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From Localized Laser Energy Absorption to Absorption Delocalization at Volumetric Glass Modification with Gaussian and Doughnut-Shaped Pulses

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29 June 2023

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30 June 2023

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Abstract
Volumetric modification of transparent materials by femtosecond laser pulses is successfully used in a wide range of practical applications. The level of modification is determined by the locally absorbed energy density, which depends on numerous factors. In this work, it is shown experimentally and theoretically that, in a certain range of laser pulse energies, the peak of absorption of laser radiation for doughnut-shaped (DS) pulses is several times higher than for Gaussian ones. This makes the DS pulses very attractive for material modification and direct laser writing applications. Details of the interaction of laser pulses of Gaussian and doughnut shapes with fused silica obtained by numerical simulations are presented for different pulse energies and compared with the experimentally obtained data. The effect of absorbed energy delocalization with increasing laser pulse energy is demonstrated for both beam shapes while, at relatively low pulse energies, the DS beam geometry provides a stronger local absorption compared to Gaussian one. Implications of a DS pulse action on post-irradiation material evolution are discussed based on thermoelastoplastic modeling.
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Subject: Physical Sciences  -   Optics and Photonics

1. Introduction

Irreversible local modification of glasses created by the impact of ultrashort laser pulses, which is manifested as an increase of the refractive index [1,2,3,4,5], is used in many applications based on direct writing of three-dimensional structures such as waveguides [1,6,7,8], waveplates [9,10], Bragg gratings [11,12,13], optical memories [14,15,16], computer-generated holograms [17], and microfluidic devices [18,19]. From its first demonstration,1 this technique has attracted considerable attention of researchers due to the importance for existing and emerging technologies. The conventional way to perform volumetric laser processing is the use of Gaussian pulses. However, the spatially and/or temporally shaped pulses can be highly advantageous for many applications [20,21,22,23,24]. For example, Bessel laser beams have been shown to be much more efficient for high aspect ratio structuring of glass as well as for drilling and cutting dielectric materials compared to conventional Gaussian pulses [22,25,26,27]. Further, top-hat laser pulses can be advantageous for uniform surface processing [28,29]. Recently via numerical modeling, we predicted that, in a given range of pulse energies, the peak absorbed energy density can be more than tenfold higher when focusing a doughnut-shaped laser pulse inside the bulk glass as compared with Gaussian pulses [30]. Temporal pulse shaping has also demonstrated a great potential to control material modifications such as inverting the regular material response resulting in a significant refractive index increase [21]. The interaction of ultrashort laser pulses with energies sufficient in the regimes of inducing local structural modification in the bulk of transparent materials is a very complicated process involving several nonlinear phenomena (self-focusing, multiphoton absorption and ionization, electron avalanche ionization, scattering of laser radiation by generated electron plasma, etc.) [31]. Despite extensive studies on this topic, the mechanisms of laser energy absorption and localization and the effects of laser beam shaping on energy localization are still not completely understood and described [25,27,31,32].
This work is focused on the experimental and theoretical studies of the laser energy absorption by fused silica in volumetric modification regimes using Gaussian and doughnut-shaped (DS) femtosecond laser pulses. We investigate the evolution of the absorbed energy distribution and the plasma shielding effect in a wide range of pulse energy. The experimental studies are supported by numerical modeling of the propagation of ultrashort laser pulses in nonlinear media by axially symmetric Maxwell’s equations. The experimental and numerical data are in good qualitative agreement, allowing us to reveal the trends of laser energy absorption and its delocalization with increasing beam intensity. We also discuss the possible consequences of a strong laser energy localization, in the case of DS laser pulses, on material modification due to enhanced stresses and the generation of elastoplastic waves.

2. Experimental

A Ti:sapphire laser system Astrella (Coherent) is used in the experiment providing ultrashort laser pulses with a time duration of τFWHM≈40 fs at the central wavelength of λ0= 800 nm. The experimental setup consists of several sections: attenuator (half-wave plate and polarizer), beam shaping section (half-wave/quarter-wave plate for polarization control, S-waveplate for converting from Gaussian to doughnut-shaped pulses), beam profiler (beam shape and size control), and focusing part (objective 10× magnification with numerical aperture NA = 0.25). The energy transmission experiments were performed with the same experimental settings. The energy of the transmitted pulse was measured by an energy meter behind the sample. The pulse duration is controlled by the compressor in the laser system.
The irradiated samples were fused silica plates with a thickness of 1 mm. The laser beam was focused 200 μm below the surface of the sample. Structural changes within the modified areas were examined with an optical microscope (Olympus BX43) by focusing on a plane of the laser-affected zone having the highest modification contrast. We primarily aimed to investigate volumetric modification by individual laser pulses. However, the contrast of the modified areas imaged can be too weak to obtain clean, low-noise data. Thus, the modifications were studied for accumulated pulses (1; 2; 3; 5; 10; 20; and 50) acting on the same sample region. We note that the modification level in the material is evolving nonlinearly with the number of applied pulses. Thus, the modification level at multiple pulses was used as a relative quantity to compare different regimes of interaction in terms of pulse energy and beam shape.

