Mode Structure and the Envelope of a Short Pulse in a Graded-Index Optical Fiber with a Longitudinal Inhomogeneity and a Spatial Bending

We consider propagation of a short optical pulse in an optical fiber whose refractive index is strongly dependent on the radial coordinate and is weakly dependent on the longitudinal coordinate with allowance for the possible weak spatial bending of the fiber axis. The three-dimensional nonlinear wave equation modelling the pulse propagation is solved asymptotically with respect to a small parameter specifying the order of magnitude of the pulse amplitude. A relationship between the propagating modes and the eigenvalues and eigenfunctions of the singular Sturm-Liouville problem is established. The pulse propagation is shown to have three scales: the high-frequency carrier is modulated by the envelope which evolves in a two-scale manner and is described by a nonlinear Schrödinger equation whose coefficients depend on the longitudinal coordinate. The transverse distribution of the wave field and the envelope soliton are obtained in terms of elementary functions for several types of transverse and longitudinal inhomogeneities of the fiber. The possibility of controlling the pulse parameters by varying the transverse and longitudinal inhomogeneities of the fiber is pointed out.     

Short chirp pulses in graded-index light guides

We consider the nonlinear process of propagation of a short chirp optical pulse in a light guide in which the refractive index of a fiber material strongly depends on the radial coordinate and weakly depends on the longitudinal coordinates. The chirped and strongly chirped pulses are distinguished by the relationship between the modulation depth and the spectrum width. The chirp-pulse propagation is simulated by a nonlinear wave equation solved asymptotically with respect to the small parameter prescribing the order of magnitude of the pulse amplitude. It is shown that the pulse propagation is three-scale. The phase of high-frequency filling and the field distribution in the fiber cross section are obtained as the eigenvalue and eigenfunction of a singular Sturm-Liouville problem, respectively. On the additional assumption of longitudinal inhomogeneity of the fiber, the general equation for the pulse envelope is reduced to the second Painlevé equation. It is shown that the linear modulation of the carrier frequency is not an independent characteristic of the propagation process, but varies in certain accordance with parameters of the transverse and longitudinal inhomogeneities of the fiber. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 49, No. 1, pp. 64–71, January 2006.     

The effect of an inhomogeneous cladding of a gradient optical waveguide on the mode and envelope characteristics of a soliton pulse

The nonlinear dynamics of a short pulse in a gradient waveguide layer is studied analytically taking into account the occurrence of a cladding layer and the longitudinal inhomogeneity of the two layers. The class of functions is presented in terms of which the transverse profiles of the refractive indices of both the gradient and the cladding layers can be represented, and, at the same time, the mode structure of the pulse can be explicitly described in terms of a hypergeometric equation. Expressions are presented that describe the variations of the propagation constant and transverse distribution of the wave field under the action of the longitudinal inhomogeneities of the gradient and cladding layers. It is shown that the envelope of the pulse satisfies the generalized nonlinear Schrödinger equation the coefficients of which are functions of the longitudinal coordinate and are expressed via the refractive indices of the waveguide layer and cladding.     

Pulse chirping effect on controlling the transverse cavity oscillations in nonlinear bubble regime

The propagation of an intense laser pulse in an under-dense plasma induces a plasma wake that is suitable for the acceleration of electrons to relativistic energies. For an ultra-intense laser pulse which has a longitudinal size shorter than the plasma wavelength, λp, instead of a periodic plasma wave, a cavity free from cold plasma electrons, called a bubble, is formed behind the laser pulse. An intense charge separation electric field inside the moving bubble can capture the electrons at the base of the bubble and accelerate them with a narrow energy spread. In the nonlinear bubble regime, due to localized depletion at the front of the pulse during its propagation through the plasma, the phase shift between carrier waves and pulse envelope plays an important role in plasma response. The carrier–envelope phase(CEP) breaks down the symmetric transverse ponderomotive force of the laser pulse that makes the bubble structure unstable. Our studies using a series of two-dimensional(2D) particle-in-cell(PIC) simulations show that the frequency-chirped laser pulses are more effective in controlling the pulse depletion rate and consequently the effect of the CEP in the bubble regime. The results indicate that the utilization of a positively chirped laser pulse leads to an increase in rate of erosion of the leading edge of the pulse that rapidly results in the formation of a steep intensity gradient at the front of the pulse. A more unstable bubble structure, the self-injections in different positions, and high dark current are the results of using a positively chirped laser pulse. For a negatively chirped laser pulse, the pulse depletion process is compensated during the propagation of the pulse in plasma in such a way that results in a more stable bubble shape and therefore, a localized electron bunch is produced during the acceleration process. As a result, by the proper choice of chirping, one can tune the number of self-injected electrons, the size of accelerated bunch and its energy spectrum to the values required for practical applications.     

