Critical Power For Self-focusing Research Articles

Impact-ionization mediated self-focusing of long-wavelength infrared pulses in gases.

We numerically investigate the propagation dynamics of intense long-wavelength infrared pulses in a weakly ionized argon gas and show that the pulses undergo self-focusing due to the transverse variations of electron-impact ionization caused by quivering electrons. We demonstrate this plasma-induced self-focusing at a power much lower than the critical power for Kerr self-focusing, and find that it can be controlled by the initial electron density and pulse duration.

Free-beam spectral self-compression at supercritical peak powers.

We demonstrate free-beam spectral self-compression of ~100-GW femtosecond laser pulses due to self-phase modulation (SPM) in a transparent dielectric. While all the earlier studies of SPM-induced spectral narrowing have been performed using optical fibers, experiments and simulations presented in this Letter show that this type of spectral transformation can be implemented as a part of a full three-dimensional field-waveform dynamics and can be extended to peak powers ∼105 times higher than the critical power of self-focusing. With a properly chosen initial chirp, spectral self-compression is accompanied by pulse compression, providing spectral-temporal mode self-compression as a whole.

Diffraction-Beam Optics of Filamentation: II–Diffraction-Beam Pattern of Laser Pulse Filamentation

Based on the diffraction-ray representation of nonlinear propagation of laser pulses, some examples of visualization of the filamentation of high-power femtosecond laser pulses in air are considered in the form of evolutionary paths of diffraction beams and light tubes. It is ascertained that a filament is supported by the light energy of the part of the beam which is inside a beam tube with the initial peak power higher than the critical power of self-focusing. This light tube is an energy reservoir for the filament. The light beam periphery holds the diffraction-beam tube which includes the filament by means of formation of a “diffractive” waveguide.

Effect of driving pulse properties on the performance of sub-terawatt laser wakefield acceleration

By introducing a sub-terawatt (TW) laser pulse into a high-density gas target, the self-focusing effect and the self-modulation instability can greatly enhance the laser peak power to a level capable of driving the laser wakefield acceleration (LWFA) of electrons. A particle-in-cell model has been developed to study the scheme in which 1030-nm pulses produced from a diode-pumped laser system are introduced into a gas cell with a flat-top density profile, allowing the LWFA to be operated at high frequencies. Because 1030-nm lasers are typically produced with a long duration >200 fs, a spectral broadening technique can be applied to reduce the pulse duration, from which a greater ponderomotive force is acquired to drive LWFA. To understand the dependence of LWFA performance on the driving pulse duration, selected durations, ranging from 200 fs to 10 fs, are assigned for 0.5-TW, 1030-nm pulses in a series of simulations. Results show that a duration around 50 fs can provide the optimal LWFA results, as a compromise between the weak ponderomotive force available from a long pulse >100 fs and the depletion effect which can rapidly diminish a short pulse <25 fs in a dense plasma. When a low laser peak power of 0.25-TW is available, the pulse depletion can be significant at a high target density and render LWFA ineffective. Using a laser pulse with a longer wavelength >2 μm represents a viable route to realize the LWFA with a low laser peak power; in this way, an appropriately selected target density which allows the laser peak power PL ∼ 1.25Pcr of self-focusing critical power is favourable for realizing an efficient LWFA process.

Similarity parameter for the process of mid-IR light bullet formation

We study the influence of the ratio of diffraction and dispersion lengths of a femtosecond mid-IR wave packet on the filamentation threshold power and the light bullet (LB) formation upon nonlinear optical interaction with solid-state dielectrics under the conditions of anomalous group velocity dispersion. It is found that the ratio of the threshold power of filamentation and LB formation to the critical power of stationary self-focusing is independent of the radiation wavelength and the medium characteristics and is determined by the similarity parameter, equal to the ratio of the diffraction length to the dispersion one. With an increase in the similarity parameter, the threshold power of filamentation and light bullet formation increases.

Path length and spectrum of single-cycle mid-IR light bullets in transparent dielectrics

Filamentation of femtosecond laser radiation with a wavelength of 800 – 3900 nm and a power slightly exceeding the critical self-focusing power is studied using the spectral method and the method of laser coloration in LiF crystal. It is found that the length of a filament formed in the single-pulse regime increases with increasing excitation wavelength from a few tens of micrometres at 80 nm to hundreds of micrometres at 3900 nm. In the spectral region of anomalous group velocity dispersion, starting from 2600 nm, the initially smooth luminescence profile of the long-lived induced colour centres acquires a periodic structure, demonstrating the formation of a light bullet with a duration of about one cycle of the light field oscillation and a diameter smaller than 10 μm. The path length of such bullets does not exceed 0.5 mm in the single-pulse regime and 2.7 mm in the waveguide regime. A consequence of periodic modulation of the bullet light field in the process of propagation, observed experimentally and confirmed by calculations, is the appearance of sidebands near the excitation wavelength, as well as the appearance of visible spectral components in the supercontinuum radiation, whose angular divergence increases with increasing wavelength.