3. Results

Numerical simulations of the experimental conditions were performed based on non-linear Maxwell’s equations written for the complex amplitudes of the vector functions and supplemented by the equations describing the excitation of electrons, their trapping, re-excitation, and oscillations in the field of the laser wave [30,33]
1 c ∂ D ∂ t − i ω c D = 4 π c e ρ v + r o t B − 8 π c E 2 ℏ ω α W P I + α S T E W P I S T E E ,
D = n 2 1 + c n 2 E 2 4 π E   ,
1 c ∂ B ∂ t − i ω c B = − r o t E
∂ ρ ∂ t = W P I + W P I S T E + W σ − ρ τ t r   ,
∂ ρ S T E ∂ t = − W P I S T E + ρ τ t r   ,
i ω v = e / m e E + v / τ c   ,
W P I = W P I 0 E 2 / E * 2 α ρ 0 − ρ − ρ S T E ρ 0   ,    
W P I S T E = W P I 0 S T E ρ S T E ρ 0   E 2 / E * 2 α S T E   ,
W σ = e 2 τ c E 2 2 m e E g 1 + ω 2 τ c 2 ρ 1 − ρ / ρ 0 − ρ S T E / ρ 0 1 + m / m h   ,    
E g = E g 0 1 + E 2 / 4 E * 2   ,
E * = ω m E g 0 e .
Here ω = 2πc/λ (λ = 800 nm) is the laser pulse frequency; ρ and v are respectively the density and the velocity of the electrons excited to the conduction band; e is the elementary charge; WPI and Wσ are the multiphoton and collisional ionization rates. We use here the value WPI0 = 3.1×1034 cm−3s−1 of 6-photon ionization (α = 6 and the band gap Eg0 = 9 eV) which is derived from the Keldysh photoionization theory at relatively low intensities of the laser field. It was found that, varying the WPI0 value in the range from 1034 to 3.7×1034 cm−3s−1, the simulation results on the laser energy absorption were not noticeably changed due to beam “self-regulation” (higher MPI rates lead to earlier electron plasma formation, resulting in earlier light scattering) [33]. The values ρSTE and W P I S T E are the density and the multiphoton ionization rate of the self-trapped excitons (STE) respectively. According to the literature [34,35,36], the absorption band related to the STE in fused silica is within the range of 5 – 6 eV. Thus, the excitation of electrons trapped in the STE states is a 4-photon process at the wavelength of 800 nm and we consider αSTE = 4. Then, the Keldysh theory at relatively low laser fields gives for 4-photon excitation process W P I S T E ≈ 1037 cm-3s-1. For simplicity, the electron excitation from the STE states was not considered in the avalanche ionization process as it is lower compared to the avalanche from the valence band. The electron collision time was taken as τc=3/ω [21]. The linear and nonlinear refractive indices of fused silica are respectively n = 1.45 and n2 = 2.48×10-16 cm2W-1. The reduced electron mass m is considered to be me/2 with me being the electron mass in vacuum [37] and m h = m m e / ( m e − m ) . The atomic density of fused silica is ρ0 = 6.6×1022 cm-3. The normalization parameter E* is the laser field strength at which the Keldysh parameter γ = 1. This corresponds to intensity I* = cε0n|E2|/2 = 2.74×1013 Wcm-2. In Eq. (6) for the electron velocity, the term ∂v/∂t≪ωv has been neglected. The simulations show that this simplification does not noticeably influence the final results. We assume here that the hot electrons cannot be trapped in the STE states during the acceleration stage in the strong field of the laser wave. Thus, the trapping time τtr = 150 fs [38] is introduced when the electric field drops below E 2 / E * 2 < 0.01 , otherwise τtr = ∞.
The equations (1)–(11) are solved in two-dimensional (2D) geometry (the coordinates (r,z)). In the case of a radially polarized DS laser pulse, this geometry is satisfied precisely. For linear polarized Gaussian pulses, the cylindrical symmetry of the beam propagation and, hence, of light absorption, can be violated, especially at high NA [33]. The validity of the 2D approach was controlled during simulations as previously described [39]. It was found that, for the parameters used in the present simulations, the cylindrical symmetry is preserved with high accuracy. The equations are solved by a finite-difference scheme [30,40]. The initial conditions for the equations correspond to the unperturbed fused silica sample. The laser pulse starts to propagate from the boundary of the simulation region (z,r) = (0,r). Its shape corresponds to the laser beam focused by a parabolic mirror [41,42]. The pulse incident on the mirror is described as
E i n c = E 0 r e x p − i ω ( t + z / c ) − t + z / c 2 / t L 2 .
The mirror has an aperture NA = 0.25 (the ratio between the initial unfocused beam radius w i n and the focal distance of the mirror) and its axis coincides with the axis z of the laser beam. In all simulations presented below, the mirror focus d was placed at the distance z = 400 µm and the FWHM pulse duration was 45 fs, slightly longer than in experiments. We note that, in the case of a linearly polarized Gaussian beam, E 0 ~ e x p − r 2 / w i n 2 while, for a radially polarized DS pulse, E 0 ~ r / w i n e x p − r 2 / w i n 2 . To calculate the electric field distribution, the Stratton-Chu integral technique is used [43,44].
The distribution of the absorbed laser energy density, which determines the level of modification inside the laser irradiated material, was integrated during the laser beam propagation from the simulation start (t0) until the laser beam left the focal zone and further light absorption becomes negligible (t1):
E a b = ∫ t 0 t 1 j E * + j * E 4 + α ℏ ω W P I + α S T E ℏ ω W P I S T E d t .

