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.     

Self-action dynamics of ultrashort electromagnetic pulses

The self-action dynamics of three-dimensional wave packets whose width is on the order of the carrier frequency is studied under fairly general assumptions concerning the dispersion properties of the medium. The condition for the wave field collapse is determined. Self-action regimes in a dispersion-free medium and in media with predominance of anomalous or normal group velocity dispersions are numerically investigated. It is shown that, for extremely short pulses, nonlinearity leads not only to the self-compression of the wave field but also to a “turn-over” of the longitudinal profile. In a dispersionless medium, the formation of a shock front within the pulse leads to the nonlinear dissipation of linearly polarized radiation and to self-focusing stabilization. For circularly polarized radiation, the wave collapse is accompanied by the formation of an envelope shock wave.     

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.     

Self-action of Bessel light beams in cubic gyrotropic photorefractive crystals

We have studied conversion and interaction of a Bessel laser beam of zero order in photorefractive crystals. We have established that in a cubic gyrotropic crystal, two Bessel light beams propagate with different wave vectors and cone angles, but with identical conicity parameters. As the power in the Bessel light beam increases, we have experimentally observed a new optical effect: self-action of a Bessel light beam. We have studied the effect of external influences and the parameters of the beam itself on the process of self-refraction in photorefractive crystals. __________ Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 73, No. 4, pp. 488–493, July–August, 2006.     

空间诱导产生艾里-贝塞尔光弹研究

利用波动方程,研究了脉冲贝塞尔光束在自由空间传输时的空间诱导群速度色散(SIGVD)效应. 结果表明,三阶SIGVD能使脉冲贝塞尔光束的时域逐渐演化为艾里分布. 由于艾里-贝塞尔光弹是一种新奇的时、空都不扩展的局域波包, 能在光与物质相互作用的很多应用领域发挥作用.因此,本文提出了 通过色散管理技术补偿二阶SIGVD,利用三阶SIGVD在自由空间产生艾里-贝塞尔光弹的方案. 为分析这种光弹的时空传输特性,数值模拟了它在色散介质中的传输情况. 结果表明,这种光弹能在色散介质中保持空域不衍射、时域不色散的稳定传输.     

Spontaneously generated walking X-shaped light bullets

In quadratic nonlinear media with normal dispersion and nonvanishing group velocity mismatch between fundamental wave and second-harmonic pulses, the wave packets of two harmonics can be locked together in propagation in the form of walking X-shaped light bullets. The output wave packets are developed into X-shaped light bullets with significant group delay time due to mutual dragging and significant shifting in spatiotemporal spectrum due to delayed nonlinear phase shift. We also show that spontaneously generated phase-front tilting can balance the dragging force induced by group velocity mismatch and lead to zero-velocity walking X-shaped light bullets.     

Spatiotemporal airy light bullets in the linear and nonlinear regimes

We demonstrate the realization of intense Airy-Airy-Airy (Airy(3)) light bullets by combining a spatial Airy beam with an Airy pulse in time. The Airy(3) light bullets belong to a family of linear spatiotemporal wave packets that do not require any specific tuning of the material optical properties for their formation and withstand both diffraction and dispersion during their propagation. We show that the Airy(3) light bullets are robust up to the high intensity regime, since they are capable of healing the nonlinearly induced distortions of their spatiotemporal profile.     

Single-focusing regime of propagation of femtosecond light packets when self-focused in a condensed medium

Numerical simulations are used to investigate the propagation of tightly focused megawatt femtosecond light packets in a nonlinear condensed medium in the single-focusing regime. A plasma is shown to be generated in a small region whose length and diameter increase with power in the single-focusing regime of propagation of a femtosecond light packet in a transparent dielectric. The limiting electron density in the microplasma formation region is virtually independent of the laser pulse power but increases with numerical aperture of the focusing optics. At a fixed femtosecond pulse power exceeding the critical self-focusing power, the transmission of light by a dielectric layer decreases with increasing numerical aperture of the focusing optics.     

Controlling Airy-Bessel Light Bullets in an Optically Induced Potential

We investigate numerically the curious evolution of self-decelerating Airy-Bessel light bullets carrying different topological charges (TC), launched in the three-dimensional (3D) Schrödinger equation with an induced parabolic potential. We present their spatiotemporal profile during propagation. In our paper, the number of TC, the modulation depth, and the induced potential are considered simultaneously. The propagation properties of light bullets result from a combination of these effects. Our scheme is distinctly different from the linear light bullets in free space, in which the localized wave packets propagate in a self-consistent trapping potential.     

Formation of ultrashort pulses in the process of the propagation of tightly focused femtosecond light packets in a transparent condensed medium

The evolution of the space-time structure of tightly focused femtosecond light packets in a transparent condensed medium (fused silica) is analyzed by means of numerical simulation. The nonlinear self-action of light packets leads to the formation of ultrashort pulses (duration of about 10 fs) propagating in various directions. The spectral composition, time structure, and position of ultrashort pulses at the time axis depend on their propagation direction.     