Critical power for self-focusing of optical beam in absorbing media

Self-focusing effects are of central importance for most nonlinear optical effects. The critical power for self-focusing is commonly investigated theoretically without considering a material’s absorption. Although this is practicable for various materials, investigating the critical power for self-focusing in media with non-negligible absorption is also necessary, because this is the situation usually met in practice. In this paper, the simple analytical expressions describing the relationships among incident power, absorption coefficient and focal position are provided by a simple physical model based on the Fermat principle. Expressions for the absorption dependent critical power are also derived; these can play important roles in experimental and applied research on self-focusing-related nonlinear optical phenomena in absorbing media. Numerical results, based on the nonlinear wave equation—and which can predict experimental results perfectly—are also presented, and agree quantitatively with the analytical results proposed in this paper.

The dependence of external focusing geometries and polarization in generation of supercontinuum by femtosecond laser pulse in air

Supercontinuum (SC) generation in ambient air using different focusing geometries and laser energy under linear and circular polarization was investigated experimentally. Under the same input laser energy, the SC spectra in the visible range became wider when smaller f-number convex lens are used and the linearly polarized laser is used as the pump source, the main nonlinear mechanism for asymmetric spectral broadening of femtosecond laser pulses towards the higher frequencies in isotropic media is that the cascade generation with GHz spectral shift for gases and the four-photon parametric wave mixing processes. Besides, the temporal differential of electron density Ne(t) play a more important role in extending the SC spectra to the blue side than the interaction length l. Under the same magnitude of the optical field and the critical power for self-focusing of linearly and circularly polarized beams, the SC spectra range is wider when circularly polarized beams as the pump source.

Simulation study of the sub-terawatt laser wakefield acceleration operated in self-modulated regime

Laser wakefield acceleration (LWFA) can be accomplished by introducing a sub-terawatt (TW) laser pulse into a thin, high-density gas target. In this way, the self-focusing effect and the self-modulation that happened on the laser pulse produce a greatly enhanced laser peak intensity that can drive a nonlinear plasma wave to accelerate electrons. A particle-in-cell model is developed to study sub-TW LWFA when a 0.6-TW laser pulse interacts with a dense hydrogen plasma. Gas targets having a Gaussian density profile or a flat-top distribution are defined for investigating the properties of sub-TW LWFA when conducting with a gas jet or a gas cell. In addition to using 800-nm laser pulses, simulations are performed with 1030-nm laser pulses, as they represent a viable approach to realize the sub-TW LWFA driven by high-frequency, diode-pumped laser systems. The peak density which allows the laser peak power PL∼2Pcr of self-focusing critical power is favourable for conducting sub-TW LWFA. Otherwise, an excessively high peak density can induce an undesired filament effect which rapidly disintegrates the laser field envelope and violates the process of plasma wave excitation. The plateau region of a flat-top density distribution allows the self-focusing and the self-modulation of the laser pulse to develop, from which well-established plasma bubbles can be produced to accelerate electrons. The process of electron injection is complicated in such high-density plasma conditions; however, increasing the length of the plateau region represents a straightforward method to realize the injection and acceleration of electrons within the first bubble, such that an improved LWFA performance can be accomplished.

Nonlinear increase in the energy input into a medium at the fusion of regularized femtosecond filaments

The fusion in air of four femtosecond laser beams each with the peak power several times higher than the critical self-focusing power has been studied experimentally. It has been shown that a superfilament formed in such a regime ensures the efficient energy input to a medium. It has been shown that the linear density of the input energy increases approximately quadratically with both the energy of a laser pulse and the number of fused beams.

Self-compression of soliton-like laser pulses in the process of self-focusing

We study the possibility of efficient self-compression of femtosecond laser pulses in nonlinear media with anomalous dispersion of group velocity during the self-focusing of wave packets with a power several times greater than the critical self-focusing power. The results of qualitative analysis of the evolution of three-dimensional wave packets with the quasi-soliton field distribution are confirmed by the computer simulation. The simulation proves that the considered regime of compression of high-power laser pulses with initial durations of about ten optical cycles is stable relative to filamentation instability, due to the influence of the nonlinear dispersion. We demonstrate the possibility of self-compression of laser pulses at a multi-millijoule energy level and up to one optical cycle with an energy efficiency of more than 50%.

Effect of ripple on self-focusing of a cosh-Gaussian laser beam in collisionless plasma

In this paper, the effect of presence of ripple on the cosh-Gaussian beam in collisionless plasma considering relativistic nonlinearity is investigated. Using the Wentzel Kramers Brillouin (WKB) paraxial-ray approximation method and eikonal method, the basic sets of equations has been derived. It is observed that when the initial power of the ripple is greater than the critical power for self-focusing of cosh-Gaussian beam the ripple gets focused over the beam.

Direct measuring of single-cycle mid-IR light bullets path length in LiF by the laser coloration method

A colour-centre structure formed in a LiF crystal under filamentation of a femtosecond mid-IR laser pulse with a power slightly exceeding the critical power for self-focusing has been experimentally and theoretically investigated. A single-cycle light bullet was recorded for the first time by observation of strictly periodic oscillations for the density of the color centers induced in an isotropic LiF crystal under filamentation of a laser beam with a wavelength tuned in the range from 2600 to 3900 nm, which is due to the periodic change in the light field amplitude in the light bullet formed under filamentation under propagation in dispersive medium. The light bullet path length was not more than one millimeter.