4. Results and Discussion

The expected result was the observation of a stronger volumetric modification in the case of the DS laser pulses as was predicted theoretically [30]. Indeed, when we apply the pulses with the relatively small energies E p ≤ 16 µJ (see Figure 1a,c), the experimental data are in agreement with this prediction (note that in [30] E p ≤ 2 µJ). However, the opposite behavior is observed for the E p values above 16 µJ (Figure 1a,b). In this work, the calculations cover a wider range of the pulse energies than in [30] and, as shown below, their results agree qualitatively with the experimental data.
The peak values of the absorbed energy density E ab peak as a function of the pulse energy for the Gaussian and DS pulses obtained in the numerical simulations are shown in Figure 2. As mentioned above, the absorbed energy density E ab plays a crucial role in material modification. According to the thermodynamic considerations [45], a gentle modification of fused silica in the form of compaction can take place already at single laser shots if E ab exceeds ~1700 J/cm3. If the E ab value is higher than ~2400 J/cm3, the material is locally melting that can lead to a stronger modification including bubble formation that depends on E ab peak and associated pressure gradients. In the Gaussian case considered here (Figure 2), the E ab peak value increases gradually while, for the DS pulses, the absorption demonstrates a strong maximum at moderate Ep, which several times (up to 5 for E p = 1.5 µJ) exceeds E ab peak of the Gaussian pulse case. However, with increasing pulse energy to ~16 µJ, the E ab peak values for the Gaussian and DS cases become approximately equal, and at E p > 16 µJ the situation overturns with achieving a higher local absorption for the Gaussian pulses. We note that in Ref. [30] a stronger enhancement peak of E ab peak was reported for the DS case in comparison with the Gaussian one at moderate pulse energies that can be explained by using more accurate boundary conditions that better describe the tightly focused laser beams. However, the main tendency that, at a certain pulse energy range, the DS pulses can lead to a stronger and more localized 3D material modification, remains the same.
Figure 3 presents the distributions of the absorbed laser energy density after the laser beam propagation through the sample (simulation region) for the Gaussian (upper panel) and DS (bottom panel) laser pulses at the E p values of 0.5, 1.5, 7, and 15 µJ. It is evident that, with increasing pulse energy, laser energy absorption starts at a larger distance before reaching the geometric focus, thus resulting in the absorbed energy delocalization similar to that reported by Zavedeev et al. [46] for the case of silicon. For the Gaussian laser pulses, this leads to the energy clamping effect [47,48]. Indeed, with increasing Ep by 30 times, from 0.5 to 15 µJ, the E ab peak increases monotonously by slightly more than two times. The behavior of light absorption in the case of DS pulses is strongly different from the Gaussian case as was studied in detail in Ref. [30]. Shortly, in the DS case, free-electron plasma generated by the pulse front in the form of a toroid scatters the remaining part of the pulse in two directions, to the periphery and the axis. The part of the pulse converging toward the beam axis is swiftly densifying in intensity, thus overcoming the intensity clamping. However, due to strong ionization accompanying beam collapse, the light intensity drops before reaching the axis, thus creating a hollow, highly ionized cylindrical zone. Both its length and E ab in the “hot cylinder” region strongly depend on the pulse energy: the higher E p , the longer the length of the “hot cylinder” and the lower is the E ab peak value (Figure 3, bottom). Thus, the absorbed energy delocalization along the way of the DS pulse shrinking upon focusing is accompanied by the effect of E ab delocalization along the excited cylindrical zone.