Soliton regimes of surface magnetostatic wave propagation in a magnet-semiconductor structure

The nonlinear properties of exchange-free surface magnetostatic spin waves in a layered structure containing films of a ferromagnet and a semiconductor are investigated theoretically. The stability of nonlinear surface magnetostatic waves relative to longitudinal disturbances is investigated using the envelope evolution equation in the weak-nonlinearity approximation. It is shown that, under certain conditions, a surface spin-wave pulse propagates in the form of an envelope soliton. Calculations are performed for the case of an yttrium iron-garnet-indium antimonide structure. Fiz. Tverd. Tela (St. Petersburg) 41, 1272–1275 (July 1999)     

等离子体中强场的演化

研究了短脉冲强激光在欠稠密均匀等离子体中的传播，得出光场的演化方程和包络所满足的非线性方程，并用这些方程对光场在等离子体中激发的相对论谐波的饱和问题和光场传播的演化特性进行了分析. 关键词：     

Envelope solitary waves on two-dimensional lattices with in-plane displacements

We investigate envelope solitary waves on square lattices with two degrees of freedom and nonlinear nearest and next-nearest neighbor interactions. We consider solitary waves which are localized in the direction of their motion and periodically modulated along the perpendicular direction. In the quasi-monochromatic approximation and low-amplitude limit a system of two coupled nonlinear Schr?dinger equations (CNLS) is obtained for the envelopes of the longitudinal and transversal displacements. For the case of bright envelope solitary waves the solvability condition is discussed, also with respect to the modulation. The stability of two special solution classes (type-I and type-II) of the CNLS equations is tested by molecular dynamics simulations. The shape of type-I solitary waves does not change during propagation, whereas the width of type-II excitations oscillates in time. Received: 4 December 1997 / Revised: 6 June 1998 / Accepted: 7 July 1998     

周期量级飞秒脉冲电场在非线性克尔介质中的传输

采用时间转换法研究了周期量级飞秒脉冲电场在非线性克尔介质中的传输.由于周期量级飞秒脉冲电场的脉宽小于介质拉曼响应的特征时间,在传输过程中脉冲电场会发生剧烈的变形和分裂,并在频谱上观察到了强烈的拉曼感应频移和色散波.由于周期量级脉冲电场依赖于载波包络相位,发现在脉冲电场传输过程中,主脉冲电场和色散波电场的相位线性地依赖于初始脉冲的载波包络相位.     

Nonlinear regimes of ultrashort pulse propagation in an array of anisotropic tunneling states

Dynamics of an ultrashort electromagnetic pulse in a system with an array of anisotropic tunneling states spanned by the pulse spectrum are analyzed. A system of nonlinear wave equations is derived for the ordinary and extraordinary components of the pulse propagating at an arbitrary angle to the anisotropy axis. Different regimes of ultrashort pulse propagation parallel and perpendicular to the anisotropy axis are examined. Ultrashort-pulse propagation regimes analogous to self-induced transparency and extraordinary transparency are identified. The properties of rational soliton-like pulses having no quasi-monochromatic analogs are analyzed. A longitudinal electric field component is generated in each regime, whereas off-resonance quasi-monochromatic pulses propagating under similar conditions (parallel and perpendicular to the anisotropy axis) have no longitudinal components. Stability of the solutions obtained and the effect of diffraction on ultrashort pulse dynamics are analyzed. The values of pulse parameters for which defocusing dominates over self-focusing are calculated.     

Nonlinear pulse propagation in periodic media with and without defects

The influence of single defects within a periodic structure on the nonlinear transmission of optical pulses through the structure is investigated numerically. A stack of alternating linear and cubically nonlinear layers of submicron thicknesses is considered. The simulations are based on a modified equation for the pulse envelope. Diffraction of the pulse has been taken into account, too. The results of simulations have been demonstrated as an essential influence of defects within the periodic structure on the nonlinear propagation of optical pulses, when the carrier frequency is chosen within the stop band of the structure with the defect.     

Controllable self-steepening of ultrashort pulses in quadratic nonlinear media

By analyzing ultrashort optical pulse propagation in quadratic nonlinear media beyond the slowly varying envelope approximation, we find that the sign and magnitude of self-steepening can be controlled through the wave vector mismatch. As an example of this phenomenon's impact on ultrashort pulse propagation, we show that it may be used to cancel the propagation effects of group-velocity mismatch. We obtain quantitative agreement between theory, simulations, and experiments.     

Space- and time-resolved Brillouin light scattering from nonlinear spin-wave packets

We have constructed a new Brillouin light scattering apparatus, based on the Sandercock multipass tandem interferometer design, for space- and time-resolved investigations of nonlinear wave packets in thin films. We have applied the method to studies of nonlinear spin-wave pulse propagation in yttrium iron garnet (YIG) films. Spatial resolution is achieved by scanning the laser spot across the YIG film surface, and temporal resolution is obtained by measuring the elapsed time between the launch of spin-wave pulses by an applied microwave pulse and the arrival of the respective inelastically scattered photons at the detector. We report the observation of nonlinear self-focusing of wave beams and pulses in one and two dimensions, the formation of one-dimensional envelope solitons, and of strongly localized, two-dimensional wave packets, 'spin-wave bullets', analogous to 'light bullets' predicted in nonlinear optics. By generating two counter-propagating wave pulses, pulse collision experiments were performed. We show that quasi-one-dimensional envelope solitons formed in narrow film stripes ('waveguides') retain their shapes after collision, while two-dimensional spin-wave packets formed in wide YIG films are destroyed in collision.     

