Open Access
Add to BibSonomy
Abstract
Ultrashort-pulse laser surface and bulk nano- and micromachining of dielectrics have multiple promising applications in micro-optics, microfluidics, and memory storage. The fundamental principles relate intrinsic inter-band multi-photon (MPA) and laser-induced intra-band free-carrier absorption (FCA) to particular ablation mechanisms and features. These principles are yet to be quantified into a complete set of basic experimental laser-matter interaction parameters, describing photoexcitation, relaxation, and final ablation. In this study, we considered the characteristic double-crater structure of single-shot ablation spots on dielectric surfaces and single-shot transmission spectra to extract crucial information about the underlying basic processes of ultrafast photoexcitation and laser energy deposition. Specifically, energy-dependent crater profiles and accompanying prompt self-phase modulation (SPM) spectral broadening were studied in single-shot surface ablation experiments on fluorite (CaF2) surface photo-excited by tightly focused 515- or 1030-nm, 300-fs laser pulses. Crater size dependence demonstrated two slopes, scaling proportionally to the squared focal 1/e-radius at higher energies (intensities) for larger ablated spots, and a much smaller squared 1/e-radius at lower energies (intensities) for (sub) micron-wide ablated spots, indicating a transition from 1D to 3D-ablation. As a result, these slopes were related to lower-intensity wavelength-dependent multi-photon inter-band transitions and wavelength-independent higher-intensity linear absorption in the emerging near-critical electron-hole plasma (EHP), respectively. Crater depth dependences on the local laser intensity fitted in the corresponding ranges by multi- and one-photon absorption provided the corresponding absorption coefficients. Spectral broadening measurements indicated even values for the red and blue shoulders of the laser pulse spectrum, representing the SPM effect in the weakly excited fluorite at the leading pulse front and providing the corresponding Kerr coefficient. In the second regime, the blue-shoulder broadening value saturated, indicating the appearance of near-critical plasma screening at the trailing pulse front, which is consistent with our calculations. These complementary experiments and related analysis provided an important set of key basic parameters, characterizing not only surface ablation, but also propagation of high-intensity ultrashort laser pulses in bulk fluorite, and enabling precise forecasting of optimal energy deposition for high-efficiency ultrashort-laser micro-structuring of this dielectric material.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Ultrashort-pulse (mostly, femtosecond/fs) laser ablative nano- and micromachining on dielectric surfaces and in volume materials is employed both in traditional applications, such as waveguide writing [1], fabrication of birefringent elements [2], 3D optical memory based on nano-void arrays [3], as well as innovative emerging fields such as optical vortex generation [4], holographic recording [5], and 5D optical memory storage [6]. These applications differ in the volume density of the deposited laser energy, enabling structural rearrangement [7], periodic nanograting fabrication [8], hollow nanovoid formation [9], or microchannel drilling [10], with varying amount of transfer/removal of the ablative material. Fundamental femtosecond-laser energy deposition mechanisms are well-known [11–19] and are related to multi-photon (MPI) or tunnel inter-band intrinsic photoionization (TI), or avalanche ionization (AI) via inverse bremsstrahlung heating of photo-generated free carriers. However, unambiguous or straightforward quantification of their key parameters, which change both in spatial and temporal domains, directly from experimental optical transmission [20–21], reflection [22], interferometric [23], or holographic [24,25] measurements is yet to be achieved. This hinders predictive linking between the input laser, focusing, material parameters, and the resulting volume energy densities and microstructures.
During femtosecond-laser ablation on dielectric surface crater depth [26–28], ablated volumes per pulse [29,30] and crater diameters [31–33] appear to be the most crucial machining parameters, which affect the efficiency, as well as spatial, longitudinal, and transversal (lateral) resolutions of ablation. Usually, these parameters are analyzed separately, without a comprehensive analysis of crater profiles that involve the diameter of the external ablation rim, neighboring above-threshold shallow crater, and the central deep depressions [34]. Specifically, numerous double-crater structures of single-shot ablated spots have been observed [35–39], with their external shallow, even flat (“gentle” ablation [36]) and central ultra-deep (“strong” ablation [36]) craters). Meanwhile, direct relationships between such important ablation features and specific regimes of photoexcitation/electron dynamics are yet to be established.
Recently, a two-step analysis procedure was proposed [40,41] for single-shot crater profiles on dielectric surfaces. Both radii and depths are simultaneously considered, covering the entire range of surface ablation modifications, from the characteristic nanometer-deep craters to submicron or even multi-micron depths. First, characteristic ranges of non-linear energy deposition were revealed through the Liu analysis [42]. For local ablation related to the energy deposition spot above the ablation threshold, the Gaussian energy distribution over the focal spot with a focal 1/e-radius Wfoc results in energy deposition, which is proportional to the Nth power of laser intensity, IN, providing the squared characteristic ablation radius Rabl2 = Wfoc2/N [28,40,41]. This procedure enables the determination of multi(N)-photon absorption processes in qualitative agreement with the conventional femtosecond-laser ionization dynamics [11–23,43–46]. Moreover, at higher femtosecond-laser intensities, linear free-carrier (near-critical electron-ion plasma) absorption could be identified according to Rabl2 ≈ Wfoc2 [28,40,41]. Second, the identified intensity ranges for different absorption processes were used for non-linear fitting of the corresponding crater depths across their radial profiles as a function of radial laser intensity [28,40,41]. This is a well-defined manner of deriving absorption coefficients [28,40,41] compared to multi-photon absorption (MPA) approximations [26,27].
