Femtosecond (FS) laser micro-machining has gained attention for its precision and minimal melting in processing various materials. However, processing speed is still far from an economical industrial use. Ultrashort pulse lasers with significantly higher average power and repetition rates than currently available will be required to overcome this limitation^[1]. An upper limit for the highest repetition rate usable is given by the interaction of the generated plasma with succeeding laser pulses, since this will distort or shield the laser beam^[2]. One of the important considerations is the critical density (nc) of the plasma corresponding to the probe laser beam wavelength, which is given by nc≈1.1×1021λ−2 where λ is the probe beam wavelength in micrometers and nc is in cm−3. For femtosecond lasers, the critical density is defined as the free electron density at which the plasma oscillation frequency is equal to the laser frequency. It is widely assumed that the ablation starts once the free electron density reaches the critical density^[3]. When the electron density of the plasma is below the critical density, the probe will propagate through the plasma. However, when ne>nc, the plasma is overdense and opaque for the subsequent pulse^[4]. So, the mechanism of FS laser micromachining is essentially determined by FS laser-electron interactions and subsequently variation of the plasma^[5,6]. Plasma shielding formation is the primary cause of the beam defocusing that prevents light from concentrating in the focal region^[7]. This phenomenon leads to a diminished energy deposition on the target area, thereby reducing the ablation efficiency^[8]. Avoiding the influence of plasma shielding from preceding pulses in the temporal domain remains a significant challenge. According to the timescales of the relevant physical processes in femtosecond laser micromachining^[9], the recombination of excited electron-hole pairs decreases the density of free electrons, thereby alleviating the impact of the plasma shielding effect^[10,11]. However, this recombination process simultaneously increases the kinetic energy of the newly generated electron-hole pairs^[12], potentially inducing shockwaves that may compromise the quality of femtosecond laser processing. Therefore, capturing the transient recovery window (TRW)—the temporal span between plasma shielding decay and shockwave initiation—becomes crucial for optimizing femtosecond laser processing parameters. Yet, the evolution of laser-produced plasma may be one of the most complex systems due to its small size, transient nature, and inherent spatial inhomogeneities^[13]. Pump-probe shadowgraphy is the most typical for characterizing FS-laser-induced plasma^[14,15]. By acquiring time-delayed frames, one can reconstruct an ultrafast movie of the time-evolution reaction of the material^[6,16]. Despite its widespread application, the fundamental mechanisms underlying plasma recombination remain actively debated in the scientific community^[17,18]. In this paper, we investigate the time-resolved spatial evolution of plasma shielding effects induced by FS pulses in water. While numerous studies have explored ultrafast interactions between FS lasers and water^[19,20], detailed elucidation of the TRW remains largely unexplored. During the investigation of femtosecond-laser-induced plasma evolution, the plasma serves as a point source; shock waves detach from the plasma and propagate into the surrounding medium, forming radially symmetric density gradients. These density gradients can symmetrically modulate the probe light propagating in the same direction as the pump light, and the modulated probe light contains key information regarding the plasma recombination time and the transient characteristic window^[21,22]. Furthermore, in the transmission detection scheme, the probe light propagates collinearly with subsequent pulses, enabling accurate characterization of the actual plasma shielding effect on the subsequent pulse. Then, it is possible to suppress the plasma shielding effect, thereby enhancing energy transfer efficiency and improving machining precision. This study reveals the TWR, which occurs at the critical juncture between the completion of plasma recombination (where the shielding effect vanishes) and the initiation of shockwave formation (marking the beginning of mechanical damage).

Precisely targeting this temporal window allows for the simultaneous avoidance of plasma shielding, shockwave formation, and subsequent cavitation bubble formation, which can affect the subsequent pulse transmission. The discovery provides an accurate temporal reference for refining high-repetition-rate pulsed laser processing techniques.

