Self-action of Bessel wave packets in a system of coupled light guides and formation of light bullets

The self-action of two-dimensional and three-dimensional Bessel wave packets in a system of coupled light guides is considered using the discrete nonlinear Schrödinger equation. The features of the self-action of such wave fields are related to their initial strong spatial inhomogeneity. The numerical simulation shows that for the field amplitude exceeding a critical value, the development of an instability typical of a medium with the cubic nonlinearity is observed. Various regimes are studied: the self-channeling of a wave beam in one light guide at powers not strongly exceeding a critical value, the formation of the “kaleidoscopic” picture of a wave packet during the propagation of higher-power radiation along a stratified medium, the formation of light bullets during competition between self-focusing and modulation instabilities in the case of three-dimensional wave packets, etc. In the problem of laser pulse shortening, the situation is considered when the wave-field stratification in the transverse direction dominates. This process is accompanied by the self-compression of laser pulses in well enough separated light guides. The efficiency of conversion of the initial Bessel field distribution to two flying parallel light bullets is about 50%.     

On the possibility of suppression of self-focusing of a femtosecond laser pulse during its propagation in a cubic nonlinear medium

Based on a computer simulation, the self-focusing of an axially symmetric beam in a cubic nonlinear medium under the anomalous dispersion conditions is studied with the account for the time dispersion of nonlinear response, which manifests for femtosecond pulses. It is shown that, at a certain value of the parameter of linear modulation of the pulse (or of its chirp), the dispersion of nonlinear response can lead either to the suppression of formation of a nonlinear focus and to the possibility of formation of optical shock waves in time or even to a change in the regime of the beam self-action owing to the action of the local response, i.e., to the change from the self-focusing of the beam to the regime of its defocusing.     

Formation of elliptically polarized ring-shaped electric field structures on the self-focusing of light in an isotropic medium featuring a spatially disperse nonlinearity

The possibility is demonstrated that the self-focusing of an elliptically polarized beam in a medium featuring a spatially disperse cubic nonlinearity can give rise to several radially symmetric ring-shaped regions of the same sense of rotation (right or left) of the electric-field vector in the cross-section of the beam. The formation dynamics and propagation features of such electric field structures are studied for various parameters of the incident radiation and nonlinear medium.     

Relativistic nonlinearity and wave-guide propagation of rippled laser beam in plasma

In the present paper we have investigated the self-focusing behaviour of radially symmetrical rippled Gaussian laser beam propagating in a plasma. Considering the nonlinearity to arise from relativistic phenomena and following the approach of Akhmanov et al, which is based on the WKB and paraxial-ray approximation, the self-focusing behaviour has been investigated in some detail. The effect of the position and width of the ripple on the self-focusing of laser beam has been studied for arbitrary large magnitude of nonlinearity. Results indicate that the medium behaves as an oscillatory wave-guide. The self-focusing is found to depend on the position parameter of ripple as well as on the beam width. Values of critical power has been calculated for different values of the position parameter of ripple. Effects of axially and radially inhomogeneous plasma on self-focusing behaviour have been investigated and presented here.     

Self-modulation of Bessel-Gaussian wave beams in a medium with cubic nonlinearity

A semi-discrete dynamic model has been developed for the formation of the spatial structure of wave fields in a medium with cubic nonlinearity. The characteristic features of self-focusing and conical modulation of intense Bessel-Gaussian light beams of different orders have been studied in different stages of their evolution during propagation. It has been shown that as a result of nonlinear refraction, in the far zone wave structures are formed consisting of three spatially separated conical beams. Increasing the cone angle of the wave vectors leads to a decrease in the effect of conical modulation of the radiation, and improves the structural stability of the beam. The considered self-modulation effects can be used for passive limiting of the laser radiation power. __________ Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 73, No. 5, pp. 626–630, September–October, 2006.     