In this study, we investigated in detail a two-crater structure on fluorite surfaces CaF2(111) photo-excited by tightly focused 515- or 1030-nm, 300-fs laser pulses. Comparing to multi-component silica glasses, this “clean” material was chosen for its crystalline character with the well-defined optical, electronic, lattice, and transport parameters, with its electronic band and absorption spectra [47] presented in Fig. 1. In this material, lack of any considerable density of defect or impurity states in the bandgap ensures no their effect on not only near-IR, visible, or UV photoexcitation, but also carrier trapping, recombination, and transport dynamics. Determining the two-slope dependence of crater size and depth on pulse energy (intensity) enabled the identification of key laser energy deposition processes in the material in the context of 3D-1D ablation transition, while inhomogeneous spectral broadening indicated the plasma dynamics during the pump pulse. Based on these results, we explain the different effective squared beam radii as fluence calibration slopes in their relationship to actual energy deposition mechanisms, and derived their numerical laser absorption and transport parameters, which are crucial for sub-wavelength ultrashort-laser nanomachining.
Fig. 1. UV spectrum of absorption coefficient in CaF2 with the blue band highlighting the effective absorption edge, and positions of multi-photon 1030-nm (red arrows) and 515-nm (green arrows) inter-band transitions (after [47]).
2. Experiment details
Laser ablation and spectral transmittance studies were performed to characterize the high-intensity non-linear interactions between focused femtosecond laser pulses, having a plane phase wave-front and well-defined waist peak intensity, on the CaF2 surface. The schematic of the experimental setup is shown in Fig. 2(a).
Fig. 2. (a) Experimental setup for ultrashort-laser ablation and spectral broadening studies with the computer (PC) control, using an example of 515-nm femtosecond-laser pulses. (b)-(c) SEM and AFM scans of representative single-shot craters, produced on CaF2 surface at different 515-nm laser intensities. (d)-(e) Their typical profiles acquired by AFM (horizontal axis in μm, vertical axis in nm) with the red dashed frames showing the shallow and deep crater zones. (f) Broadened spectra of transmitted 515-nm laser pulses at different peak intensities (pink color), comparing to corresponding reference spectra in air (no sample, blue color), with the spectral FWHM shown by the blue arrows at 4 TW/cm2 and spectral broadening shown by the red arrows. (g) Representative broadened (red curve) and reference (black curve) spectra of transmitted 1030-nm laser pulses, with its FWHM and broadening shown by the black and red arrows, respectively.
In these experiments, we used 300-fs full-width at half maximum (FWHM), quasi-monochromatic 515-nm (FWHM Δλ ≈ 1.7 nm) or 1030-nm (FWHM Δλ ≈ 7 nm) laser pulses (TEM00-mode, M2 ≤ 1.07, 1/e-radii σ(1030 nm) ≈ 10 mm, and σ(515 nm) ≈ 8 mm). The pulses were tightly focused onto a 2-mm-thick optically-polished UV-grade CaF2 slab by a microscope objective with numerical apertures (NA) of 0.25 (effective focal distance f0.25 = 16 mm) into the wavelength-dependent focal spots with the 1/e-radii wfoc(515 nm) ≈ 2 μm and wfoc(1030 nm) ≈ 4 μm [48] (the calculated 1/e-radii w0(515 nm) = λf0.25/(2πσ*) ≈ 1.7 μm and w0(1030 nm) = λf0.25/(2πσ*) ≈ 3.5 μm) owing to the limited objective aperture. The corresponding calculated wavelength-dependent Rayleigh lengths in fluorite, which are relevant for our SPM spectral broadening studies as the corresponding effective interaction lengths, were zCaF2(515 nm) = λf0.252/(4πnCaF2σ2) ≈ 12 μm and zCaF2(1030 nm) = λf0.252/(4πnCaF2σ*2) ≈ 24 μm, where nCaF2(500 nm) = 1.44 and nCaF2(1.0 μm) = 1.43 are the corresponding refractive indices [47]. For 0.65-NA focusing at the 1030-nm wavelength (f0.65 = 4 mm), the employed focusing parameters were wfoc(1030 nm) ≈ 0.9 μm (the calculated 1/e-radii w0(1030 nm) = λf0.65/(2πσ*) ≈ 0.84 μm) due to the limited objective aperture in air and zCaF2(1030 nm) = λf0.652/(4πnCaF2σ*2) ≈ 1.5 μm in fluorite. All these focal parameters are summarized in Table 1.
Table 1. Experimentally measured and calculated focusing parameters at 1030-nm and 515-nm wavelengths and focusing micro-objectives with NA = 0.25, 0.65.
Single-shot laser exposition occurred at the variable incident pulse energies E = 0.6-3.6 μJ (1030 nm) and 0.1-1.3 μJ (515 nm), providing the NA-dependent peak fluence F0 = E/(πwfoc2) ≈ 1.2-110 J/cm2 (1030 nm) and 0.8-11 J/cm2 (515 nm), peak intensity I0 = F0/τ≈ 4-370 TW/cm2 (1030 nm) and 3-37 TW/cm2 (515 nm).
The CaF2 slab was arranged on a computer-driven motorized 3D-positioning platform. It was scanned from shot to shot to produce a linear pattern of ten 120-μm spaced single-shot micro-craters at each pulse energy, which were flat and shallow (≈25-nm deep) near the crater edge and deep in the center (Figs. 2(b) and 2(c)). The crater profiles were characterized by atomic force microscopy (AFM). AFM topography scans were performed over 10 μm × 10 μm CaF2 surface spots at 0.04-μm steps through a microscope Solver Pro P6 (NT-MDT) in a semi-contact mode with a 10-μm long high-resolution silicon probe HA_NC (tip curvature – 10 nm, tip angle – 30°) mounted at the angle of 20° in the scan head “Smena”.