When an FS laser pulse (a pump pulse; red lines in Fig. 1) is focused inside water, the material absorbs the laser energy through multiphoton ionization or tunneling ionization. Excited electron energy is subsequently transferred to the lattice, inducing localized temperature rise. Thermoelastic relaxation and potential chemical reactions lead to a refractive index gradient change, forming a lens-like structure transient lens (TrL)^[21,23]. The probe beam co-propagates collinearly with the pump beam, with its wavefront phase subject to modulation by transient refractive index gradient variations. Modulated by the TrL, the probe light manifests as detectable distortions in the far-field beam profile and these distortions contain information about transient refractive index changes. If the TrL exhibits a Gaussian-shaped negative refractive index distribution, it equivalently acts as a concave lens, and the far-field beam diverges. Conversely, when the TrL region has a Gaussian-shaped positive refractive index distribution, it functions as a convex lens, leading to the convergence of the far-field beam. The detection plane is located at z=F2 shown in Fig. 1. When there is no TrL (no pump beam), the electric field of the probe beam at the detection plane may be expressed as E0(z,t)=A0ej(kz−ωt),(1)where A0 is the amplitude of the wave, k=2π/λ is the wave number, ω represents the angular frequency, and j is the imaginary unit. When the probe beam passes through the TrL region, the phase of the probe beam is modulated by the refractive-index distribution. Since the spatial distributions of the laser-induced refractive-index change and the electric field of the probe beam are cylindrically symmetric around the z-axis, the electric field of the probe beam just after the TrL region can be expressed as E1(r)=E0(r)ejΔϕ(r),(2)where r is the radial distance from the center of the beam, and E0(r) and ϕ(r) are the electric field of the probe beam just before TrL and the phase distribution function of TrL, respectively. The evolution of plasma induced by an FS laser exhibits axial symmetry about the optical axis. The Hankel transform is an integral transform specifically designed for symmetric systems. This mathematical framework facilitates dimensionality reduction from the original 2D Cartesian coordinates to a 1D radial representation, effectively. Then, according to Fresnel diffraction theory, the propagation of light in a homogeneous medium can be calculated using the Hankel transform for cylindrically symmetric electric fields^[24]. Therefore, after propagating through a distance z0, the probe electric field on the detection plane ESIG(s) is given by ESIG(s)=2πjλz0ejπs2λz0×∫0∞E1(r)ejπs2λz0J0(2πrsλz0)rdr,(3)where s is a radial position from the beam axis on the detection plane, λ is the wavelength of the probe beam, z0 corresponds to the distance between the TrL and the detection plane, and J0(r) is the zeroth order of the Bessel function. The intensity profile of the probe beam ISIG(s) on the detection plane is given by the square of ESIG(s): ISIG(s)=|ESIG(s)|2.(4)

The femtosecond-laser-induced plasma, as analytically described by the four governing equations [Eqs. (1)–(4)], modulates the probe light, leading to observable alterations in its intensity.

The experimental setup is shown schematically in Fig. 2. A commercial femtosecond fiber laser system (HR-Femtosecond-IR-50-40B, Huaray, China) was employed to generate a laser beam with a pulse width of 350 fs, a central wavelength of 1035 nm, and a repetition rate of 800 kHz. The laser was split into two beams by a polarizing beam splitter (PBS) cube. One beam that had 30% of the total power was focused into a β-barium borate (BBO) crystal by a 250 mm focal-length lens. This nonlinear optical configuration generated a frequency-doubled probe pulse at 518 nm through second-harmonic generation. Then the probe pulse, transmission through a 950 nm short-pass filter, was focused using a lens with a 400 mm focal length. Subsequently, the beam traversed a dichroic mirror before being directed towards the objective lens. It is imperative to meticulously adjust the distance between the focusing lens and the objective lens (Plan Apo NIR Infinity Mitutoyo 20×, NA=0.4) to ensure that the probe light illuminating the sample remains perfectly parallel, enabling wide-field illumination as shown in Fig. 3. The pump beam, comprising 70% of the total power, was directed through a half-wave plate (HWP) followed by a PBS.

