Wavelength dependence of nanosecond infrared laser-induced breakdown in water: Evidence for multiphoton initiation via an intermediate state

Investigation of the wavelength dependence (725–1025 nm) of the threshold for nanosecond optical breakdown in water revealed steps consistent with breakdown initiation by multiphoton ionization, with an initiation energy of about 6.6 eV. This value is considerably smaller than the autoionization threshold of about 9.5 eV, which can be regarded as band gap relevant for avalanche ionization. Breakdown initiation is likely to occur via excitation of a valence band electron into a solvated state, followed by rapid excitation into the conduction band. Theoretical analysis based on these assumptions suggests that the seed electron density required for initiating avalanche ionization amounts to $2.5\times {10}^{15}\mathrm{c}{\mathrm{m}}^{-3}$ at $725\mathrm{nm}$ and drops to $1.1\times {10}^{12}\mathrm{c}{\mathrm{m}}^{-3}$ at 1025 nm. These results demand changes of future breakdown modeling for water, including the use of a larger band gap than previously employed, the introduction of an intermediate energy level for initiation, and consideration of the wavelength dependence of seed electron density.

Figure 1

Literature data on solvated electron generation and ionization pathways in liquid water. (a) Energy dependence of quantum efficiency ${QE}_{\mathrm{esc}}$ for the creation of long-lived solvated electrons $e_{\mathrm{aq}\left(\mathrm{esc}\right)}^{-}$ that have escaped geminate recombination [32]. (b) Probability $P_{\mathrm{esc}}$ for excess electrons to escape recombination [30]. (c) Average ejection length $r_{\mathrm{ej}}$ of the excess electrons [30]. (d) Initial quantum efficiency $Q{E}_{\mathrm{ini}}$ of excess electron formation derived from (a) and (b) by $Q{E}_{\mathrm{ini}}=Q{E}_{\mathrm{esc}}/P_{\mathrm{esc}}$. (e) Density of preexisting trap sites for solvated electron formation derived from (c) and (d) by ${\chi }_{\mathrm{trap}}=Q{E}_{\mathrm{ini}}/(4/3\pi r_{\mathrm{ej}}^3)$. The energy dependence of $P_{\mathrm{esc}}$ and $r_{\mathrm{ej}}$ in (b) and (c) suggests that vertical ionization into the CB dominates for $E_{\mathrm{exc}}\ge 11\mathrm{eV}$, and autoionization becomes important for $E_{\mathrm{exc}}\ge 9.5\mathrm{eV}$. For $E_{\mathrm{exc}}<9.3\mathrm{eV}$, all excess electrons relax into the solvated state or recombine. Nevertheless, breakdown initiation is possible if $e_{\mathrm{aq}}^{-}$ absorb further photons that promote them into the CB, as depicted as “upconversion path” in Fig. 2.

Figure 2

Ionization and geminate recombination pathways in liquid water, as suggested by the data in Fig. 1. For large excitation energies, ionization can proceed via vertical ionization $(E_{\mathrm{exc}}\ge 11\mathrm{eV})$ or autoionization $(E_{\mathrm{exc}}\ge 9.5\mathrm{eV})$, while for $E_{\mathrm{exc}}<9.3\mathrm{eV}$, ionization is possible only as a two-step process involving solvated electron creation followed by upconversion of $e_{\mathrm{aq}}^{-}\mathrm{into}$ the CB. The latter process competes with geminate recombination.

Figure 3

Setup for the examination of the wavelength dependence of IR ns optical breakdown in water by means of a SLM OPO.

Figure 4

Pulse shape of a SLM OPO pulse of 900 nm wavelength and 2.3 ns duration (a), compared to single-frequency and longitudinal multimode Nd:YAG laser pulses of 1064 nm wavelength and 11.2 ns duration in (b) and (c), respectively. Below each pulse shape, the corresponding breakdown probability curves are shown in (d)–(f). The threshold sharpness is given by $S=E_{\mathrm{th}}/\mathrm{\Delta }E$, with $\mathrm{\Delta }E$ being the energy range between 10 and 90% breakdown probability.

Figure 5

Wavelength dependence of duration and $M^2$ values of laser pulses used in the present paper determined for focusing at NA = 0.9. The beam quality is optimal around the center wavelength of each of the two optics sets used for the OPO and deteriorates at the borders of each range. Since the $M^2$ values exhibited little scatter and a clear $M^2\left(\lambda \right)$ trend, measurements were performed for only 12 wavelengths, and intermediate values were interpolated. For the pulse duration, no systematic dependence on λ is observed.

Figure 6

Wavelength dependence of the threshold for plasma-mediated bubble formation by SLM OPO pulses focused at NA = 0.8 and NA = 0.9 and averaged values. The order of the multiphoton process required to cross the band gap in different regions of the $I_{\mathrm{th}}\left(\lambda \right)$ spectrum is denoted by $k$. Transition zones are marked in gray.

Figure 7

Wavelength dependence of AI rate (dashed line) and MPI rate (solid line) calculated for $E_{\mathrm{gap}}=9.5\mathrm{eV}$ and $E_{\mathrm{ini}}=6.6\mathrm{eV}$, respectively. The MPI rate is plotted in log scale, while AI rate is in linear scale. All calculations assume an irradiance of $3.5\times {10}^{11}\mathrm{W}/\mathrm{c}{\mathrm{m}}^2$, which is the average $I_{\mathrm{th}}$ value in the investigated wavelength range.

Figure 8

Comparison of predictions for $I_{\mathrm{th}}\left(\lambda \right)$ based on Eq. (2), with the experimentally determined spectrum (average values from both NAs). Calculations were performed for 2 ns pulse duration. (a) Fits for $E_{\mathrm{ini}}=6.6\mathrm{eV}$ assuming either a constant ${\rho }_{\mathrm{seed}}$ value of $3.3\times {10}^{14}\mathrm{c}{\mathrm{m}}^{-3}$ (blue line) or a wavelength-dependent seed electron density that varies according to ${\rho }_{\mathrm{seed}}(\mathrm{c}{\mathrm{m}}^{-3})={10}^{A\lambda \left(nm\right)+B}$ (green line). (b) Fit assuming a wavelength-dependent ${\rho }_{\mathrm{seed}}$ and a linear decrease of $E_{\mathrm{ini}}$ from 6.7 eV at the position of the first peak to 6.43 eV at the second peak (red line; for fit parameters see text).

Figure 9

Temporal evolution of the density of electrons entering the CB via photoionization. The solid line depicts ${\rho }_{\mathrm{ini}}$($t$) obtained via the initiation channel through multiphoton excitation into the intermediate energy level, ${\mathrm{E}}_{\mathrm{ini}}=6.6\mathrm{eV}$, followed by immediate upconversion into the CB. The dashed line represents the electron density produced by MPI across the entire band gap, ${\mathrm{E}}_{\mathrm{gap}}=9.5\mathrm{eV}$, which is almost six orders of magnitude smaller than ${\rho }_{\mathrm{ini}}$. Calculation parameters are the same as for Fig. 8 at $\lambda =800\mathrm{nm}$: $I_{\mathrm{th}}=3.76\times {10}^{11}\mathrm{W}/{\mathrm{cm}}^2, t_{\mathrm{gem}-\mathrm{rec}}=60\mathrm{ps}$, and ${\rho }_{\mathrm{seed}}=3.67\times {10}^{14}\mathrm{c}{\mathrm{m}}^{-3}$. The arrow indicates the time at which the critical seed electron density for AI is reached (45 ps after the peak of the 2 ns laser pulse). Afterwards, the free-electron density rapidly increases to full ionization [4, 64].