Similarly, spectral acquisition of the pump-pulse transmission was performed on fresh CaF2 surface spots in a scanning mode over 50 laser pulses at each pulse energy (Fig. 2(d)). A collecting silica-glass optical fiber was arranged just behind the rear sample surface without any additional collecting optics and coupled to a PC-controlled, single-grating spectrometer ASP-150SF.
3. Results and discussion
3.1 Crater profiles and their interpretation
The profiles of the two-crater single-shot ablated spots provide two important characteristics of laser-matter interactions, namely energy-dependent radii of the external shallow crater and the central deep crater. Further, we acquired radial depth variations across the focal spots, which can be converted into local intensity- or fluence dependence of depth. Because the rather narrow and deep central craters could be perturbed during material removal by non-local effects such as lateral melt displacements and redeposition, the control curves of the maximal crater depth in the central peak intensity points were used for comparison.
3.1.1 a) Analysis of crater diameters
We used the squared radii Rabl2 of the external shallow and central deep craters versus the natural logarithm of incident pulse energy, lnE, to characterize the focusing and energy deposition conditions [28,40,41]. According to the Liu analysis [42], the surface modification features appearing above the threshold IM for the Gaussian beam with energy E and 1/e-radius wfoc,
exhibit the energy-dependent dimensions of the modification spotsThis expression can be employed for the linear absorption/energy deposition on the surface, directly replicating the focal energy distribution, resulting in
providing wfoc2 as the slope of the RM2-lnE dependence and the modification threshold energy EM (fluence FM, intensity IM). In a more general case, for example, for (sub)micrometer-wide focal spots on “thermally thin” metallic films, the lateral thermal conductivity expands the energy deposition spot during the hot-carrier relaxation stage [49] and, later, till the picosecond- or multi-picosecond-scale ablation onset (depending on femtosecond-laser ablation mechanisms [50]).In dielectrics, where multi(N)-photon absorption of optical photons is the key initial process of energy deposition at low and moderate intensities of ultrashort laser pulses, the effective focal spot size ∼ wfoc/√N is determined by the main energy deposition region
However, for threshold-like modification processes such as ablation, the squared modification radius again reads similarly to Eq. (3).
Our quantitative examination of the experimental data for both the 1030-nm and 515-nm wavelengths indicates that Rabl2-lnE curves in Fig. 3 exhibit two characteristic ranges: range #1 for small and range #2 for large pulse energies, coinciding with small and large ablated spots, respectively. At smaller pulse energies, the derived slopes w12(1030 nm) ≈ 0.40 μm2 at NA = 0.65 and w12(515 nm) ≈ 0.87 μm2 at NA = 0.25 are unexpectedly almost two-fold and five-fold lower than their corresponding focal 1/e-radii -radius wfoc(1030 nm)2 ≈ 0.92 μm2 and wfoc(515 nm)2 ≈ 22 μm2 (Fig. 3), respectively. In contrast, at higher pulse energies for large ablated spots, the curve slopes w22 (1030 nm) ≈ 0.95 μm2 at NA = 0.65 and w22(515 nm) ≈ 4.3 μm2 at NA = 0.25 are in good agreement with their corresponding regular squared values wfoc2.
Fig. 3. Squared crater radius Rc2 versus pulse energy E (bottom logarithmic scale), (a) at 1030-nm (0.65-NA focusing) and (b) 515-nm (0.25-NA focusing) laser wavelength with the highlighted zones at lower and higher pulse energies, with the thresholds Iabl1(2) and slopes w1(2)2, indicating the different power slopes and corresponding ablation regimes.
The observed integer reduction of the curve slopes in the low-energy (low-intensity) range could indicate multi-photon — 2, 3, or 5-photon — absorption in the material at these particular wavelengths, while the linear free-carrier absorption at high energies (intensities) is in agreement with previous interferometric observations [23]. However, in Eqs. (4), and (5) we have revealed that threshold-like multi-photon processes do not change the curve slopes. Hence, the corresponding low-energy crater sizes appear to be enormously large ablation features.
A possible explanation is as follows. For very small ablation spots (in both Figs. 3(a) and 3(b) - Rabl2 <1 μm2), a transition is expected versus the decreasing pulse energy E from 1D in-depth ambipolar diffusion of EHP and the following thermal diffusion over the energy deposition distance LD, to their 3D hemispherical diffusion within the ultra-narrow, (sub) micron-wide focal and ablation spots. The transition occurs during the characteristic ablation onset time [49], which is a characteristic of broad focal and ablation spots. In a phase explosion regime, implying a hydrodynamic expulsion of supercritical fluid, the characteristic ablation onset time is determined by Z/Cl ∼10-100 ps, where Z is the thickness of the material in the supercritical state (volume energy density ε ≥ εabl) and Cl is the longitudinal sonic velocity. Then, for large focal spots wfoc » LD with the effective nonlinear energy deposition/ablation scale LD « Rabl « wfoc in the axial coordinates,
As a result, the low-energy values w1(1030 nm) ≈ 0.63 μm at NA = 0.65 and w1(515 nm) ≈ 0.94 μm at NA = 0.25 can be related to the energy deposition distance LD,S along the surface during the characteristic ablation onset time, which could be represented as follows [52]:
At 1030-nm wavelength and NA = 0.65, for N = 9 (Fig. 1) the focal contribution to LD,S ≈ w1≈ 0.63 μm (LD,S2 = 0.40 ± 0.04 μm2) in the MPA assumption tends to wfoc/√9 ≈ 0.3 μm, where the rest value = 0.54 ± 0.02 μm is the transport length σS (1030 nm). At 515-nm wavelength for N = 5 (Fig. 1), the focal contribution to LD,S ≈ w1≈ 0.93 μm (LD,S2 = 0.87 ± 0.28 μm2) in the MPA assumption tends to wfoc/√5 ≈ 0.9 μm, where the rest value as the transport length σS(515 nm) = 0.3 ± 0.3 μm is of the same order as at the 1030-nm laser wavelength. Typically, these lengths could be different at different focusing conditions realizing different EHP and temperature gradients. These transport lengths are expected to determine also the in-depth laser energy deposition through the EHP and thermal diffusion processes, and the final ablation depth, as considered next in crater depth analysis for both small and large craters in fluorite.