线偏振激光在磁化等离子体中的调制不稳定性

 采用洛伦兹变换推导了线性偏振激光在磁化等离子体中的非线性色散关系,根据Karpman方法推导出横波的非线性控制方程,利用线性偏振激光在磁化等离子体中的非线性色散关系和非线性控制性方程,分析了在磁化等离子体中有限振幅的扰动引起的调制不稳定性,得到了线性偏振激光的调制不稳定的时间增长率与扰动波数之间的函数关系。分析结果表明：激光等离子体的临界面附近的磁调制不稳定性的时间增长率显著增大。     

非局域高次非线性介质中的多极暗孤子

研究一维非局域三-五次非线性模型下,暗孤子和多极暗孤子的新解和传输特性.发现非局域程度和非线性参量变化对暗孤子的峰值和束宽产生影响,并且在特定的竞争非局域非线性参数下存在稳定基态暗孤子和多极暗孤子的束缚态.另外,讨论了在局域自聚焦三次和非局域自散焦五次非线性介质中暗孤子和两极暗孤子的传输特性,发现孤子比在自散焦三次和自聚焦五次的非线性介质中传输更加稳定.进一步研究了单暗孤子和三极暗孤子的功率与传播常数和非局域程度的关系,并讨论了不同类型暗孤子的线性稳定性问题.     

Rytov transformation in the problem of the self-focusing of a light beam

A method of the complex phase of the envelope of a light field has been proposed for the problem of the self-focusing of a beam in a medium with cubic nonlinearity. The complex phase has been introduced by means of the Rytov transformation. Boundary conditions have been obtained under the assumption that the light fields at the periphery of the beam undergoing self-focusing and linear diffraction coincide with each other. The transition from the slowly varying amplitude to its complex phase provides a significant expansion of the ranges of the amplitude and intensity in the light beam in theoretical investigations. The applicability of the complex phase method is illustrated on particular examples.     

X and Y waves in the spatiotemporal Kerr dynamics of a self-guided light beam

The nonlinear stage of development of the spatiotemporal instability of the monochromatic Townes beam in a medium with self-focusing nonlinearity and normal dispersion is studied by analytical and numerical means. Small perturbations to the self-guided light beam are found to grow into two giant, splitting Y pulses featuring shock fronts on opposite sides. Each shocking pulse amplifies a co-propagating X wave, or dispersion- and diffraction-free linear wave mode of the medium, with super-broad spectrum.     

Induced spatiotemporal modulation instability in a noninstantaneous self-defocusing medium

We demonstrate theoretically and experimentally that induced spatiotemporal modulation instability can exist in a self-defocusing medium if the nonlinearity is noninstantaneous. We predict the growth rate as a function of the spatial and temporal frequencies of the modulation and the response time of the nonlinearity and confirm it by our experiments.     

Weakly nonparaxial spatial optical solitons in different mechanisms of Kerr nonlinearity

The structure of spatial (two-dimensional transverse) weakly nonparaxial solitons is determined by solving the Maxwell equations for a medium characterized by different mechanisms of Kerr (cubic) nonlinearity in the approximation of beams with a width greatly exceeding the wavelength of light. Two modes are distinguished for these solitons: a trapping mode, with a constant transverse field profile, and a beating mode, with longitudinal oscillations of the field structure. The angular structure of the field in the beating mode (which is realized when the radiation power slightly exceeds the critical power of self-focusing) is determined.     

Soliton-like propagation modes of picosecond acoustic pulses in a paramagnetic crystal

The nonlinear propagation of picosecond acoustic pulses at an arbitrary angle to an external magnetic field is studied in an elastically isotropic paramagnetic crystal at low temperatures. Various soliton-like propagation modes arising due to spin-phonon interaction and acoustic anharmonicity are revealed, and the stability of these modes with respect to transverse perturbations is analyzed. In the case of defocusing cubic nonlinearity, the crystal can support the propagation of compression pulses, which undergo defocusing, and rarefaction pulses can propagate in the self-channeling mode. In the case of focusing cubic nonlinearity, only compression pulses can propagate if the conditions of stability with respect to self-focusing are satisfied.     

Instability-driven recovery of diffused images

We demonstrate the nonlinear recovery of diffused images in a self-focusing photorefractive medium. The method is based on the convolution property of nonlinearity, in which related modes reinforce each other as they propagate. The resulting mode coupling enables energy transfer from the scattered light to the underlying signal. The dynamics is well described by a model in which the signal seeds a modulation instability in the diffused background.     