Comparing the E ab distributions for the Gaussian and DS cases, we admit that, in the first case, E ab peak is always located slightly before the geometric focus while, in the DS case, it shifts towards the laser with increasing pulse energy (Figure 3) that is understood from the light scattering geometry. Interestingly, in the DS case the second maximum of E ab emerges straight behind the geometric focus at enhanced E p (Figure 3, 7 µJ and 15 µJ). This peak is explained by the filamentation of the beam. After shrinking to the focal region, the beam has still enough energy to be refocused with creating a new “hot spot”, presumably assisted by interfering with light scattered from the “hot cylinder”. However, the E ab peak value in the second absorption region is relatively small and cannot induce a noticeable modification as compared with the peak in the front of the “hot cylinder”.
The simulation results shown in Figure 2 and Figure 3 are in reasonable qualitative agreement with the experimental results (Figure 1), including the overall change in the E ab peak tendency from the higher values at relatively low energies for the DS pulses to a larger modification level for the Gaussian laser pulses with increasing pulse energy. Interestingly, the measured transmitted energy has an opposite tendency as is seen in Figure 4. At low laser pulse energies, ≤0.6 µJ, more laser light is transmitted through the sample for the DS pulses while at 0.6 µJ < E p ≤ 1.5 µJ the light transmission is measured as equal in the DS and Gaussian cases. When the beam energy approaches and exceeds 2 µJ, the Gaussian beam is transmitted slightly better (by only ~2–3%). As the maximum local absorption of light from the DS pulses is considerably higher at relatively low energies (see, e.g., Figure 1a,c, Figure 2 and Figure 3), this indicates much more efficient laser energy coupling compared to Gaussian pulses that represents one of the solutions on the roadmap to achieve extreme laser-processing scales [49].
A similar trend was found in the simulations as an evaluation of the initial beam energy minus the absorbed one. Although quantitatively the theoretical data diverge from the measured transmittance values, at relatively low beam energies the transmittance of the laser pulse is higher for the DS case while, with increasing the beam energy, the situation flips over demonstrating a higher transmittance for the Gaussian pulses. A quantitative discrepancy between the experimental and numerical results is conditioned by several factors. First of all, the material parameters such as the rates of photo- and avalanche ionization from both ground and trapped excitonic states are still poorly known. Besides, the photoionization rates can swiftly vary during irradiation due to the laser-induced evolution of the band structure with possible band splitting and metallization of a dielectric in the strong field of the laser wave [50,51]. An important factor is the difference between the perfect shapes of laser beams used in modeling and the real experimental beam shapes. The difference is demonstrated in Figure 5 for the Gaussian and DS beams where curves 1 represent the theoretical beams and curves 2 refer to the pulses used in the present experiments. Although the theoretical curves are designed to reproduce the experimental beam shapes, the evident disparities can lead to a considerable difference in the laser excitation given the nonlinear nature of bandgap material excitation.
However, it must be underlined that our numerical model has proven to be a predictive tool as it forecasted a higher efficiency of laser energy coupling for the DS pulses as compared to the Gaussian ones [30] which has been supported experimentally in this work. Here we have also found that the model describes qualitatively well the experimentally observed tendencies in material modification in a wide range of pulse energies. We anticipate that the DS pulses upon proper shaping and focusing can be efficiently used in such applications as bringing the matter to extreme states for exploring the warm dense matter and inducing implosion of the absorbed laser energy with the creation of high-pressure material phases. In this respect, modeling can be used for the prediction and optimization of the regimes bringing the matter to extreme thermodynamic conditions. In the next section, we discuss the routes of volumetric modification of transparent materials exposed to ultrashort DS laser pulses and demonstrate a possible scenario of the material dynamics after extreme energy coupling for the DS irradiation case reported in Ref. [30].

