Self-focusing Threshold Research Articles

Threshold of stochastic self-focusing from the Poisson property of extreme-event statistics.

Statistics of self-focusing induced by a stochastic laser driver is shown to converge, in the large-sample-size limit, to a generalized Poisson distribution whose mean is given by the exponent of the respective extreme-value statistics. For a given ratio of the laser peak power to the self-focusing threshold Pcr, the mean number of self-focusing counts in a large sample of laser pulses is shown to depend on the number of pulses in the sample, N, and the signal-to-noise ratio of laser pulses, a. We derive a closed-form solution for the threshold of stochastic self-focusing, which, unlike its deterministic counterpart, Pcr, is a function of the sample size N and the signal-to-noise ratio a. The parameter Na = exp (a2/2) is shown to set a borderline between the deterministic and stochastic regimes of self-focusing. When the number of laser pulses in a sample becomes comparable to Na, self-focusing can no longer be viewed as deterministic even for high signal-to-noise laser beams.

Femtosecond Laser Cutting of 110-550 µm Thickness Borosilicate Glass in Ambient Air and Water.

The cutting quality and strength of strips cut with femtosecond-duration pulses were investigated for different thicknesses of borosilicate glass plates. The laser pulse duration was 350 fs, and cutting was performed in two environments: ambient air and water. When cutting in water, a thin flowing layer of water was formed at the front surface of the glass plate by spraying water mist next to a laser ablation zone. The energy of pulses greatly exceeded the critical self-focusing threshold in water, creating conditions favorable for laser beam filament formation. Laser cutting parameters were individually optimized for different glass thicknesses (110-550 µm). The results revealed that laser cutting of borosilicate glass in water is favorable for thicker glass (300-550 µm) thanks to higher cutting quality, higher effective cutting speed, and characteristic strength. On the other hand, cutting ultrathin glass plates (110 µm thickness) demonstrated almost identical performance and cutting quality results in both environments. In this paper, we studied cut-edge defect widths, cut-sidewall roughness, cutting throughput, characteristic strength, and band-like damage formed at the back surface of laser-cut glass strips.

Cross-Filament Stochastic Acceleration of Electrons in Kilojoule Picosecond Laser Interactions with Near-Critical-Density Plasmas

Understanding the interaction of a kilojoule picosecond laser pulse with long-scale-length preplasma or homogeneous near-critical-density (NCD) plasma is crucial for guiding experiments at national short-pulse laser facilities. Using full three-dimensional particle-in-cell simulations, we demonstrate that in this regime, cross-filament stochastic acceleration is an important mechanism that contributes to the production of superponderomotive high-flux electron beams. Since the laser power significantly exceeds the threshold of the relativistic self-focusing, multiple filaments are generated and can propagate independently over a long distance. Electrons jump across the filaments during the acceleration and their motion becomes stochastic. We find that the effective temperature of electrons increases with the total interaction time following a scaling like ${T}_{\mathrm{eff}}\ensuremath{\propto}{\ensuremath{\tau}}_{i}^{0.65}$. By irradiating a submillimeter-thick NCD target, the space charge of electrons with energy above 2.5 MeV reaches tens of microcoulombs. Such high-flux electrons with superponderomotive energies significantly facilitate applications in high-energy-density science, nuclear science, secondary sources, and diagnostic techniques.

Simulating the filamentation of smoothed laser beams with three-dimensional nonlinear dynamics

In a plasma, the ponderomotive force of an inhomogeneous electromagnetic field expels plasma from regions of high intensity. When a laser propagates through a plasma, this force creates density wells that subsequently modify the index of refraction. The beam refracts and focuses into these wells and may filament. In extreme cases, the laser beam will spray due to increasing angular divergence of the beam. The threshold for ponderomotive self-focusing is well established for isolated laser hotspots or speckles. Here, we define a practical threshold for characterizing the filamentation of thousands of speckles that are found in the focal plane of high-power laser beams spatially smoothed with random phase plates as used at high energy and power laser facilities studying inertial confinement fusion. This threshold is tested against three-dimensional simulations of speckled laser light propagating through plasma. Four metrics are applied to assess filamentation: the fraction of power above five times the average intensity, an effective f-number, the mean-squared perpendicular wavenumber, and the fraction of rarefied density with deviation from the initial density exceeding |δn/n| = 0.1. The speckled beams studied are generated by random phase plates, both with and without additional polarization smoothing, in a parameter regime of relevance to indirect drive experiments. While filamentation has been discussed extensively in the literature, we believe this to be the first published simulation study with three-dimensional nonlinear hydrodynamics that addresses the onset threshold of ponderomotive filamentation and establishes the lengths and time scales necessary to reach a statistical steady state.