3.1.2 b) Analysis of crater depths
Purely “optical” analysis of the crater depth dependence on laser intensity in the ranges Iabl,1 ≤ I0 ≤ Iabl,2 and I0 ≥ Iabl,2 could be performed in approximations of pure MPA and free-carrier absorption (FCA) regimes, enabling quantification of their corresponding coefficients. This was done via analysis of the acquired crater profiles, assuming that, across the ablated spot, the ablation threshold is achieved not only on the surface, but also at a certain depth Z via the nonlinear transmission of the incident intensity I [28,40,41]. The crater depth dependence on local intensity Z(I) is demonstrated in Fig. 4 for both these ranges, where the depth increases slowly in the MPA regime for lower I and much faster in the FCA regime for higher I. Following previous studies [28,40,41], in the first range, the crater depth variation versus I was fitted considering the N-photon absorption as follows:
Fig. 4. Single-shot ablated depth in CaF2 versus laser intensity at (a) 1030 nm and (b) 515 nm: light circles – maximal crater depths at different peak intensities, dark circles – the crater profiles at the peak intensity ≈ (a) 410 and (b) 33 TW/cm2, respectively. The orange fitting curve in (a) indicates the effective two-photon (orange region, coefficient βeff) absorption regime, the green fitting curve in (b) indicates the effective 5-photon (green region, coefficient β5) absorption regime. The pink and blue fitting curves in (a) and (b) indicate one-photon FCA (pink and blue regions, coefficient α) regime, respectively. The regimes are delimited by the corresponding ablation thresholds Iabl,1(2).
In the high-intensity range (I0 ≥ Iabl,2) the logarithmic approximation of the linear absorption regime,
yields the effective coefficient values α ≈ (3.5 ± 0.3) × 104 cm-1 at 1030 nm (Fig. 4(a)) and (1.8 ± 0.2) × 104 cm-1 at 515 nm (Fig. 4(b)), potentially indicating the strong FCA process in the near-critical EHP, which is more pronounced for the near-IR laser radiation.Our analysis according to Eq. (10), including the energy transport depths σB(1030 nm) = 0.54 ± 0.02 μm and σB(515 nm) = 0.3 ± 0.3 μm, indicates their magnitudes to be comparable to the abovementioned values 1/α, including the transport length σB. Moreover, since the maximal (plateau) crater depth at higher intensities approaches rather similar wavelength-independent magnitudes ≈ 350-400 nm in the high-intensity range (Fig. 4), this may indicate the predominant contribution of the EHP/thermal transport in the energy deposition. This implies that the optical absorption depth δabs « 1/α ∼ 0.1–1 μm-1 could be realized as a strong FCA process in near-critical EHP. Despite the much stronger FCA for 1030-nm femtosecond laser pulses, the much higher threshold intensities in Fig. 4 demonstrate the much lower efficiency of overall photoionization for the longer-wavelength photons, which is in good agreement with previous studies [11,12].
Finally, in the low-intensity range, the shallow craters exhibited nearly constant depths Z ≤ 50 nm within the experimental error bars, representing a slightly violent ablation character (see (Figs. 2(b), 2(d), 2(e)). Such a double-crater structure with the external shallow and central ultra-deep crater is rather universal and is well known for many dielectric materials [11,35].
3.2 SPM spectral broadening
Kerr self-focusing coefficients n2 and cumulative EHP appearance at the trailing pump-pulse part were revealed during the 1030-nm and 515-nm femtosecond-laser pump pulses in our spectral broadening studies (see Figs. 2(f) and 2(g)). The broadening magnitude in the spectral inflection points follows the time-derivative of the pulse envelope, according to the following equation for the spectral component spectral component at a wavelength λ0 over the propagation length L [54]:
Fig. 5. “Red” (orange and pink symbols) and “blue” (violet and blue symbols) spectral broadening magnitudes of the laser pulses at (a) 1030 nm (circles - NA = 0.25, squares - NA = 0.65) and (b) 515 nm versus peak laser intensity, with the linear fitting of the red broadening dataset. The highlighted regions show the characteristic ablation ranges above the thresholds Iabl,1(2), while the dashed curves in (a) indicate the anticipated experimental trends.
In the range #1 in Fig. 5, representing lower femtosecond-laser intensities the “red” and “blue” broadening is uniform; however, at higher intensities in the range #2, the “blue” component saturates first and even decreases, while the “red” component persists at much higher intensities. Since the “blue” shoulder broadens at the trailing pulse front, its saturation and drop could indicate the screening effect of the accumulated opaque near-critical EHP, emerging in CaF2 at the trailing edge of the transmitted femtosecond-laser pulses and decreasing their laser intensity. The same saturation and drop for the “red” shoulder exhibits dense EHP formation already at the leading 1030-nm pulse front, screening the four-wave interactions, related to the Kerr effect, with much stronger screening for the “blue” shoulder (Fig. 5(a)).