5. Possible implications of volumetric modification of transparent dielectrics by doughnut-shaped laser pulses

Three scenarios of volumetric modification of transparent solids by focused DS laser pulses, on the example of fused silica, can be imagined to be realized with increasing pulse energy.
(i) At very low laser pulse energies, pulse-to-pulse defect accumulation leads to glass restructuring accompanied by densification within the laser-affected zone similar to observed at UV glass aging [52]. Such regimes of modification require hundreds or even thousands of pulses coupling to the same material volume. The resulting structure can be seen in the form of a tube with a “wall” of a higher refractive index than the surrounding glass matrix. By slow longitudinal beam scanning [21], the final structure can plausibly represent a “hollow waveguide” imprinted in glass, although with lower contrasts than in hollow fibers where the air is substituted by the virgin glass.
ii) At higher beam energies when glass exceeds the annealing point and approaches melting, fused silica enters the thermodynamic region where its density increases with temperature [53]. Upon fast cooling, the glass is frozen in a compacted state characterized by a fictive temperature. This regime will presumably yield the same structure as in (i) but more optimally with a smaller number of pulses and a higher contrast in the refractive index.
(iii) A more complicated structure is formed by further increasing the laser beam energy when glass experiences melting, with or without bubble formation. Under multi-pulse action with alternate melting and solidification within the laser-affected zone at low pulse repetition rates or, at high repetition rates of the order of 1 MHz when the irradiated region is kept to be molten during irradiation, various defect-related zones [54,55] or, for multicomponent glasses, elemental separation can be achieved in a controlled way [56,57].
An attractive regime of irradiation within (III) was predicted in Ref. [30] is the formation of long tubular structures with hot “walls” which can produce an implosion of material with the creation of the high-pressure phases when the material is brought into a highly non-equilibrium state. The swift formation of the hot-walled tubular structures inside transparent matter will initiate the generation of intriguing hydrodynamics, an example of which is shown below for the conditions of Ref. [30].
In Ref. [45], we applied thermoelastoplastic modeling to follow the evolution of the laser-excited fused silica under the action stress waves generated due to sudden volumetric heating by Gaussian laser pulses. The details of the model can be found in Ref. [58]. We followed the dynamics of the stress waves and relocation of material with the creation of compacted and rarefied zones. Here we applied this model to simulate the extreme conditions and the shock wave dynamics for the 2-µJ pulse (see Ref. [30]). As the initial condition, the distribution of the absorbed laser energy was used which was converted to the lattice temperature distribution based on thermodynamic relations [45]. The results of the modeling are presented in Figure 6.
In the snapshot for 12 ps, the stress distribution is shown when the material has not started to move yet. The stress reaches the value of ~0.4 TPa. Such stress levels can potentially induce transient [59] or permanent [60] formation of new phases and/or high-pressure material polymorphs. The snapshot for 50 ps demonstrates that the highly stressed cylindrical region emits two shock waves, one of which propagates to the periphery, similar to that generated by the Gaussian pulse [45] and another one converges to the center of the laser-affected zone. The latter wave upon its imploding to the center reflects and starts to propagate to the periphery, thus following the first wave (the time moment of 100 ps in Figure 6). At this time moment, the maximum pressure in the waves is still exceeding 200 GPa. The stress level is gradually decreasing upon further propagation of the waves with dropping the maximum pressure below 100 GPa by the time of app. 650 ps. Interestingly, the velocity of the double wave propagation is ~16.5 km/s which is in good agreement with the experimental data on the fused silica Hugoniot using laser-driven shocks [61]. We remind that the Rankine–Hugoniot relations describe the relationship between the states of a solid on two sides of a shock wave [62]. If the initial pressure and density are known, measurements of particle and shock velocities allow the determination of equation-of-state. McCoy et al. [61] performed the measurements over a wide range of pressures from 200 to 1600 GPa. For 341 GPa and 393 GPa, the measured shock velocities were respectively 16.18 km/s and 17.25 km/s. This indicates that our thermoelastoplastic model catches very well the laser-induced shock formation and its propagation. Thus, by measuring the shock wave in dynamics [63], it is possible to determine the pressure level generated upon the volumetric laser excitation of transparent materials. However, there are still open questions about structural transformations, which such a sequence of extremely strong shock waves can induce in materials, and if such transformations are transient or they can permanently be frozen. Such kind of research may open new perspectives for gaining new knowledge on thermodynamic conditions in laser-irradiated, highly nonequilibrium matter.

6. Conclusions

In this work, we have investigated experimentally and theoretically the effect of the pulse shape of ultrashort laser excitation of fused silica in the regimes of volumetric modification. We focused on two shapes of the laser pulses, Gaussian and doughnut-shaped ones. It has been found that, at relatively low pulse energies, in the range of ~1–5 µJ, the DS laser pulses are much more efficient in volumetric structural changes as compared with Gaussian pulses, as was predicted theoretically [30]. It is explained by the effect of intensity clamping for the Gaussian pulses which leads to the delocalization of the laser energy absorption. In the DS case, this effect is overcome due to the geometry of the focused beam propagation accompanied by the electron plasma formation which scatters light toward the beam axis. However, it was also found that, at the beam energies of ~10 µJ and higher, the efficiency of the DS pulses drops, and, at E p > 16 µJ, the situation overturns, showing a higher modification for the Gaussian pulses.
The thermoelastoplastic modeling performed for the DS pulses has revealed an intriguing dynamic of the shock waves generated as a result of tubular energy absorption. We anticipate that such a double shock wave structure can induce the formation of the high-pressure polymorphs of transparent materials and, thus, can be used for the investigation of nonequilibrium thermodynamics of warm dense matter that calls for further studies.