Study of quasimonoenergetic electron bunch generation in self-modulated laser wakefield acceleration using TW or sub-TW ultrashort laser pulses

This work presents a study on laser wakefield electron acceleration in the self-modulated regime (SM-LWFA) using 50-fs laser pulses with energy on the mJ scale, at λ = 0.8 µm, impinging on a thin H2 gas jet. Particle-in-cell simulations were performed using laser peak powers ranging from sub-terawatt to a few terawatts and plasma densities varying from the relativistic self-focusing threshold up to values close to the critical density. The differences in the obtained acceleration processes are discussed. Results show that bunched electron beams with full charge on the nC scale and kinetic energy in the MeV range can be produced and configurations with peak density in the range 0.5–5 × 1020 atoms/cm3 generate electrons with maximum energies. In this range, some simulations generated quasimonoenergetic bunches with ∼0.5% of the total accelerated charge and we show that the beam characteristics, process dynamics, and operational parameters are close to those expected for the blowout regime. The configurations that led to quasimonoenergetic bunches from the sub-TW SM-LWFA regime allow the use of laser systems with repetition rates in the kHz range, which can be beneficial for practical applications.

Beam collapse and refractive index changes inside fused silica induced by loosely focused femtosecond laser

Femtosecond laser-induced optical and structural changes inside transparent materials are crucial to ultrafast laser micromachining. In this work, on-axis beam collapse has been predicted by theoretical simulations and further demonstrated by the experimental results where a femtosecond pulse was loosely focused into a fused silica with the energy far above the self-focusing threshold. A detailed discussion of the energy thresholds and the starting locations on the optical axis of beam collapse for different beam waist radiuses is given. In addition, the spatial distribution of the refractive index has been determined using a spectroscopic ellipsometer and a roughly uniform decrease of 0.1 has been observed in the laser-modified region. Further, the relationship between the spatial distribution of the refractive index and the pulse energy density has been discussed quantitatively. The observed modulation of the beam collapse and the refractive index distribution can be expected to be a useful tool for femtosecond laser micromachining.

Numerical modelings of ultrashort pulse propagation and conical emission in multimode optical fibers

We make use of two well-known numerical approaches of nonlinear pulse propagation, namely, the unidirectional pulse propagation equation and the multimode generalized nonlinear Schrödinger equation, to provide a detailed comparison of ultrashort pulse propagation and possible conical emission in the context of multimode optical fibers. We confirm the strong impact of the frequency dispersion of the nonlinear response on pulse splitting and supercontinuum dynamics in the femtosecond regime for pumping powers around the critical self-focusing threshold. Our results also confirm that the modal distribution of optical fibers provides a discretization of conical emission of the corresponding bulk medium (i.e., here fused silica). This study also provides some criteria for the use of numerical models, and it paves the way for future nonlinear experiments in commercially available optical fibers.

Role of Dislocations in the Process of Degradation of Semiconductor Lasers with Electronic Energy Pumping. Experimental Research

