Self-focusing Dynamics Research Articles

Excitation of optically trapped single particles using femtosecond pulses.

Excitation from optically trapped particles is examined through laser-induced breakdown spectroscopy following interactions with mJ-level fs pulses. Optical emissions from sub-ng ablation of precisely positioned cupric oxide microparticles are used as a method to spatially resolve laser-particle interactions resulting in excitation. External focusing lenses are often used to change the dynamics of nonlinear self-focusing of fs pulses to form laser filaments or, alternatively, to form very intense air plasmas. Given the significant implications external focusing has on laser propagation and plasma conditions, single-particle emissions are studied with focusing lenses ranging from 50 to 300 mm. It is shown that, while single particles are less excited at longer focal lengths due to limited energy transfer through laser-particle interactions, the cooler plasma results in a lower thermal background to reveal resolved single-shot emission peaks. By developing an understanding in the fundamental interaction that occurs between single particles and fs pulses and filaments, practical improvements can be made for atmospheric remote sensing of low-concentration aerosols.

Self-channeling of spatially modulated femtosecond laser beams in the post-filamentation region

The propagation of high-intensity femtosecond laser pulses in air under conditions of superposed spatial phase modulation is considered theoretically. The numerical simulations are carried out on the basis of the reduced form of a nonlinear Schrödinger equation for a time-averaged electric field envelope. Initial spatial modulations are applied to pulse wavefront profiling by a staggered ( T E M 22 ) phase plate, which is simulated numerically. The dynamics of laser pulse self-focusing, filamentation, and post-filamentation self-channeling after the phase plates with variable phase jumps is studied. We show that, with specific phase modulations, the pulse filamentation region in air can be markedly shifted further and elongated compared with a nonmodulated pulse. Moreover, during the post-filamentation propagation of spatially structured radiation, the highly localized light channels are formed, possessing enhanced intensity and reduced angular divergence, which enables post-filamentation pulse self-channeling on the distance multiple exceeding the Rayleigh range.

Spatiotemporal dynamics of ultrarelativistic beam-plasma instabilities

An electron or electron-positron beam streaming through a plasma is notoriously prone to micro-instabilities. For a dilute ultrarelativistic infinite beam, the dominant instability is a mixed mode between longitudinal two-stream and transverse filamentation modes, with a phase velocity oblique to the beam velocity. A spatiotemporal theory describing the linear growth of this oblique mixed instability is proposed, which predicts that spatiotemporal effects generally prevail for finite-length beams, leading to a significantly slower instability evolution than in the usually assumed purely temporal regime. These results are accurately supported by particle-in-cell (PIC) simulations. Furthermore, we show that the self-focusing dynamics caused by the plasma wakefields driven by finite-width beams can compete with the oblique instability. Analyzed through PIC simulations, the interplay of these two processes in realistic systems bears important implications for upcoming accelerator experiments on ultrarelativistic beam-plasma interactions.

Numerical study of self-focusing and filament formation of intense vortex beams in plasmas

We have studied the self-focusing and filamentation of vortex laser beams propagating in underdense plasmas with different values of the topological charge and initial laser powers. The self-focusing dynamics of vortex laser beams is closely related to the topological charge, which has attracted widespread attention. Based on the paraxial approximation of the Helmholtz equation, the steady-state solution of vortex beams propagating in underdense plasmas is deduced, and the expression for critical power of vortex laser beams is obtained. Furthermore, using the split-step Fourier method to solve the wave equation, we analyze the numerical images of vortex laser beams propagating in underdense plasma under different parameters. The simulation results show that the critical power for self-focusing is positively correlated with the topological charge of vortex laser beams. When the initial laser power is high enough, the vortex laser beam will first be focused into a thin ring, and then the modulation amplitude increases continuously, which eventually leads to the ring structure breaking into filaments. The number of filaments has an integer multiple relationship with the topological charge. In the process of filamentation, the radius and the maximum light intensity of vortex laser beam both change drastically. After the filamentation process is completed, the vortex laser beam continues to propagate with a new topological type. We further increase the incident laser power and find that the number of filaments of the vortex laser beam increases. The increased number of filaments is the value of its topological charge at each time. With the development of filament instability, higher-order modulation instability can be excited in the later stage, and the intensity of filaments will exhibit angular modulation. Our results show that in compared with the standard Gaussian beam, the propagation behavior of vortex laser beams in underdense plasmas is much more stable under the same power, wavelength and plasma parameters. The propagation characteristics of vortex laser beams are helpful to the theoretical and experimental study of stimulated backward Raman amplification of ultra-strong vortex beam in underdense plasmas.

Nonlinear beam self-imaging and self-focusing dynamics in a GRIN multimode optical fiber: theory and experiments.