3.3 Plasma parameters
Numerical analysis was performed to relate the measured effective linear FCA coefficient α ≈ (1.8 ± 0.4) × 104 cm-1 to the peak EHP density during the pulse. Prompt optical constants of the photo-excited fluorite versus EHP density ρ were described using the common expression for the dielectric function with the inter-band and intra-band (Drude) contributions (the first and second terms, respectively) [59]
The electronic high-frequency dielectric constant εHF ≈ εIB, and e–h pair relaxation time in the Fermi-liquid approximation adapted from [60] is taken in the form
The electronic bandgap renormalization (shrinkage, ω* ≥ ω) [60] and band filling effect (ρ ≤ ρbf) [61] were neglected. The calculated magnitudes of ε* were converted into plasma density-dependent prompt true absorption and reflection coefficients, α0 and R, respectively, assuming Fresnel reflection from a homogeneous photo-excited surface layer of fluorite to yield the corresponding effective absorption coefficients α(ρ) = (1 − R(ρ))α0(ρ).
The calculated effective absorption coefficients α(ρ) rapidly increased with respect to ρ (Fig. 6) for near-critical EHP densities (according to Eq. (14), ρcrit(515 nm) ≈ 8 × 1021 cm-3 in CaF2), saturating for ρ > ρcrit (515 nm) at the level ≈ 1.2 × 104 cm-1, which is reasonably close to the experimental value α (515 nm) ≈ (1.8 ± 0.4) × 104 cm-1. Such self-consistent saturated effective absorption coefficient of the near- and supercritical EHP results from the strongly increasing true absorption coefficient α0 and reflection coefficient R (Fig. 6).
Fig. 6. Calculated true absorption (α0) and reflection (R) coefficients and the resulting effective absorption coefficient α = (1−R)α0 at the 515-nm pump femtosecond-laser wavelength versus EHP density ρ. The vertical orange dashed line shows the critical density value ρcrit (515 nm) ≈ 8 × 1021 cm-3, while the green shadowed band indicates the measured effective absorption coefficient with its error bars (shown above).
3.4 Characteristic electron dynamics and related absorption mechanisms
Our experimental determination of narrow-crater size dependence on incident pulse energy enabled the evaluation of the optical nonlinearity, describing the femtosecond-laser energy deposition rate η in fluorite to facilitate ablation. This is generally not possible for broad, multi-micron craters. Below, we will discuss a few main regimes of femtosecond-laser generation EHP evolution and energy deposition dynamics, considering the standard rate equation [53] to provide useful insights into these dynamics.
The common rate equation for EHP (not multiple-rate equations, MRE [62]), not subjected to self-trapping inside the bandgap [63], can be described in the simplified form as follows
Here, the first term describes the saturable N-photon absorption/ionization (MPA(I), saturation threshold ρ0); the second term represents the avalanche ionization (AI) transforming into free-carrier absorption (FCA) at sub/near-critical EHP densities ρ, and the third term indicates the reverse Auger recombination (AR) rate with its coefficient γ. Since the quantitative values of the material parameters ρ0 and γ are not known, as for many other dielectrics, we will next perform a qualitative analysis. For the given dielectric bandgap, it is based on incident femtosecond-laser intensity magnitudes and characteristic ranges of EHP density, which related to the critical density ρcrit at the given laser wavelength and the characteristic Auger-recombination density ρauger; this makes the Auger-relaxation time ∼1/(γρauger2) comparable to the laser pulse width.
Specifically, we can find several characteristic cases.
- ii) Medium NIR-laser intensities ∼ 10 TW/cm2, ρ ≤ ρcrit < ρauger (unlimited MPI-seeded FCA):
- iv) Low visible/UV laser intensities « 10 TW/cm2, ρauger < ρ < ρcrit (Auger recombination-limited MPI):
In this study, particularly for the narrow craters in Fig. 3, we observed the slope ≈2 at 1030-nm pumping and ≈5 at 515-nm pumping, respectively, describing the femtosecond-laser energy deposition relationships with intensity during the ablation. At 515-nm pumping, the 5-photon dependence represents simply either case i) (ρ < ρauger, ρcrit), or case iv) (ρauger < ρ < ρcrit), describing the sub-critical EHP generation regime via the multi-photon absorption. In contrast, at 1030-nm pumping, the square dependence represents the interplay between the low-intensity MPI-dominated regimes i) and iv) and high-intensity FCA-dominated regime v) (ρauger < ρ < ρcrit), which are temporally convoluted over the laser pulse.
4. Conclusions
In conclusion, single-shot femtosecond-laser surface ablation studies at both 1030- and 515-nm wavelengths revealed a double-crater structure, where the external shallow crater demonstrates its characteristic radius, considerably smaller than the focal radius, while the central deep crater follows the focal radius in its extension versus increasing femtosecond-laser pulse energy. The ablation depth varies differently in the corresponding intensity ranges, indicating potentially not only different ablation mechanisms – low-intensity spallation and high-intensity phase explosion, but also the corresponding multi-photon and free-carrier absorption mechanisms. For smaller intensities, the different size dependence for the shallow craters was related to their 3D energy deposition (absorption + transport) character, as compared to the broader high-intensity craters with their strong FCA absorption, resulting in 1D energy deposition. These finding are qualitatively justified by our spectral broadening studies for the 1030-nm and 515-nm pump pulses, enabling also to evaluate their wavelength-dependent Kerr coefficients. Our analysis of ultrafast laser energy deposition and electron dynamics in fluorite photo-excited by tightly focused near-IR and visible-range femtosecond laser pulses in the framework of the general rate equation supports the observed trends in terms of incident intensity, laser wavelength, and characteristic plasma density ranges.
Funding
Ministry of Science and Higher Education of the Russian Federation (0705-2020-0041).
Disclosures
The authors declare no conflicts of interest.