This configuration enables the independent modulation of the pump beam’s energy, thereby ensuring that the intensity of the probe light remains unaffected. Then the pump beam traversed a time delay device (ODL220/M, Thorlabs, USA), which modulates the optical path difference between the pump and probe beams. The pump and probe beams, after being combined by a dichroic mirror, were both focused onto the sample within the specimens by an objective lens. The sample is a deionized water solution (WLT-DI-500). Finally, the probe light, collected by a 50× (Plan Apo NIR Infinity Mitutoyo 50×, NA=0.65) objective lens, was filtered through a filter (Semrock FF01-511/20) before being focused through a tube lens onto the camera sensor (MV-SUF401GM; sensor: 1-inch CMOS; pixel: 5.5μm×5.5μm), thereby achieving high-resolution ultrafast imaging. In this study, two distinct objective lenses are selected to simultaneously expand the operational workspace for sample manipulation and improve the imaging resolution of the system. The camera was triggered by synchronized signals generated by the DG645 (SRS), which was synchronized with the FS laser source. To increase the signal-to-noise ratio (SNR), the exposure time of the camera for each image was set at 20 ms.

In this research, plasma was excited with water by a single FS pulse, and its shielding effect on transmitted light was evaluated within the hundreds-of-picoseconds timescale. Typical transient maps at different delay time after excitation are displayed in Fig. 3. Four rows of images correspond to the ultra-fast processes observed after water is exposed to pump pulses of four different energies. Each row contains nine transient scenes. In imaging analysis, we define the change in the gray transient value integral of the pump-irradiated region of interest (ROI), denoted as ΔΣG, as the effective signal. By statistically analyzing the background measurement data from100 measurements under pump-free conditions, we calculate the mean fluctuation of the gray value integral in the same ROI, represented as μN, which serves as the benchmark for system noise. When the SNR is below 10 dB, we determine that the region has not undergone a significant photoresponse change. Images in the top row correspond to pump pulses with peak fluences of 1.77J/cm2. The images exhibit no significant photoresponse change (SNR<10dB) for the energy being near the breakdown threshold of 1.4J/cm2 (300 fs, 580 nm)^[25]. Under these conditions, the plasma density is extremely low, which results in a virtually negligible impact on the transmission of the probe light. The peak fluences reach 2.15J/cm2, corresponding to the images in the second row. A clearly visible dark spot (red arrow in Fig. 3) was observed at 6.6 ps after the pump pulse irradiation. Subsequently, the dark spot gradually faded and completely returned to its initial state at 231.0 ps. In the image sequences of the third and fourth rows, dark spots were also observed, first appearing at 6.6 ps. These rows correspond to pump pulse energies of 2.77 and 3.72J/cm2, respectively. The black regions demonstrate minimal variation in optical response across different pump pulse energies, owing to the saturation of reflectivity at a value approaching unity (R≈1). Compared to those under lower energies, the dark spots induced by higher-energy pump pulses exhibited significantly enhanced contrast and faded more rapidly, indicating a faster recovery process. As depicted in Fig. 4(a), the formation of the dark spot is attributed to the shielding effect of the plasma on the probing light. The detection shielding plane of the imaging system is precisely aligned with the focal plane. The highest plasma density at the center causes the parallel probing light to undergo continuous refraction or even reflection when passing through, thereby forming the central dark zone (Region 1). Meanwhile, the deflected light rays accumulate around the dark spot, thus forming a characteristic bright annulus (Region 2). Labeled regions in Fig. 4(a) correspond exactly with those in Fig. 4(b). Figure 4(b) captures the transient state of water at 6.6 ps after excitation by a pump pulse with an energy density of 3.72J/cm2, as recorded by the imaging system. Subsequently, the dark spots in the third and fourth rows vanished at 125.4 and 112.2 ps, respectively, indicating completion of the plasma recombination process. The plasma density returns to its pre-excitation baseline level (yellow arrow in Fig. 3). Then, a bright spot emerges in the central region at 178.2 and 132.0 ps. This phenomenon originates from shockwave-driven refractive index modulation that creates a TrL, inducing convergent modulation on the probe light. Images in the two rows exhibit similar dynamic evolution characteristics. However, the bright spots in the fourth row appear earlier in time than those in the third row. No bright spots were detected in the second row; while potential emergence at later temporal phases could occur, such delayed temporal regimes exceed the system’s detection range. The temporal evolution of the spot diameter measured under peak fluences of 2.77 and 3.72J/cm2 is shown in Figs. 5(a) and 5(b), respectively. To ensure experimental reliability, six replicate measurements were performed under constant pulse peak fluences with a temporal resolution of 6.6 ps. Figure 5 reveals three distinct characteristic evolutionary regimes: (I) plasma recombination (black square), (II) plasma recovery (star), and (III) shockwave and water vapor expansion (white square). In Fig. 5(a), Phase I (0–125.4 ps) represents the plasma dynamics, including plasma generation and electron-ion recombination. This phenomenon is uniformly represented by black squares and the diameter of the dark spot is positively correlated with the plasma density. At 6.6 ps, the diameter of the dark spot reaches its maximum, indicating that the plasma density reaches its maximum among the detectable data points in Phase I. Literature studies have shown that within hundreds of fs after FS laser irradiation, the plasma density rapidly peaks^[26]. Subsequently, as the femtosecond laser pulse ceases, the plasma density gradually decays. Limited by temporal resolution, the system cannot capture the earlier transient process of plasma density rise. However, this limitation does not affect the overall assessment of the ultrafast dynamics. The pump pulse energy was set at 2.15, 2.77, and 3.72J/cm2, and the corresponding recombination time were measured to be 231.0, 125.4, and 112.2 ps, respectively. It reveals that the recombination time exhibits strong functional dependence on incident pulse energy density. The recombination time are in excellent agreement with the 20 ps reported in Ref. [27]. It must be emphasized that the specific influence of the material played a crucial role in the recombination process. Fused silica showed a fast relaxation of approximately 150 fs^[28] mainly due to self-trapping of free electrons, whereas multi-component glasses such as soda lime glass show decay time of 100 ps^[29]. In Phase II (125.4–178.2 ps), the plasma density recovers to equilibrium for recombination and dissipation. In the third row, the plasma density returns to the initial state (yellow arrows in Fig. 3) at 125.4 ps. This state represents a pivotal temporal window—TRW. During this phase, the plasma shielding effect has fully subsided, whereas the refractive index gradients induced by the shockwave have not yet formed. Consequently, nonlinear attenuation and phase modulation effects on subsequent pulses are effectively mitigated, thereby establishing an optimal temporal regime for efficient multi-pulse train coupling. In Phase III (178.2–257.4 ps), following plasma recombination and recovery, vaporized water^[27] and shock waves^[30] are generated ahead of the objective lens focal plane. The shockwave-driven refractive index gradient in the pre-focal region generates a TrL, which induces phase modulation of the probe light field. The TrL can potentially function as either a converging or a diverging lens, depending on the intensity of the shockwave, the density of the plasma, and the geometric conditions of the interaction between the probe light and the plasma^[22]. In Fig. 5(a), the pump pulse energy (2.77J/cm2) significantly exceeds the breakdown threshold. A characteristic bright spot signal is detected by the system with a time delay of 178.2 ps. This phenomenon is uniformly represented by squares.

