Femtosecond Pulsed Laser Ablation in Liquid

• Fs-PLAL is a process employing ultrashort laser pulses in a liquid medium to induce localized ablation and generate colloidal nanoparticles with controlled morphology.
• The technique leverages nonlinear light–matter interactions and two-temperature dynamics to achieve precise energy deposition, enabling phase transitions and defect engineering.
• Optimization of laser fluence, pulse duration, and solvent conditions in fs-PLAL directly governs nanoparticle yield, size distribution, and functional properties for advanced material synthesis.

Femtosecond pulsed laser ablation in liquid (fs-PLAL) is a material processing technique that exploits ultrashort (tens to hundreds of femtoseconds) laser pulses to induce highly localized ablation at a solid–liquid interface, leading to the formation of colloidal nanoparticles, surface structuring, or localized modification of material properties. The extremely high peak intensities achieved within the short pulse duration drive nonlinear ionization, rapid energy deposition, and a complex sequence of non-equilibrium processes—ranging from electron–lattice decoupling to bubble dynamics and Rayleigh–Taylor instabilities—culminating in phase transitions and rapidly quenched nanostructure formation. Fs-PLAL possesses a unique capacity for clean, chemical-free synthesis and phase engineering of nanomaterials in liquid confinement, with fine control over yield, morphology, and defect content tunable via laser and environmental parameters (Hoppius et al., 2018, Petrov et al., 2018, Ushkov et al., 9 Dec 2025, Axente et al., 2010, Sahoo et al., 20 May 2024).

1. Nonlinear Light–Matter Interaction and Pulse Propagation in Liquids

Fs-PLAL is defined by the propagation of intense, ultrashort laser pulses into a liquid environment, where the slowly-varying pulse envelope $A(\mathbf{r}_\perp,t,z)$ is governed by a generalized nonlinear Schrödinger equation:

$$i\,\frac{\partial A}{\partial z} + \frac{k''}{2}\,\frac{\partial^2 A}{\partial t^2} + \frac{1}{2k_0}\nabla_\perp^2 A + k_0 n_2 |A|^2 A - \frac{\omega_0}{2c\,n_0}\,\rho_e\,A = 0$$

The dynamics incorporate group-velocity dispersion (GVD), Kerr self-focusing ($n_2$), and plasma defocusing from the generated free-carrier density $\rho_e$:

$$\frac{\partial \rho_e}{\partial t} = W_{\rm MPI}(I)\bigl(\rho_{\rm at}-\rho_e\bigr) \;+\;\sigma_K\,I\,\rho_e \quad,\quad I = \frac{n_0c\varepsilon_0}{2}\,|A|^2$$

Key material constants for water at 800 nm include: $k''\approx400\,\text{fs}^2/\text{mm}$, $n_2 = 4.1\times10^{-20}\,\text{m}^2/\text{W}$ (for ethanol, $n_2 = 7.7\times10^{-20}$), multiphoton ionization order $K=7$, and low linear absorption ($<0.01\,\text{cm}^{-1}$) (Hoppius et al., 2018).

Chirped pulse duration due to group-delay dispersion (GDD) obeys

$$\tau_{\rm chirp} = \sqrt{\tau_0^2 + \left(\frac{\phi''}{\tau_0}\right)^2}$$

where increasing $\tau_{\rm chirp}$ via positive GDD reduces peak intensity and delays self-focusing deeper into the liquid, mitigating supercontinuum generation and window damage.

2. Ultrafast Ablation Mechanisms and Two-Temperature Model

Energy deposition in fs-PLAL is distinguished by strong optical nonlinearity, ultrafast absorption, and two-temperature (2T) electron–lattice dynamics. The 2T model for a metal target describes

$$C_e(T_e)\frac{\partial T_e}{\partial t} = \nabla\cdot[\kappa_e(T_e)\nabla T_e] - G(T_e-T_l)+S(z,t)$$

$C_l\frac{\partial T_l}{\partial t} = G(T_e - T_l)$

where $C_e$ is the electron heat capacity, $C_l$ the lattice heat capacity, $\kappa_e$ the electron thermal conductivity, and $G$ the electron–phonon coupling constant ($\sim10^{17}-10^{19}$ W/m³ K for Au). The ultrashort laser pulse ($\tau_p < t_{\text{eq}}$) heats electrons to several thousand kelvin in <100 fs, with coupling to the lattice following over 1–10 ps (Petrov et al., 2018).