References
1. F. Chen and J. V. de Aldana, “Optical waveguides in crystalline dielectric materials produced by femtosecond-laser micromachining,” Laser Photonics Rev. 8(2), 251–275 (2014). [CrossRef]
2. Y. Shimotsuma, M. Sakakura, P. G. Kazansky, M. Beresna, J. Qiu, K. Miura, and K. Hirao, “Ultrafast Manipulation of Self-Assembled Form Birefringence in Glass,” Adv. Mater. 22(36), 4039–4043 (2010). [CrossRef]
3. M. H. Hong, B. Luk’Yanchuk, S. M. Huang, T. S. Ong, L. H. Van, and T. C. Chong, “Femtosecond laser application for high capacity optical data storage,” Appl. Phys. A 79(4-6), 791–794 (2004). [CrossRef]
4. M. Beresna, M. Gecevičius, P. G. Kazansky, and T. Gertus, “Radially polarized optical vortex converter created by femtosecond laser nanostructuring of glass,” Appl. Phys. Lett. 98(20), 201101 (2011). [CrossRef]
5. R. Drevinskas and P. G. Kazansky, “High-performance geometric phase elements in silica glass,” APL Photonics 2(6), 066104 (2017). [CrossRef]
6. J. Zhang, M. Gecevičius, M. Beresna, and P. G. Kazansky, “Seemingly unlimited lifetime data storage in nanostructured glass,” Phys. Rev. Lett. 112(3), 033901 (2014). [CrossRef]
7. R. Stoian, “Volume photoinscription of glasses: three-dimensional micro- and nanostructuring with ultrashort laser pulses,” Appl. Phys. A 126(6), 438 (2020). [CrossRef]
8. A. E. Rupasov, P. A. Danilov, M. P. Smaev, M. S. Kovalev, A. S. Zolot’ko, A. A. Ionin, and S. I. Kudryashov, “3D Microstructuring of Silicate Glass by Femtosecond Laser Radiation,” Opt. Spectrosc. 128(7), 928–931 (2020). [CrossRef]
9. T. Chen, G. Zhang, Y. Wang, X. Li, R. Stoian, and G. Cheng, “Reconstructing of Embedded High-Aspect-Ratio Nano-Voids Generated by Ultrafast Laser Bessel Beams,” Micromachines 11(7), 671 (2020). [CrossRef]
10. X. Zhao and Y. C. Shin, “Femtosecond laser drilling of high-aspect ratio microchannels in glass,” Appl. Phys. A 104(2), 713–719 (2011). [CrossRef]
11. S. Guizard, A. Semerok, J. Gaudin, M. Hashida, P. Martin, and F. Quéré, “Femtosecond laser ablation of transparent dielectrics: measurement and modelisation of crater profiles,” Appl. Surf. Sci. 186(1-4), 364–368 (2002). [CrossRef]
12. B. C. Stuart, M. D. Feit, S. Herman, A. M. Rubenchik, B. W. Shore, and M. D. Perry, “Nanosecond-to-femtosecond laser-induced breakdown in dielectrics,” Phys. Rev. B 53(4), 1749–1761 (1996). [CrossRef]
13. M. Lenzner, J. Krüger, S. Sartania, Z. Cheng, Ch. Spielmann, G. Mourou, W. Kautek, and F. Krausz, “Femtosecond Optical Breakdown in Dielectrics,” Phys. Rev. Lett. 80(18), 4076–4079 (1998). [CrossRef]
14. L. V. Keldysh, “Ionization in the field of a strong electromagnetic wave,” Sov. Phys. JETP 20, 1307 (1965).
15. T. Apostolova and Y. Hahn, “Modeling of laser-induced breakdown in dielectrics with subpicosecond pulses,” J. Appl. Phys. 88(2), 1024–1034 (2000). [CrossRef]
16. N. Sanner, O. Utéza, B. Bussiere, G. Coustillier, A. Leray, T. Itina, and M. Sentis, “Measurement of femtosecond laser-induced damage and ablation thresholds in dielectrics,” Appl. Phys. A 94(4), 889–897 (2009). [CrossRef]
17. B. Rethfeld, O. Brenk, N. Medvedev, H. Krutsch, and D. H. H. Hoffmann, “Interaction of dielectrics with femtosecond laser pulses: application of kinetic approach and multiple rate equation,” Appl. Phys. A 101(1), 19–25 (2010). [CrossRef]
18. P. Balling and J. Schou, “Femtosecond-laser ablation dynamics of dielectrics: basics and applications for thin films,” Rep. Prog. Phys. 76(3), 036502 (2013). [CrossRef]
19. G.D. Tsibidis and E. Stratakis, “Ionisation processes and laser induced periodic surface structures in dielectrics with mid-infrared femtosecond laser pulses,” Sci. Rep. 10(1), 8675 (2020). [CrossRef]
20. F. Quéré, S. Guizard, and P. Martin, “Time-resolved study of laser-induced breakdown in dielectrics,” Europhys. Lett. 56(1), 138–144 (2001). [CrossRef]
21. S. S. Mao, F. Quéré, S. Guizard, X. Mao, R. E. Russo, G. Petite, and P. Martin, “Dynamics of femtosecond laser interactions with dielectrics,” Appl. Phys. A 79(7), 1695–1709 (2004). [CrossRef]
22. A. Y. Vorobyev and C. Guo, “Reflection of femtosecond laser light in multipulse ablation of metals,” J. Appl. Phys. 110(4), 043102 (2011). [CrossRef]
23. B. Kim, “Interferometric analysis of ultrashort pulse laser-induced pressure waves in water,” J. Appl. Phys. 94(1), 709–715 (2003). [CrossRef]
24. G. Krasin, M. Kovalev, N. Stsepuro, P. Ruchka, and S. Odinokov, “Lensless Scheme for Measuring Laser Aberrations Based on Computer-Generated Holograms,” Sensors 20(15), 4310 (2020). [CrossRef]
25. V. Yu. Venediktov, A. V. Gorelaya, G. K. Krasin, S. B. Odinokov, A. A. Sevryugin, and E. V. Shalymov, “Holographic wavefront sensors,” Quantum Electron. 50(7), 614–622 (2020). [CrossRef]