Author Contributions

Conceptualization, N.M.B.; methodology, M.Z. and N.M.B.; validation, M.Z., V.P.Z., and N.M.B.; formal analysis, V.P.Z. and Y.P.M.; Investigation, M.Z., V.P.Z., Y.P.M., and N.M.B.; resources, N.M.B.; data curation, M.Z. and N.M.B.; writing – original draft, M.Z., V.P.Z. and N.M.B.; writing – review & editing, M.Z., V.P.Z., Y.P.M., and N.M.B; supervision, N.M.B.; funding acquisition, N.M.B.

Funding

This research was funded by the European Regional Development Fund and the state budget of the Czech Republic (project BIATRI: No. CZ.02.1.01/0.0/0.0/15_003/0000445).

Data Availability Statement

The data supporting this study’s findings are available from the corresponding author upon reasonable request.

Dedication

This paper is our tribute to the memory of Dr. Alexander M. Rubenchik, our dear friend, teacher, and an outstanding scientist, who inspired this work and provided very helpful comments.

Conflicts of Interest

The authors declare no conflict of interest.

References

  1. Davis, K.M.; Miura, K.; Sugimoto, N.; Hirao, K. Writing waveguides in glass with a femtosecond laser. Opt. Lett. 1996, 21, 1729–1731. [Google Scholar] [CrossRef] [PubMed]
  2. Homoelle, D.; Wielandy, S.; Gaeta, A.L.; Borrelli, N.F.; Smith, C. Infrared photosensitivity in silica glasses exposed to femtosecond laser pulses. Opt. Lett. 1999, 24, 1311–1313. [Google Scholar] [CrossRef] [PubMed]
  3. Burakov, I.M.; Bulgakova, N.M.; Stoian, R.; Mermillod-Blondin, A.; Audouard, E.; Rosenfeld, A.; Husakou, A.; Hertel, I. V. Spatial distribution of refractive index variations induced in bulk fused silica by single ultrashort and short laser pulses. J. Appl. Phys. 2007, 101, 043506. [Google Scholar] [CrossRef]
  4. Juodkazis, S.; Kohara, S.; Ohishi, Y.; Hirao, N.; Vailionis, A.; Mizeikis, V.; Saito, A.; Rode, A. Structural changes in femtosecond laser modified regions inside fused silica. J. Opt. 2010, 12, 124007. [Google Scholar] [CrossRef]
  5. Alimohammadian, E.; Ertorer, E.; Uzeda, E.M.; Li, J.; Herman, P. R. Inhibition and enhancement of linear and nonlinear optical effects by conical phase front shaping for femtosecond laser material processing. Sci. Rep. 2020, 10, 21528. [Google Scholar] [CrossRef]
  6. Kononenko, V.V.; Pashinin, V.P.; Komlenok, M.S.; Konov, V.I. Laser-induced modification of bulk fused silica by femtosecond pulses. Laser Phys. 2009, 19, 1294–1299. [Google Scholar] [CrossRef]
  7. Canning, J.; Lancry, M.; Cook, K.; Weickman, A.; Brisset, F.; Poumellec, B. Anatomy of a femtosecond laser processed silica waveguide. Opt. Mater. Express 2011, 1, 998–1008. [Google Scholar] [CrossRef]
  8. Cheng, G.H. , Lin, L.; Mishchik, K.; Stoian, R. Polarization-dependent scattering of nanogratings in femtosecond laser photowritten waveguides in fused silica. Materials 2022, 15, 5698. [Google Scholar] [CrossRef]
  9. Ohfuchi, T.; Sakakura, M.; Yamada, Y.; Fukuda, N.; Takiya, T.; Shimotsuma, Y.; Miura, K. Polarization imaging camera with a waveplate array fabricated with a femtosecond laser inside silica glass. Opt. Express 2017, 25, 23738–23754. [Google Scholar] [CrossRef] [PubMed]
  10. Tian, J.; Yao, H.; Cavillon, M.; Garcia-Caure, E.; Ossikovski, R.; Stchakovsky, M.; Eypert, C.; Poumellec, B.; Lancry, M. A comparison between nanogratings-based and stress-engineered waveplates written by femtosecond laser in silica. Micromachines 2020, 11, 131. [Google Scholar] [CrossRef]