On three-dimensional dissipative optical solitons: Collisions of laser bullets and topological solitons

Results of numerical simulation of collisions of two fundamental laser bullets—three-dimensional solitons formed in a medium with saturable amplification and absorption and frequency dispersion—are presented. A new collision regime resulting in the formation and the propagation of a switching wave is revealed. The existence of a metastable topological (with a wave front dislocation and an annular intensity distribution) three-dimensional dissipative optical soliton is demonstrated.     

Generation of quadrature-squeezed light of ultrashort pulses in a medium with inertial cubic nonlinearity

A consistent quantum theory of self-action and cross-interaction of coherent light pulses in a cubically nonlinear medium is developed by using the momentum operator of the field, which takes into account the inertial nonlinearity. Specific features of generation of the quadrature-squeezed states of light pulses are considered. The spectrum of fluctuations of a quadrature below the shot-noise level is analyzed as a function of the relaxation time of nonlinearity and the magnitude of nonlinear phase additions, related to the self-action and cross-interaction.     

Self-generation of two-dimensional spin-wave bullets

The experimental observation of self-generation of two-dimensional, self-focusing nonlinear spin wave packets-spin wave bullets-in an active ring is reported. The ring is composed of a ferrite film with two antennae for excitation and detection of the wave packets, and a microwave amplifier connecting the antennae and closing the ring. Experimental observation has been made by using the time and space resolved Brillouin light scattering technique. The parameters of spin wave bullets self-generated from noise in an active ring are similar to those of bullets coherently excited by external microwave pulses. The observed self-generation process provides unambiguous evidence that wave bullets are intrinsic excitations of a two-dimensional nonlinear medium with dissipation that is focusing in both directions.     

Numerical Simulation of SRS of Cylindrical Wave Beams

A method for numerical simulation of stimulated Raman scattering of cylindrical wave beams in a nonlinear medium has been developed. The features of the spatial structure formation of interacting wave fields in the regime of conservation of azimuthal angular distributions of amplitudes have been investigated. The radial intensity profiles of diffracting light beams in the near-field zone and their angular spectra in the far-field zone corresponding to different stages of energy exchange in the process of amplification from the noise in the barium nitrate crystal have been calculated. It has been shown that in the field of Bessel beams waveguide structures of the soliton type with a peak intensity of the self-channeling Stokes component significantly exceeding the initial pumping intensity are formed. A comparison of the conversion efficiencies under pumping by Gaussian and Bessel light beams has been made.     

Self-action of Bessel light beams in medium with large nonlinearity

The modifications of an angular spectrum of the intense Bessel J₀ and J₁ beams caused by self-action in the medium with large cubic nonlinearity are investigated. The appearance of an outer ring of triple radius was observed. The phenomenon can be explained as Bragg diffraction of Bessel beam on Bessel lattice in nonlinear medium. Experimental results are in qualitative agreement with the theoretical predictions.     

Two-dimensional extremely short optical pulses with a Bessel cross section in inhomogeneous medium of carbon nanotubes

The problem of dynamics of propagation of extremely short optical pulses (light bullets) with a Bessel cross section in inhomogeneous medium of carbon nanotubes has been considered. It is numerically shown that the optical pulse propagation is stable and steady.     

General quasi-nonspreading linear three-dimensional wave packets

We introduce a general approach for generation of sets of three-dimensional quasi-nonspreading wave packets propagating in linear media, also referred to as linear light bullets. The spectrum of rigorously nonspreading wave packets in media with anomalous group velocity dispersion is localized on the surface of a sphere, thus drastically restricting the possible wave packet shapes. However, broadening slightly the spectrum affords the generation of a large variety of quasi-nonspreading distributions featuring complex topologies and shapes in space and time that are of interest in different areas, such as biophysics or nanosurgery. Here we discuss the method and show several illustrative examples of its potential.     

Generation of three-dimensional versatile vortex linear light bullets(Invited Paper)

We generate and measure the versatile vortex linear light bullet,which combines a high-order Bessel beam and an Airy pulse.This three-dimensional optical wave packet propagates without distortion in any medium,while carrying an orbital angular momentum.Its non-varying feature in linear propagation is verified by a threedimensional measurement.Such a novel versatile linear light bullet can be useful in various applications such as micromachining.     

Nonlinear effects of self-action of waves in 2D coupled ferromagnetic structures

Magnetostatic wave self-action effects in a 2D structure consisting of two ferromagnetic films have been studied using a numerical solution to the system of two-dimensional nonlinear Schrödinger equations. Main features of these effects have been analyzed in comparison with similar effects in a 2D structure based on a single film. The applicability of coupled structures to control the formation of 2D nonlinear wave beams and magnetostatic wave packets has been considered.     

Self-focusing of laser radiation in cluster plasma

The self-focusing of laser radiation in plasma with ionized gaseous clusters is studied both analytically and numerically. An electrodynamic model is proposed for cluster plasma in a field of ultrashort laser pulse. The radiation self-action dynamics are studied using the equation for wave-field envelope with allowance for the electronic nonlinearity of the expanded plasma bunches and the group-velocity dispersion in a nanodispersive medium. It is shown that, for a laser power exceeding the self-focusing critical power, the wave-field self-compression occurs in a medium with dispersion of any type (normal, anomalous, or combined). Due to the strong dependence of the characteristic nonlinear field on the size of ionized cluster, the corresponding processes develop faster than in a homogeneous medium and give rise to the ultrashort pulses.