Beam self-imaging in nonlinear graded-index multimode optical fibers is of interest for many applications, such as implementing a fast saturable absorber mechanism in fiber lasers via multimode interference. We obtain a new exact solution for the nonlinear evolution of first and second order moments of a laser beam of arbitrary transverse shape carried by a graded-index multimode fiber. We have experimentally directly visualized the longitudinal evolution of beam self-imaging by means of femtosecond laser pulse propagation in both the anomalous and the normal dispersion regime of a standard telecom graded-index multimode optical fiber. Light scattering out of the fiber core via visible photo-luminescence emission permits us to directly measure the self-imaging period and the beam dynamics. Spatial shift and splitting of the self-imaging process under the action of self-focusing are also revealed.

Dynamics of channel formation and self-focusing of q-Gaussian laser pulse

Dynamics of low-density channel formed by the radial expulsion of electrons and ions due to the ponderomotive force of the q-Gaussian laser is investigated. Under perturbation approximation, an expression for channel density is derived in order to analyze the depletion of density inside the channel. WKB approximation is employed to study the propagation of q-Gaussian laser in the self-formed channel. For realizing better channeling and self-focusing of laser, laser and plasma parameters are optimized. The effect of q-parameter on the channel formation and spot size has been graphically presented and discussed.

The Physics of the one-dimensional nonlinear Schrödinger equation in fiber optics: Rogue waves, modulation instability and self-focusing phenomena

We review the different dynamical mechanisms leading to the emergence of coherent structures in physical systems described by the integrable one-dimensional nonlinear Schrödinger equation (1DNLSE) in the focusing regime. In this context, localized and coherent structures are very often associated to rogue wave events. We focus on one-dimensional optical experiments and in particular on (single mode) optical fibers experiments. In the focusing regime of 1DNLSE, the so-called modulation instability (MI), arising from nonlocal perturbation of the plane waves, is the most common phenomenon. Alongside the standard MI, other mechanisms are responsible for the emergence of rogue waves. We classify the different scenarii by considering those induced by small perturbations of unstable stationary state (the plane waves) and the ones arising from the self-focusing of large pulses without any perturbation. In the former case, the perturbations can be local, global, random or deterministic. In the latter case, the self-focusing dynamics can be observed both with isolated pulses or with large initial fluctuations of the optical power. We review the dynamics of emergence of localized structures in all these different scenarii.

Influence of the spatial confinement on the self-focusing of ultrashort pulses in hollow-core fibers

The collapse of a laser beam propagating inside a hollow-core fiber is investigated by numerically solving different nonlinear propagation models. We have identified that the fiber confinement favors the spatial collapse, especially in case of pulses with the input peak power close to the critical value. We have also observed that when using pulses in the femtosecond range, the temporal dynamics plays an important role, activating the spatial collapse even for pulses with input peak powers below the critical value. The complex self-focusing dynamics observed in the region below the critical power depends on the temporal evolution of the pulse and, also, on the interaction between the different spatial modes of the hollow-core fiber.

Counterpropagating interactions of self-focusing Airy beams

We study the first experimental collisions of two incoherent self-focused counterpropagating Airy beams in a nonlinear crystal. Their interactions demonstrate that the self-focusing dynamics of the Airy beams can be spatially controlled by the counterpropagating Airy beam. By tuning the misalignment and the size of the beams, we can control the output position of the self-focused Airy beam and switch to multiple outputs. Also the nonlinearity strength enables to engineer the temporal stability of the resulting waveguide structure.

Self-focusing dynamics of patches of ripples

The dynamics of focussing of extended patches of nonlinear capillary–gravity waves within the primitive fluid dynamic equations is presented. It is found that, when the envelope has certain properties, the patch focusses initially in accordance to predictions from nonlinear Schrödinger equation, and focussing can concentrate energy to the vicinity of a point or a curve on the fluid surface. After initial focussing, other effects dominate and the patch breaks up into a complex set of localised structures–lumps and breathers–plus dispersive radiation. We perform simulations both in the inviscid regime and for small viscosities. Lastly we discuss throughout the similarities and differences between the dynamics of ripple patches and self-focussing light beams.

Filamentation and supercontinuum generation in solid-state dielectric media with picosecond laser pulses

Filamentation and supercontinuum generation with 1.3-ps, 1055-nm laser pulses in YAG crystal is investigated numerically and experimentally. Numerical simulations based on solving the unidirectional nonparaxial propagation equation uncover that the self-focusing dynamics of a picosecond laser pulse markedly differs from that observed in a femtosecond filamentation regime. We show that spatiotemporal transformation of the picosecond pulse is governed by the free electron plasma, which defocuses and absorbs its rear part, resulting in the formation of several subpulses of femtosecond duration, which thereafter undergo peculiar spatiotemporal dynamics and have different contributions to spectral superbroadening. The numerical findings are confirmed experimentally by measuring the spatiotemporal intensity profiles of the wave packet at various stages of propagation where relevant events of the spectral broadening occur.