Light self-destruction-degradation of the second type has been observed in samples of semiconductor lasers with electronic energy pumping with high optical homogeneity and good quality of surface treatment. In these samples, damage appeared in the form of cords perpendicular to the ends of the resonator. According to the current understanding of the passage of powerful light streams through various media, the emergence of narrow light channels is due to the phenomenon of self-focusing. It refers to the fundamental physical mechanisms of propagation of laser radiation and is caused by nonlinear phenomena arising in a medium under the influence of high-power laser radiation. The physical reason for self-focusing is an increase in the refractive index n in a strong light field. Thermal self-focusing is the most probable cause of radiation redistribution in the active region of the crystal. However, it is possible that in the initial stage of the appearance of light channels a certain role is played by the growth of the intensity of radiation in certain sections of the crystal because of the instability of generation or small fluctuations in the pump current density. Then the process acquires an avalanche character, since the localization of the ray in the channel increases the density of light radiation which can lead to overheating of the substance and the activation of the thermal self-focusing mechanism. The experiments performed in this paper have shown that optically homogeneous crystals possess maximum resistance to degradation processes. In them, the critical power of light destruction is determined by the self-focusing threshold of radiation in a material. Since the nonlinear addition to the refractive index Δn = n2E2 at the self-focusing threshold is determined by the change in the concentration of non-equilibrium carriers ΔN(E2), the value of the maximum fluctuation DΔNmax itself is proportional to the value of the non-equilibrium carrier concentration at the generation threshold ΔNpores and the relative excess of the generation threshold J = (j – jn)/jn. Thus, a low threshold concentration of non-equilibrium carriers is one of the conditions for increasing material resistance to degradation processes. In doped crystals ΔNpores is less than in pure materials. This, perhaps, explains the rather higher value of Pcritial in the optimally doped homogeneous n-GaAs. Smaller values of Pcritial in p-type samples doped with zinc can be associated not only with the inhomogeneity of these crystals, but also with large generation thresholds. In addition, the cross section for absorption of radiation by holes is about 3–4 times larger than by electrons, which can also reduce the self-destruction threshold of lasers. At Т = 300 K, the lasing thresholds are higher that naturally reduces the value of the self-focusing threshold.

Nonlinear rovibrational response in the propagation of long-wavelength infrared pulses and pulse trains

The propagation of long-wavelength pulses is affected by a multitude of near-resonant rovibrational transitions in atmospheric constituents, of which water vapor is generally the most abundant. We extract the pure nonlinear response of these transitions from a high-resolution transmission-based effective model, which is additive to the spectrally resolved linear response, and study the influence of this on the propagation of laser pulses and pulse trains. Compared to simulations with only electronic Kerr self-focusing, we find that the nonlinear rovibrational response introduces an additional modification to strongly self-focused laser pulses and stark changes to pulses that are close to the self-focusing threshold.

Self-focusing of CW laser beam with variable radius in rubidium atomic vapor

Abstract Self-focusing of cw laser beam in a rubidium atomic vapor was studied. The beam radius and power at the entrance of a rubidium vapor cell were variable parameters. A steep grow of the self-focusing threshold power for the small beam radius ( ≤ 30 μ m) was observed. Our experimental data are in a qualitative agreement with the recently published theoretical results obtained for a conventional non-resonant gas. Additional experiments in the resonance and transparent non-resonant media are suggested in order to check and extend our measurements.

Ionization-assisted spatiotemporal localization in gas-filled capillaries.

We demonstrate numerically and experimentally that intense pulses propagating in gas-filled capillaries can undergo localization in space and time due to strong plasma defocusing. This phenomenon can occur below or above the self-focusing threshold Pcr as a result of ionization-induced refraction that excites higher-order modes. The constructive interference of higher-order modes leads to spatiotemporal localization and resurgence of the intensity. Simulations show that this confinement is more prominent at shorter wavelength pulses and for smaller capillary diameters. Experiments with ultraviolet pulses show evidence that this ionization-induced refocusing appears below Pcr and thus represents a mechanism for spatiotemporal confinement without self-focusing.

High Energy (100 mJ) and High Peak Power (8 MW) Nanosecond Pulses Delivered by Fiber Lasers and Self-Focusing Analysis Based on a Novel Mode Decomposition Method

Nanosecond (∼10 ns) laser pulses with high peak power of 8 MW and high energy of 100 mJ are reported, which are generated by a cascaded pulsed Yb-doped fiber amplifier system working at a repetition frequency of 10 Hz. The peak power that is higher than the self-focusing threshold for Gaussian beams is achieved for the first time in the fiber lasers. To analyze the self-focusing threshold for multimode lasers in fibers, a novel mode decomposition based on the beam quality measurements is introduced. Based on the mode decomposition and nonlinear laser propagation simulations, the threshold of self-focusing for our case is estimated.

Multi-pass-cell-based nonlinear pulse compression to 115 fs at 7.5 µJ pulse energy and 300 W average power.