  11. Mihailov, S.J.; Smelser, C.W.; Grobnic, D.; Walker, R.B.; Lu, P.; Ding, H.M.; Unruh, J. Bragg gratings written in all-SiO2 and Ge-doped core fibers with 800-nm femtosecond radiation and a phase mask. J. Light. Technol. 2004, 22, 94–100. [Google Scholar] [CrossRef]
  12. Martinez, A.; Dubov, M.; Khrushchev, I.; Bennion, I. Direct writing of fibre Bragg gratings by femtosecond laser. Electron. Lett. 2004, 40, 1170–1172. [Google Scholar] [CrossRef]
  13. Li, H.; Yang, B.; Wang, M.; Gao, C.; Wu, B.; Zeng, L.; Xi, X.; Chen, Z.; Wang, X.; Wang, Z.; Chen, J. Femtosecond laser fabrication of large-core fiber Bragg gratings for high-power fiber oscillators. APL Photonics 2023, 8, 046101. [Google Scholar] [CrossRef]
  14. Glezer, E.N.; Milosavljevic, M.; Huang, L.; Finlay, R.J.; Her, T.-H.; Callan, J.P.; Mazur, E. Three-dimensional optical storage inside transparent materials. Opt. Lett. 1996, 21, 2023–2025. [Google Scholar] [CrossRef] [PubMed]
  15. Qiu, J.R.; Miura, K.; Hirao, K. Three-dimensional optical memory using glasses as a recording medium through a multi-photon absorption process. Jpn. J. Appl. Phys. 1998, 37, 2263–2266. [Google Scholar] [CrossRef]
  16. Shimotsuma, Y.; Sakakura, M.; Kazansky, P.G.; Beresna, M.; Qiu, J.R.; Miura, K.; Hirao, K. ; Ultrafast manipulation of self-assembled form birefringence in glass. Adv. Mater. 2010, 22, 4039–4043. [Google Scholar] [CrossRef] [PubMed]
  17. Cai, W.J.; Libertun, A.R.; Piestun, R. Polarization selective computer-generated holograms realized in glass by femtosecond laser induced nanogratings. Opt. Express 2006, 14, 3785–3791. [Google Scholar] [CrossRef]
  18. Sugioka, K.; Cheng, Y. Femtosecond laser processing for optofluidic fabrication. Lab Chip 2012, 12, 3576–3589. [Google Scholar] [CrossRef]
  19. Sima, F.; Sugioka, K.; Vazquez, R.M.; Osellame, R.; Kelemen, L.; Ormos, P. Three-dimensional femtosecond laser processing for lab-on-a-chip applications. Nanophotonics 2018, 7, 613–634. [Google Scholar] [CrossRef]
  20. Diez-Blanco, V.; Siegel, J.; Ferrer, A.; de la Cruz, A. R.; Solis, J. Deep subsurface waveguides with circular cross section produced by femtosecond laser writing, Appl. Phys. Lett. 2007, 91, 051104. [Google Scholar] [CrossRef]
  21. Mermillod-Blondin, A.; Burakov, I.M.; Meshcheryakov, Y.P.; Bulgakova, N.M.; Audouard, E.; Rosenfeld, A.; Husakou, A.; Hertel, I.V; Stoian, R. Flipping the sign of refractive index changes in ultrafast-laser-irradiated borosilicate crown optical glass at high repetition rates. Phys. Rev. B 2008, 77, 104205. [Google Scholar] [CrossRef]
  22. Zambon, V.; McCarthy, N.; Piché, M. Laser micromachining of transparent glass using ultrafast Bessel beams, Proc. SPIE 2009, 7386, 738632. [Google Scholar] [CrossRef]
  23. Courvoisier, F.; Stoian, R.; Couairon, A. Ultrafast laser micro- and nano-processing with nondiffracting and curved beams. Opt. Laser Technol. 2016, 80, 125–137. [Google Scholar] [CrossRef]
  24. Shen, T.; Tian, D.; Chen, T.; Li, P.; Hou, X. The spatiotemporal dynamics of electron plasma in femtosecond laser double pulses induced damage in fused silica. Photonics, 2023, 10, 702. [Google Scholar] [CrossRef]
  25. Paipulas, D.; Mikutis, M.; Sirutkaitis, V.; Juodkazis, S. Volumetric modifications in fused silica using Gaussian and Bessel femtosecond laser beams, Proc. SPIE 2013, 8786, 87860D. [Google Scholar] [CrossRef]