Pyroelectric Self-Focusing of Light Beams in Reduced Lithium Niobate Crystals

We have experimentally studied the dynamics of self-focusing of light beams in chemically reduced lithium niobate crystals when they are uniformly heated. We have established that the pyroelectric effect leads to a change in the light-induced space-charge fi eld, which results in compensation of the photorefractive self-action of the beams.

Extreme events in resonant radiation from three-dimensional light bullets

We report measurements that show extreme events in the statistics of resonant radiation emitted from spatiotemporal light bullets. We trace the origin of these extreme events back to instabilities leading to steep gradients in the temporal profile of the intense light bullet that occur during the initial collapse dynamics. Numerical simulations reproduce the extreme valued statistics of the resonant radiation which are found to be intrinsically linked to the simultaneous occurrence of both temporal and spatial self-focusing dynamics. Small fluctuations in both the input energy and in the spatial phase curvature explain the observed extreme behavior.

Nonlinear refractive index induced collision and propagation of nematicons

Nematic liquid crystals (NLCs) have proved to be excellent materials for nonlinear optics and its applications because of their large nonresonant nonlinearity and their extended spectral transparency. We demonstrate the exemplary collision scenario of both optical solitons and nematicons induced by the nonlinear refractive index in nematic liquid crystals. We invoke Hirota's bilinearization method for two coupled partial differential equations governing the dynamics of self-focusing of a laser light in a nematic liquid crystal system. We believe that this type of collision of optical solitons and nematicons reveals the many possibilities of all-optical switching schemes for spatial demultiplexing, network reconfiguration and logic gates.

Dynamic Control of Collapse in a Vortex Airy Beam

Here we study systematically the self-focusing dynamics and collapse of vortex Airy optical beams in a Kerr medium. The collapse is suppressed compared to a non-vortex Airy beam in a Kerr medium due to the existence of vortex fields. The locations of collapse depend sensitively on the initial power, vortex order, and modulation parameters. The collapse may occur in a position where the initial field is nearly zero, while no collapse appears in the region where the initial field is mainly distributed. Compared with a non-vortex Airy beam, the collapse of a vortex Airy beam can occur at a position away from the area of the initial field distribution. Our study shows the possibility of controlling and manipulating the collapse, especially the precise position of collapse, by purposely choosing appropriate initial power, vortex order or modulation parameters of a vortex Airy beam.

Curvature aided long range propagation of short laser pulses in the atmosphere

The pre-filamentation regime of propagation of a short and intense laser pulse in the atmosphere is considered. Spatiotemporal self-focusing dynamics of the laser beam are investigated by calculating the coupled differential equations for spot size, pulse length, phase, curvature, and chirp functions of a Gaussian laser pulse via a variational technique. The effect of initial curvature parameter on the propagation of the laser pulse is taken into consideration. A method relying on the adjustment of the initial curvature parameter can expand the filamentation distance of a laser beam of given power and chirp is proposed.

Self-focusing dynamics of ultraintense accelerating Airy waveforms in water

We report experiments and numerical simulations on the self-focusing and filamentation of ultraintense femtosecond Airy waveforms in water. The accelerating property of Airy waveforms results in the generation of distinct features in the angularly resolved spectra of forward-propagating supercontinuum emission. Fitting these features with appropriate phase-matching conditions allows for the quantification of the propagation history of the waveforms.

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.

Pulse splitting in the anomalous group-velocity-dispersion regime

We investigate experimentally the role that the initial temporal profile of ultrashort laser pulses has on the self-focusing dynamics in the anomalous group-velocity dispersion (GVD) regime. We observe that pulse-splitting occurs for super-Gaussian pulses, but not for Gaussian pulses. The splitting does not occur for either pulse shape when the GVD is near-zero. These observations agree with predictions based on the nonlinear Schrödinger equation, and can be understood intuitively using the method of nonlinear geometrical optics.

Self-focusing in air with phase-stabilized few-cycle light pulses

We investigate the nonlinear optical phenomenon of self-focusing in air with phase-stabilized few-cycle light pulses. This investigation looks at the role of the carrier-envelope phase by observing a filament in air, a nonlinear phenomenon that can be utilized for few-cycle pulse compression [Appl. Phys. B79, 673 (2004)]. We were able to measure the critical power for self-focusing in air to be 18+/-1 GW for a 6.3 fs pulse centered at 800 nm. Using this value and a basic first-order theory, we predicted that the self-focusing distance should deviate by 790 mum as the carrier-envelope phase is shifted from 0 to pi/2 rad. In contrast, the experimental results showed no deviation in the focus distance with a 3sigma upper limit of 180 mum. These counterintuitive results show the need for further study of self-focusing dynamics in the few-cycle regime.