Kerr非线性介质中聚焦像散高斯光束的传输特性

当高功率激光通过Kerr非线性介质传输时,Kerr效应会严重影响激光的传输特性.实际应用中常遇到像散光束.迄今为止,像散光束传输特性的研究大都局限于在线性介质中的传输,而在非线性介质中传输的研究较少,且还未涉及像散激光束通过含光学系统的Kerr非线性介质传输变换的研究.本文主要研究Kerr效应对聚焦光束像散特性和焦移特性的影响,以及聚焦像散高斯光束的自聚焦焦距和光束焦点调控.在光束扩展情况下,推导出了聚焦像散高斯光束在Kerr非线性介质中传输的束宽、束腰位置和焦移的解析公式,研究表明:在自聚焦介质中,随着自聚焦作用增强(如光束功率增强),光束像散越强,但焦移越小;在自散焦介质中,随着自散焦作用增强(如光束功率增强),光束像散越弱,但焦移越大.另一方面,在光束自聚焦情况下,推导出了自聚焦焦距的解析公式,研究表明利用光束像散可以调控光束焦点个数.     

Formation of Hot Images in Laser Beams through a Self-defocusing Kerr Medium Slab

A nonlinear hot image is usually thought as of a special case of self-focusing, and thus occurs when a laser beam propagates through a slab of self-focusing medium. Here we show theoretically that a hot image may also be formed by a thin slab of self-defocusing medium. The physical origin for this hot image formation is akin to the in-line volume-phase holographic imaging due to the intensity-dependent refractive-index modulation of the self- defocusing medium. NumericM simulations confirm the theoretical prediction and further identify the dependence of the hot image on the beam power, the modulation depth of obscuration and the thickness of self-defocusing medium. The analysis presented here brings new insight into the physics of hot image formation in the high power laser system.     

Further Theoretical Investigations for Laser Relative Intensity Noise with Fiber Nonlinearities and Higher-Order Dispersion

In this article, we theoretically investigate relative intensity noise (RIN) in optical communication systems with fiber nonlinearities due to optical Kerr effects and higher-order dispersion. The impact of modulation frequencies, launch power, and laser bias current on RIN has been illustrated. We show that RIN increases with modulating frequencies up to the resonance frequency, launch power, and decrease in the laser bias current. We also show that higher-order dispersion terms have no impact on the RIN, but with first-order dispersion compensation the higher-order dispersion terms have significant impact at high modulating frequencies. The RIN with and without fiber nonlinearities is further investigated. It has been shown that the RIN with fiber nonlinearity is more than the RIN without nonlinearity and the effect of nonlinearity appears at higher modulation frequencies only.     

Self-focusing of femtosecond diffraction-resistant vortex beams in water

We report experiments on self-focusing of femtosecond diffraction-resistant vortex beams in water. These beams are higher-order Bessel beams with weak azimuthal modulation of the transverse intensity patterns. The modulation overrides the self-focusing dynamics and results in the formation of regular bottlelike filament distributions. The peak-power thresholds for filamentation, at a particular distance, are relatively accurately estimated by the adaptation of the Marburger formula derived earlier for Gaussian beams. The nonlinear conversion of the incident conical waves into the localized spatial wave packets propagating near the beam axis is observed.     

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.     

Dynamics of the spatial spectrum of a self-focusing optical wave in a nonlinear medium

A new nonlinear equation for the dynamics of the spatial spectrum of a self-focusing monochromatic wave in a medium with cubic nonlinearity is derived in the nonparaxial approximation. The formation of optical beams with cross section on the order of a wavelength is considered. Backward self-reflection is found to be the fundamental cause for the limitation of optical self-focusing     

Evolution of spatial modulation of broadband laser pulses with different pulse durations in medium with non-instantaneous Kerr nonlinearity

We experimentally investigate the evolution of spatial modulation of broadband laser pulses with different pulse durations through a medium with non-instantaneous Kerr nonlinearity. By modifying the input laser pulse width, we observe the nonlinear growth of the spatial stripes that arise from interference with different modulation frequencies, and then obtain the gain spectra of the spatial modulation which clearly reveal the influence of relaxation effect on spatiotemporal modulation instability. We find that all gain spectra have the similar fastest growing frequency, but they have tails at higher frequency region in which the growth rate of gain is bigger for shorter pulse duration. The experimental results are confirmed by the perturbational analysis.