We demonstrate nonlinear pulse compression by multi-pass cell spectral broadening (MPCSB) from 860 fs to 115 fs with compressed pulse energy of 7.5 µJ, average power of 300 W and close to diffraction-limited beam quality. The transmission of the compression unit is >90%. The results show that this recently introduced compression scheme for peak powers above the threshold for catastrophic self-focusing can be scaled to smaller pulse energies and can achieve a larger compression factor than previously reported. Good homogeneity of the spectral broadening across the beam profile is verified, which distinguishes MPCSB among other bulk compression schemes.

Influence of strong magnetic fields on laser pulse propagation in underdense plasma

We examine the interaction between intense laser pulses and strongly magnetised plasmas in the weakly relativistic regime. An expression for the electron Lorentz factor coupling both relativistic and cyclotron motion nonlinearities is derived for static magnetic fields along the laser propagation axis. This is applied to predict modifications to the refractive index, critical density, group velocity dispersion and power threshold for relativistic self-focusing. It is found that electron quiver response is enhanced under right circularly-polarised light, decreasing the power threshold for various instabilities, while a dampening effect occurs under left circularly-polarised light, increasing the power thresholds. Derived theoretical predictions are tested by one- and three-dimensional particle-in-cell simulations.

Self-focusing threshold of a beam of laser radiation in rubidium vapor

This paper describes the self-focusing of laser radiation in atomic rubidium vapor close to the 5S1/2–5P3/2 resonance transition (780 nm). The self-focusing threshold power is measured at various transverse beam sizes of the laser radiation at the input of a cell with rubidium vapor. An increase of the self-focusing threshold power was observed at small beam diameters of the laser radiation. The results of the measurements were compared with the data of theoretical studies.

Nonlinear pulse compression in a multi-pass cell.

We demonstrate a scheme for nonlinear pulse compression at high average powers based on self-phase modulation in a multi-pass cell using fused silica as the nonlinear medium. The scheme is suitable for compression of pulses with peak powers exceeding the threshold for critical self-focusing. At >400 W of input power, the pulses of a Yb:YAG-Innoslab laser system (10MHz repetition rate, 850fs pulse duration) are spectrally broadened from 1.6 to >13.5 nm bandwidth while maintaining almost diffraction-limited beam quality. The chirp is removed with a dispersive mirror compressor, and pulse durations of 170fs at an output power of 375W are achieved. The compression unit reaches an overall transmission of >90%.

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.

Light self-focusing in the atmosphere: thin window model.

Ultra-high power (exceeding the self-focusing threshold by more than three orders of magnitude) light beams from ground-based laser systems may find applications in space-debris cleaning. The propagation of such powerful laser beams through the atmosphere reveals many novel interesting features compared to traditional light self-focusing. It is demonstrated here that for the relevant laser parameters, when the thickness of the atmosphere is much shorter than the focusing length (that is, of the orbit scale), the beam transit through the atmosphere in lowest order produces phase distortion only. This means that by using adaptive optics it may be possible to eliminate the impact of self-focusing in the atmosphere on the laser beam. The area of applicability of the proposed “thin window” model is broader than the specific physical problem considered here. For instance, it might find applications in femtosecond laser material processing.

Self-focusing threshold of partially coherent light in large mode area fibers

Coherent property of light is taken into consideration by utilizing Wigner transform method in solving self-focusing threshold of partially coherent light in LMA silica fibers. The formula for self-focusing threshold applicable for both coherent and partially coherent light in LMA silica fibers is derived, which only depends on beam quality factor M2 and bandwidth Δλ. It can be conveniently used to estimate self-focusing threshold in experiment and design partially coherent high power fiber amplifiers.

Coherent combination of spectrally broadened femtosecond pulses for nonlinear compression.

The coherent combination of ultrashort pulses has recently been established as a technique to overcome the limitations of laser amplifiers regarding pulse peak-power, pulse energy, and average power. Similar limitations also occur in nonlinear compression setups. In a proof-of-principle experiment, we show that the techniques developed for the combination of amplifiers can be adapted to nonlinear compression. We create two spatially separated pulse replica that undergo self-phase modulation in independent optical fibers and are recombined afterwards. Using this technique we demonstrate operation above the self-focusing threshold of a single pulse. Furthermore, we prove that the recombined pulses can be temporally compressed. This experiment paves the way for higher energy or average power operation of various nonlinear compression setups.