For oxides, chalcogenides, and semiconductors, the two-temperature approach can be combined with carrier dynamics and nonthermal melting criteria. The energy required for ablation, $F_{\rm th}$, typically satisfies

$F_{\rm th} \approx \rho\,c_p\,\Delta T + \sigma$

where $\Delta T$ can approach the critical temperature for phase explosion under stress confinement, resulting in pressures up to several GPa for $F_{\rm abs}\sim0.3-1\,\text{J/cm}^2$, and enabling spallation, phase explosion, or supercritical expansion (Petrov et al., 2018).

3. Hydrodynamics: Bubble Formation, Scattering, and Instabilities

Following ablation, a dense plasma is generated at the solid–liquid interface, resulting in rapid heating and formation of a vapor bubble whose dynamics are classically described by the Rayleigh–Plesset equation:

$$\rho_l\left(R\,\frac{d^2R}{dt^2} + \frac{3}{2}\left(\frac{dR}{dt}\right)^2\right) = p_b - p_\infty - \frac{2\sigma}{R} - 4\mu\frac{dR/dt}{R}$$

Bubble radii, life times, and number densities ($R_b\sim20-100\,\mu\text{m}$, $N_b\sim10^4-10^6\,\text{cm}^{-3}$) directly impact photon scattering cross sections ($\sigma_s = Q_s(\alpha)\pi R_b^2$ with $Q_s\sim2-4$), mean free path $\ell_{\rm sc}\sim0.5-5\,\text{mm}$, and thus on-target intensity (Hoppius et al., 2018). Surface waves introduce additional local focusing/defocusing, modulating ablation by up to ±20%.

Bubble growth and collapse govern nanoparticle release, secondary shock waves, and mixing. Deceleration at the interface drives Rayleigh–Taylor instability with growth rate $\omega_{\rm RT} = \sqrt{Akg}$, producing interface wrinkling and facilitating atomic intermixing and nucleation (Petrov et al., 2018).

Table: Key Bubble Parameters in fs-PLAL (Hoppius et al., 2018, Petrov et al., 2018)

Parameter	Typical Value	Significance
Bubble radius, $R_b$	20–100 μm	Controls scattering cross section
Number density, $N_b$	$10^4$–$10^6$ cm⁻³	Governs light attenuation, mean free path
Lifetime, $T_b$	100–200 μs	Sets optimal repetition rate

4. Nanoparticle Formation and Defect/Phase Engineering

Nanoparticle nucleation proceeds within the expanding bubble under ultrafast cooling rates ($10^9$–$10^{11}$ K/s), resulting in bottom-up condensation into size- and phase-selected colloids. For metals and semiconductors, the pulse-resolved ablation depth follows

$d_{\text{pulse}} \approx \delta\,\ln(F/F_{\rm th})$

with $\delta = 1/\alpha$ (optical penetration depth) (Ushkov et al., 9 Dec 2025, Hoppius et al., 2018). Nanoparticle size and distribution are highly sensitive to pulse parameters and delay schemes: dual-pulse fs-PLAL can increase NP diameter (to ~14 nm at Δt ≃ 100 fs) or decrease polydispersity at longer delays (Δt > 600 fs yields ≈8 nm for Au) (Axente et al., 2010).

Phase and defect engineering emerge in complex targets; fs-PLAL enables transformation of CdPS₃ to CdS and metallic Cd by solvent selection (DI water preserves ternary phase, IPA leads to 89% CdS QDs and metallic Cd) (Ushkov et al., 9 Dec 2025). In TMDCs such as MoS₂, fs-PLAL in water yields QDs with controlled surface oxidation to MoO₃₋ₓ, tuning band alignment and inducing blue-shifted photoluminescence via electron transfer between phases (Sahoo et al., 20 May 2024).