26. L. Jiang and H. L. Tsai, “Prediction of crater shape in femtosecond laser ablation of dielectrics,” J. Phys. D: Appl. Phys. 37(10), 1492–1496 (2004). [CrossRef]
27. A. Ben-Yakar, “Femtosecond laser ablation properties of borosilicate glass,” J. Appl. Phys. 96(9), 5316–5323 (2004). [CrossRef]
28. D. Puerto, J. Siegel, W. Gawelda, M. Galvan-Sosa, L. Ehrentraut, J. Bonse, and J. Solis, “Dynamics of plasma formation, relaxation, and topography modification induced by femtosecond laser pulses in crystalline and amorphous dielectrics,” J. Opt. Soc. Am. B 27(5), 1065–1076 (2010). [CrossRef]
29. T. Donnelly, J. G. Lunney, S. Amoruso, R. Bruzzese, X. Wang, and X. Ni, “Double pulse ultrafast laser ablation of nickel in vacuum,” J. Appl. Phys. 106(1), 013304 (2009). [CrossRef]
30. J. Bonse, M. Geuss, S. Baudach, H. Sturm, and W. Kautek, “The precision of the femtosecond-pulse laser ablation of TiN films on silicon,” Appl. Phys. A 69(7), S399–S402 (1999). [CrossRef]
31. B. C. Stuart, M. D. Feit, S. Herman, A. M. Rubenchik, B. W. Shore, and M. D. Perry, “Optical ablation by high-power short-pulse lasers,” J. Opt. Soc. Am. B 13(2), 459–468 (1996). [CrossRef]
32. A. Semerok, B. Sallé, J. Wagner, and G. Petite, “Femtosecond, picosecond, and nanosecond laser microablation: Laser plasma and crater investigation,” Laser Part. Beams 20(1), 67–72 (2002). [CrossRef]
33. A.H. Galmed, A. du Plessis, S.G. le Roux, E. Hartnick, H. Von Bergmann, and M. Maaza, “Three dimensional characterization of laser ablation craters using high resolution X-ray computed tomography,” Spectrochim. Acta, Part B 139, 75–82 (2018). [CrossRef]
34. D.M. Karnakis, “High power single-shot laser ablation of silicon with nanosecond 355 nm,” Appl. Surf. Sci. 252(22), 7823–7825 (2006). [CrossRef]
35. N. M. Bulgakova, R. Stoian, A. Rosenfeld, I. V. Hertel, and E. E. B. Campbell, “Electronic transport and consequences for material removal in ultrafast pulsed laser ablation of materials,” Phys. Rev. B 69(5), 054102 (2004). [CrossRef]
36. R. Stoian, A. Rosenfeld, D. Ashkenasi, I. V. Hertel, N. M. Bulgakova, and E. E. B. Campbell, “Surface charging and impulsive ion ejection during ultrashort pulsed laser ablation,” Phys. Rev. Lett. 88(9), 097603 (2002). [CrossRef]
37. S. I. Kudryashov, A. Joglekar, G. Mourou, A. A. Ionin, V. D. Zvorykin, and A. J. Hunt, “Femtosecond laser surface ablation of transparent solids: understanding the bulk filamentation damage,” Proc. SPIE 6733, 67332H (2007). [CrossRef]
38. N. Kodama, T. Takahashi, T. Inoue, M. Kudo, and M. Tsukamoto, “Morphological characteristics of nanoholes induced by single-shot femtosecond laser ablation of borates and aluminate silicates,” J. Laser Appl. 32(1), 012015 (2020). [CrossRef]
39. S. I. Kudryashov, G. Mourou, A. Joglekar, J. F. Herbstman, and A. J. Hunt, “Nanochannels fabricated by high-intensity femtosecond laser pulses on dielectric surfaces,” Appl. Phys. Lett. 91(14), 141111 (2007). [CrossRef]
40. D. A. Zayarny, A. A. Ionin, S. I. Kudryashov, I. N. Saraeva, E. D. Startseva, and R. A. Khmelnitskii, “Nonlinear absorption mechanisms during femtosecond laser surface ablation of silica glass,” JETP Lett. 103(5), 309–312 (2016). [CrossRef]
41. S. I. Kudryashov, P. A. Danilov, E. D. Startseva, and A. A. Ionin, “Multi-zone single-shot femtosecond laser ablation of silica glass at variable multi-photon ionization paths,” J. Opt. Soc. Am. B 35(10), B38–B42 (2018). [CrossRef]
42. J. M. Liu, “Simple technique for measurements of pulsed Gaussian-beam spot sizes,” Opt. Lett. 7(5), 196–198 (1982). [CrossRef]
43. J. P. Geindre, P. Audebert, A. Rousse, F. Falliès, J. C. Gauthier, A. Mysyrowicz, A. Dos Santos, G. Hamoniaux, and A. Antonetti, “Frequency-domain interferometer for measuring the phase and amplitude of a femtosecond pulse probing a laser-produced plasma,” Opt. Lett. 19(23), 1997–1999 (1994). [CrossRef]
44. V. V. Temnov, K. Sokolowski-Tinten, P. Zhou, A. El-Khamhawy, and D. von der Linde, “Multiphoton Ionization in Dielectrics: Comparison of Circular and Linear Polarization,” Phys. Rev. Lett. 97(23), 237403 (2006). [CrossRef]
45. C. Sarpe, J. Köhler, T. Winkler, M. Wollenhaupt, and T. Baumert, “Real-time observation of transient electron density in water irradiated with tailored femtosecond laser pulses,” New J. Phys. 14(7), 075021 (2012). [CrossRef]
46. S. Kudryashov, A. Samokhvalov, S. Shelygina, A. Karabutov, G. D. Tsibidis, D. Pankin, and V. Veiko, “Electronic and vibrational processes in absorbing liquids in femtosecond laser sub-and filamentation regimes: ultrasonic and optical characterization,” Laser Phys. Lett. 17(10), 105302 (2020). [CrossRef]