Pulse self-compression to single-cycle pulse widths a few decades above the self-focusing threshold

We identify a physical scenario whereby optical-field waveforms with peak powers several decades above the critical power of self-focusing can self-compress to subcycle pulse widths. With beam breakup, intense hot spots, and optical damage of the material avoided within the pulse compression length by keeping this length shorter than the modulation-instability buildup length, the beam is shown to preserve its continuity at the point of subcycle pulse generation.

Periodic colour-centre structure formed under filamentation of mid-IR femtosecond laser radiation in a LiF crystal

A colour-centre structure formed in a LiF crystal under filamentation of a femtosecond mid-IR laser pulse with a power slightly exceeding the critical power for self-focusing has been experimentally and theoretically investigated. Strictly periodic oscillations have been detected for the first time for the density of the colour centres induced in an isotropic LiF crystal under filamentation of a laser beam with a wavelength tuned in the range from 2600 to . The structure period is found to be about . With an increase in the laser radiation wavelength, the period of the oscillations decreases and their amplitude increases. The maximum colour centre density, observed under filamentation of a beam, is related to the increased contribution of the direct generation of colour centres as a result of the absorption of an integer number of photons by the exciton band. It is numerically shown that the formation of a periodic colour-centre structure in LiF is due to the periodic change in the light field amplitude in the light bullet (1.5 optical periods long) formed under filamentation.

Supercontinuum generation in a multi-plate medium

We analyze femtosecond supercontinuum generation in a distribution of thin solid plates to show that the distributed scheme inhibits processes leading to pulse breakup while allowing spectral expansion to proceed as desired. We introduce basic criteria for setting the plate thickness or initial laser intensity and the location of each plate in the laser beam path and confirm that under these conditions a fully-coherent and intense supercontinuum can be generated for input peak power of as much as two thousand times the critical power for self-focusing of the solid medium.

Critical power and clamping intensity inside a filament in a flame

We report on measurements of both the critical power for self-focusing of a Ti: Sapphire 800 nm femtosecond laser and the peak intensity clamped inside a single filament in an ethanol-air flame on an alcohol burner array. By observing the shift of focal position of femtosecond laser pulses, we determine the critical power in the flame to be 2.2 ± 0.3 GW, which is 4-5 times smaller than the usually quoted one in air. The clamped laser intensity inside the filament is measured to be roughly half of that in air. Our results provide insights into the understanding of femtosecond laser filamentation in flames for practical application of combustion diagnostics.

Kerr effect-assisted self-compression in dielectric to single-cycle pulse width and to terawatt power level in mid-IR

The self-compression of sub-TW mid-IR (λ=4–5µm) femtosecond laser pulse in a non-linear dielectric medium was numerically modeled. Combination of the Kerr non-linearity and negative group velocity dispersion in CaF2 crystal was found to result in compression of the incident laser pulse to a 1–2-cycle pulse width. The possibility for suppression of small-scale self-focusing in conditions when the pulse power was several orders of magnitude above the critical self-focusing power was analyzed. Intrinsic concentration of free carriers was found to play important role in pulse evolution during its propagation.

Long-term Stability of Nonlinear Pulse Compression using Solid-core Large-mode-area Fibers

Long-term stability of a laser system is crucially important for applications such as ultrafast laser spectroscopy. Unfortunately, this topic received little attention in novel pulse compression schemes. Through the ultra-stable beam pointing of the 50 kHz laser system, the long-term stability of nonlinear pulse compression (NPC) was measured for up to 17 hours at different peak powers in a fiber core. The required spectral broadening was achieved in largemode- area photonic-crystal-fibers with linearly and circularly polarized light. The optimal parameters of a NPC system operating close to the fundamental limit of the critical self-focusing peak power were found. A further compression to sub-10 fs pulses in a second fiber stage is also discussed.

Self-trapped elliptical super-Gaussian beam in cubic–quintic media

We find self-trapped propagation of elliptical super-Gaussian beam in cubic–quintic nonlinear media. The soliton beam preserves its shape and size during propagation in Kerr media. Both defocusing and focusing quintic nonlinearities are considered. In a cubic (focusing)-quintic (defocusing) media breather like beam propagation with intriguing beam width oscillation is observed. The influence of beam ellipticity, super-Gaussian nature and quintic nonlinearity on self-trapping has been studied. A formula for critical power for self-focusing has been derived and it readily agrees with the results obtained by variational method. In Kerr and focusing quintic media beam collapse occurs quicker for higher order super-Gaussian beam. The critical power of self-focusing in defocusing (focusing) quintic medium prominently increases (decreases) with increasing strength of quintic nonlinearity. This variation rate is greater for higher order super Gaussian beam. A beam with greater ellipticity requires larger power for self-trapping.