5. Optimization of fs-PLAL: Laser, Optical, and Fluidic Parameters

Reproducible and efficient fs-PLAL depends on a matrix of laser and environmental parameters (Hoppius et al., 2018, Petrov et al., 2018, Axente et al., 2010):

• Pulse duration: τ = 0.5–1.5 ps (chirped) for metals, τp≲1 ps under stress confinement maximizes fine NP formation and efficiency.
• Pulse energy/fluence: 0.2–1.0 mJ (0.5–3 J/cm²); threshold fluences for ablation are typically 0.5 J/cm² for Cu in water, with depth per pulse peaking at ≈0.8–1 J/cm². For semiconductors, F=12.5–75 J/cm² used for MoS₂ QDs (Sahoo et al., 20 May 2024).
• Repetition rate: 0.5–2 kHz optimal for metals, set to match bubble collapse time and maximize ablation volume (volumetric ablation rates 1–5×10⁻⁴ mm³/min).
• Focusing/NA: Moderate NA=0.08–0.12 (f-number ∼8) balances focusing with depth of field, tolerating ∆z=200–500 μm surface waves.
• Liquid layer thickness: 3–5 mm, set deeper than maximum bubble but shallower than filamentation onset.
• Flow and scanning: Gentle flow (5 mL/min) and raster scanning (~100 μm/s) mitigate bubble accumulation.

Liquid choice affects nonlinear propagation and post-ablation chemistry: water delays filament onset, ethanol increases NP yield but enhances white-light emission (Hoppius et al., 2018); solvents such as isopropanol induce phase reduction and defect formation in chalcogenides (Ushkov et al., 9 Dec 2025).

Table: Optimal fs-PLAL Windows for Cu in Water (Hoppius et al., 2018)

Parameter	Range	Yield/Outcome
Pulse duration	0.5–1.5 ps (chirped)	Depth/p: 10–50 nm
Fluence	0.5–3 J/cm²
Repetition rate	0.5–2 kHz	Vol. rate: 1–5×10⁻⁴ mm³/min
Focus NA	0.08–0.12
Liquid thickness	3–5 mm

6. Control of Material Properties via fs-PLAL

Fs-PLAL uniquely enables tailoring of phase composition, defect architecture, band structure, and functional properties—without surfactants or post-processing:

• Metal targets: NP size distribution and yield can be finely tuned by pulse delay and fluence (Axente et al., 2010).
• Complex chalcogenides: Solvent-driven phase conversion, e.g., CdPS₃→CdS/Cd in IPA, facilitates type-II and Schottky-like heterojunctions for visible-light photocatalysis ($\sim90\%$ MB degradation in 30 min under 532 nm) (Ushkov et al., 9 Dec 2025).
• TMDCs (e.g., MoS₂): Controlled oxidation (via power, ablation time) to MoO₃₋ₓ yields QD heterostructures, blue/UV emission with large Stokes shift, and tunable PL kinetics (Sahoo et al., 20 May 2024).

These schemes rely on the interplay between non-equilibrium ablation conditions, rapid plasma–liquid quenching, and solvent-specific redox pathways.

7. Applications, Limitations, and Outlook

Fs-PLAL is established for the synthesis of monodisperse colloidal nanoparticles (metals, oxides, chalcogenides), defect- and phase-engineered nanocrystals, and functional materials for photocatalysis, optoelectronics, and bioimaging. Its chemical-free, surfactant-free nature and scalable throughput support advanced manufacturing. However, process throughput remains limited by cavitation bubble dynamics and the need for continual liquid/target renewal (Petrov et al., 2018).

Current work extends fs-PLAL toward broader classes of van der Waals materials, in situ heterojunction fabrication, and integration with time-resolved diagnostics for ultrafast process control. Quantitative modeling (NLS, 2T models, Rayleigh–Plesset, atomistic simulations) has converged with experiment to yield parameter maps for optimized nanomaterial synthesis.

Key advances demonstrate precise control of nanoparticle size, phase, and electronic structure by tuning pulse sequence and solvent environment—not achievable by nanosecond LAL or chemical routes—making fs-PLAL a cornerstone technique for advanced colloidal nanomaterial engineering (Hoppius et al., 2018, Petrov et al., 2018, Axente et al., 2010, Ushkov et al., 9 Dec 2025, Sahoo et al., 20 May 2024).

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References:

(Hoppius et al., 2018, Petrov et al., 2018, Ushkov et al., 9 Dec 2025, Axente et al., 2010, Sahoo et al., 20 May 2024)