具有几个光振荡周期的飞秒激光脉冲

从麦克斯韦方程组出发 ,推导出了具有几个光振荡周期的飞秒激光脉冲在非线性光纤中传输的方程和非线性光纤的折射率。给出了描述具有几个光振荡周期的飞秒激光脉冲在非线性光纤中传输方程的解。研究了在非线性光纤中自相位调制导致具有几个光振荡周期的飞秒激光脉冲频谱展宽 (脉宽压缩 )的详细物理过程。研究了非线性光纤中飞秒光孤子产生的条件     

Transient response of dielectric materials exposed to ultrafast laser radiation

We present results describing several characteristics of energy coupling into dielectric materials (fused silica) irradiated by ultrashort laser pulses in a regime close to the surface optical breakdown threshold. The results intend to illustrate the energy balance in the interaction process by observing the spatio-temporal variations of a laser pulse transversing a dielectric slab as a function of its energy. The measurements are based on real-time observations of the self-action of the laser pulse and associated effects on its temporal envelope, as well as on ex-situ phase-contrast microscopy of induced permanent material reactions. The experimental results are accompanied by numerical simulations of the pulse traces inside the dielectric material at different energetic conditions. The optical observations allow insights into the development and the dynamics of the laser-induced free carrier population, emphasizing the role of the bulk effects related to the nonlinear wave propagation into the transparent material during laser exposure. PACS 79.20.Ds; 52.50.Jm     

Diffraction of light beams in media with longitudinal-transverse inhomogeneity

A theory has been developed to describe the propagation of planar wave beams in media with linear or nonlinear susceptibility modulated in the transverse and longitudinal directions. The diffraction in curved coupled waveguides and from wedge-shaped inhomogeneities is considered. Ray trajectories are found and the Schrödinger equation for the beam envelope is solved numerically. The spatial dynamics of energy redistribution in the beam cross section is described. Conditions for suppressing the beam spread due to the refractive index modulation are found.     

Nonlinear pulse propagation: a time-transformation approach

We present a time-transformation approach for studying the propagation of optical pulses inside a nonlinear medium. Unlike the conventional way of solving for the slowly varying amplitude of an optical pulse, our new approach maps directly the input electric field to the output one, without making the slowly varying envelope approximation. Conceptually, the time-transformation approach shows that the effect of propagation through a nonlinear medium is to change the relative spacing and duration of various temporal slices of the pulse. These temporal changes manifest as self-phase modulation in the spectral domain and self-steepening in the temporal domain. Our approach agrees with the generalized nonlinear Schr?dinger equation for 100 fs pulses and the finite-difference time-domain solution of Maxwell's equations for two-cycle pulses, while producing results 20 and 50 times faster, respectively.     

Soliton-induced supercontinuum generation in liquid-filled photonic crystal fibre

We aim to study the nonlinear optical phenomena with ultra-broadband radiation in photonic crystal fibre (PCF). While PCFs with cores made from different glasses are well studied in previous works, in this paper, it is planned to investigate the dynamics of nonlinear processes of supercontinuum generation (SCG) in liquid-filled PCF (LCPCF) to understand the physical phenomena of femtosecond pulse propagation, particularly, the temporal and spectral changes of the pulse propagating through specific PCFs. Since the CS₂-filled LCPCF has complex nonlinear phenomena, we intend to analyse the role of saturable nonlinear response and slow nonlinear response on SCG in detail. For the physical explanation, soliton fission and modulational instability techniques will be implemented to investigate the impact of slow nonlinear response and saturable nonlinear response respectively, in SCG process.     

强时间非局域系统中自相位调制诱导的“脉冲镜像”啁啾

非局域非线性是目前非线性光学乃至非线性科学研究领域的热点. 本文研究了时间非局域系统中的脉冲啁啾特性, 发现了一个非常有趣的现象：当系统的时间非局域程度很强时, 由自相位调制引起的非线性啁啾可以近似成为脉冲强度的“镜像”, 并且, 这种特性与脉冲包络的具体形式无关. 利用这种特性, 分析了脉冲在强时间非局域系统中传输的时间演化过程.     

Allowable propagation of short pulse laser beam in a plasma channel and electromagnetic solitary waves

Nonparaxial and nonlinear propagation of a short intense laser beam in a parabolic plasma channel is analyzed by means of the variational method and nonlinear dynamics. The beam propagation properties are classified by five kinds of behaviors. In particularly, the electromagnetic solitary wave for finite pulse laser is found beside the other four propagation cases including beam periodically oscillating with defocussing and focusing amplitude, constant spot size, beam catastrophic focusing. It is also found that the laser pulse can be allowed to propagate in the plasma channel only when a certain relation for laser parameters and plasma channel parameters is satisfied. For the solitary wave, it may provide an effective way to obtain ultra-short laser pulse.