conditions of forming soliton-like pulses are examined for various polarization angles of input radiation with allowance for the dispersion effects of the first and second orders and of the nonlinear effects caused by phase self-and cross-modulation. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 3, pp. 50–55, March, 2007.     

高阶效应对超短艾里-高斯脉冲相互作用的影响

本文运用分步傅里叶变换,对满足高阶耦合非线性薛定谔方程的超短艾里脉冲与超短高斯脉冲,利用MATLAB数值模拟了在高阶效应下两脉冲相互作用后的演化过程以及时域上的强度变化。结果表明：负三阶色散效应使超短脉冲相互作用能传输更远距离;正三阶色散效应会减慢超短脉冲相互作用的传输。自陡峭效应通过孤子分裂现象的形式使超短脉冲相互作用产生时域位移,内拉曼效应可以将超短脉冲相互作用的能量由前沿处转移到后沿处。     

高阶效应对超短艾里-高斯脉冲相互作用的影响

本文运用分步傅里叶变换,对满足高阶耦合非线性薛定谔方程的超短艾里脉冲与超短高斯脉冲,利用MATLAB数值模拟了在高阶效应下两脉冲相互作用后的演化过程以及时域上的强度变化.获得了负三阶色散效应使超短脉冲相互作用能传输更远距离;正三阶色散效应会减慢超短脉冲相互作用的传输.自陡峭效应通过孤子分裂现象的形式使超短脉冲相互作用产生时域位移.内拉曼效应可以将超短脉冲相互作用的能量由前沿处转移到后沿处.