47. E.D. Palik, Handbook of Optical Constants of Solids (Academic Press, 1998).
48. N. A. Smirnov, S. I. Kudryashov, P. A. Danilov, A. A. Nastulyavichus, A. A. Rudenko, A. A. Ionin, A. A. Kuchmizhak, and O. B. Vitrik, “Femtosecond laser ablation of a thin silver film in air and water,” Opt. Quantum Electron. 52(2), 71 (2020). [CrossRef]
49. P. Danilov, A. Ionin, R. Khmelnitskii, I. Kiseleva, S. Kudryashov, N. Mel’nik, A. Rudenko, N. Smirnov, and D. Zayarny, “Electron-ion coupling and ambipolar diffusion in dense electron-hole plasma in thin amorphous Si films studied by single-shot, pulse-width dependent ultrafast laser ablation,” Appl. Surf. Sci. 425, 170–175 (2017). [CrossRef]
50. A. A. Ionin, S. I. Kudryashov, L. V. Seleznev, D. V. Sinitsyn, A. F. Bunkin, V. N. Lednev, and S. M. Pershin, “Thermal melting and ablation of silicon by femtosecond laser radiation,” J. Exp. Theor. Phys. 116(3), 347–362 (2013). [CrossRef]
51. M. Garcia-Lechuga, O. Utéza, N. Sanner, and D. Grojo, “Evidencing the nonlinearity independence of resolution in femtosecond laser ablation,” Opt. Lett. 45(4), 952–955 (2020). [CrossRef]
52. A.A. Ionin, S.I. Kudryashov, S.V. Makarov, L.V. Seleznev, and D.V. Sinitsyn, “Electron dynamics and prompt ablation of aluminum surface excited by intense femtosecond laser pulse,” Appl. Phys. A 117(4), 1757–1763 (2014). [CrossRef]
53. M. Mero, J. Liu, W. Rudolph, D. Ristau, and K. Starke, “Scaling laws of femtosecond laser pulse induced breakdown in oxide films,” Phys. Rev. B 71(11), 115109 (2005). [CrossRef]
54. Femtosecond Laser PulsesC. Rulliere, ed., 4th ed. (Springer, 2005).
55. Y. Guo, S. Lu, L. Su, C. Zhao, H. Zhang, and S. Wen, “Z-scan measurement of the nonlinear refractive index of Nd3+, Y3+-codoped CaF2 and SrF2 crystals,” Appl. Opt. 54(4), 953–958 (2015). [CrossRef]
56. A.E. Dormidonov, V.O. Kompanets, S.V. Chekalin, and V.P. Kandidov, “Giantically blue-shifted visible light in femtosecond mid-IR filament in fluorides,” Opt. Express 23(22), 29202–29210 (2015). [CrossRef]
57. H. Liang, P. Krogen, R. Grynko, O. Novak, C. L. Chang, G. J. Stein, D. Weerawarne, B. Shim, F. X. Kärtner, and K. H. Hong, “Three-octave-spanning supercontinuum generation and sub-two-cycle self-compression of mid-infrared filaments in dielectrics,” Opt. Lett. 40(6), 1069–1072 (2015). [CrossRef]
58. V.Y. Fedorov and V.P. Kandidov, “A nonlinear optical model of an air medium in the problem of filamentation of femtosecond laser pulses of different wavelengths,” Opt. Spectrosc. 105(2), 280–287 (2008). [CrossRef]
59. K. Sokolowski-Tinten and D. von der Linde, “Generation of dense electron-hole plasmas in silicon,” Phys. Rev. B 61(4), 2643–2650 (2000). [CrossRef]
60. P. A. Danilov, A. A. Ionin, S. I. Kudryashov, S. V. Makarov, A. A. Rudenko, P. N. Saltuganov, L. V. Seleznev, V. I. Yurovskikh, D. A. Zayarny, and T. Apostolova, “Silicon as a virtual plasmonic material: Acquisition of its transient optical constants and the ultrafast surface plasmon-polariton excitation,” J. Exp. Theor. Phys. 120(6), 946–959 (2015). [CrossRef]
61. K. Seibert, G. C. Cho, W. Kütt, H. Kurz, D. H. Reitze, J. I. Dadap, H. Ahn, M. C. Downer, and A. M. Malvezzi, “Femtosecond carrier dynamics in graphite,” Phys. Rev. B 42(5), 2842–2851 (1990). [CrossRef]
62. B. Rethfeld, “Unified model for the free-electron avalanche in laser-irradiated dielectrics,” Phys. Rev. Lett. 92(18), 187401 (2004). [CrossRef]
63. S.I. Kudryashov, A. O. Levchenko, P. A. Danilov, N. A. Smirnov, A. E. Rupasov, R. A. Khmelnitskii, O. E. Kovalchuk, and A. A. Ionin, “Fine structure of photoluminescence spectra in diamond at multiple emission of optical phonon during self-trapping of photoexcited electrons,” JETP Lett. 112(9), 579–583 (2020).