Figure 5(b) also encompasses these three evolutionary phases, with two critical temporal markers: 112.2 ps (indicating full plasma recombination) and 132.0 ps (corresponding to shockwave nucleation and water vaporization). It is important to note that in this experiment, the plasma recombination time is correlated with the pump laser pulse energy. By comparing Figs. 5(a) and 5(b), it is evident that the mechanisms of plasma generation and evolution are similar. However, superior pulse energies lead to faster recombination and recovery time. This phenomenon may be attributed to the dominance of Auger recombination at high energies and the predominance of self-trapped excitation capture at low energies. Further comparison of Figs. 5(a)(III) and 5(b)(III) reveals that under high-energy conditions, the rapid formation of shockwaves results in a shorter TRW. From a broader perspective, this plasma shielding evaluation method can be extended to other transparent material systems. The proposed approach provides a new technical pathway for optimizing laser processing techniques. Building upon the current research foundation, future work will focus on investigating the dynamic characteristics of shielding evolution under multi-pulse excitation conditions.

Integrating pump-probe and transient lens techniques, this study investigated the three-stage evolution of plasmas induced by FS laser-water interactions and established the concept of a TRW. Experimental results demonstrated that the plasma recovery time exhibited a strong dependence on laser pulse intensity. This method applies not only to the study of ultrafast evolution of plasma shielding induced by FS laser interaction with water but also to other transparent materials. It may provide a valuable reference for optimizing femtosecond laser processing parameters.