  26. Vetter, C.; Giust, R.; Furfaro, L.; Billet, C.; Froehly, L.; Courvoisier, F. High aspect ratio structuring of glass with ultrafast Bessel beams. Materials 2021, 14, 6749. [Google Scholar] [CrossRef]
  27. Ardaneh, K.; Giust, R.; Charpin, P.-J.; Morel, B.; Courvoisier, F. Electron heating and radiation in high aspect ratio sub-micron plasma generated by an ultrafast Bessel pulse within a solid dielectric. Eur. Phys. J. Spec. Top. 2022. [Google Scholar] [CrossRef]
  28. Le, H.; Penchev, P.; Henrottin, A.; Bruneel, D.; Nasrollahi, V.; Ramos-de-Campos, J.A.; Dimov, S. Effects of top-hat laser beam processing and scanning strategies in laser micro-structuring. Micromachines 2020, 11, 221. [Google Scholar] [CrossRef] [PubMed]
  29. Möhl, A.; Kaldun, S.; Kunz, C.; Müller, F.A.; Fuchs, U.; Gräf, S. Tailored focal beam shaping and its application in laser material processing, J. Laser Appl. 2019, 31, 042019. [Google Scholar] [CrossRef]
  30. Zhukov, V.P.; Rubenchik, A.M.; Fedoruk, M.P.; Bulgakova, N.M. Interaction of doughnut-shaped laser pulses with glasses, J. Opt. Soc. Am. B 2017, 34, 463–471. [Google Scholar] [CrossRef]
  31. Couairon, A.; Mysyrowicz, A. Femtosecond filamentation in transparent media. Phys. Rep. 2007, 441, 47–189. [Google Scholar] [CrossRef]
  32. Gildenburg, V.B.; Pavlichenko, I.A. High contrast periodic plasma pattern formation during the laser-induced breakdown in transparent dielectric. Phys. Plasmas 2017, 24, 122306. [Google Scholar] [CrossRef]
  33. Bulgakova, M.M.; Zhukov, V.P.; Meshcheryakov, Y.P.; Gemini, L.; Brajer, J.; Rostohar, D.; Mocek, T. Pulsed laser modification of transparent dielectrics: what can be foreseen and predicted by numerical simulations? J. Opt. Soc. Am. B 2014, 31, C8–C14. [Google Scholar] [CrossRef]
  34. Itoh, C.; Tanimura, K.; Itoh, N. Optical studies of self-trapped excitons in SiO2, J. Phys. C: Solid State Phys. 1988, 21, 4693–4702. [Google Scholar] [CrossRef]
  35. Audebert, P.; Daguzan, P.; Dos Santos, A.; Gauthier, J.C.; Geindre, J.P.; Guizard, S. , Hamoniaux, G. ; Krastev, K.; Martin, P.; Petite, G.; Antonetti, A. Space-time observation of an electron gas in SiO2, Phys. Rev. Lett. 1994, 73, 1990–1993. [Google Scholar] [CrossRef] [PubMed]
  36. Grojo, D.; Gertsvolf, M.; Lei, S.; Barillot, T.; Rayner, D.M.; Corkum, P.B. Exciton-seeded multiphoton ionization in bulk SiO2, Phys. Rev. B 2010, 81, 212301. [Google Scholar] [CrossRef]
  37. Kaiser, A.; Rethfeld, B.; Vicanek, M.; Simon, G. Microscopic processes in dielectrics under irradiation by subpicosecond laser pulses, Phys. Rev. B 2000, 61, 11437–11450. [Google Scholar] [CrossRef]
  38. Martin, P.; Guizard, S.; Daguzan, P.; Petite, G.; D’Oliveira, P.; Meynadier, P.; Perdrix, M. Subpicosecond study of carrier trapping dynamics in wide-band-gap crystals, Phys. Rev. B 1997, 55, 5799. [Google Scholar] [CrossRef]
  39. Bulgakova, N.M.; Zhukov, V.P.; Meshcheryakov, Y.P. Theoretical treatments of ultrashort pulse laser processing of transparent materials: towards understanding the volume nanograting formation and “quill” writing effect. Appl. Phys. B 2013, 113, 437–449. [Google Scholar] [CrossRef]
  40. Zhukov, V.P; Fedoruk, M.P. Numerically implemented impact of a femtosecond laser pulse on glass in the approximation of nonlinear Maxwell equations, Math. Models Comput. Simul. 2020, 12, 77–89. [Google Scholar] [CrossRef]
  41. Popov, K.I.; Bychenkov, V.Y.; Rozmus, W.; Sydora, R.D.; Bulanov, S.S. Vacuum electron acceleration by tightly focused laser pulses with nanoscale targets. Phys. Plasmas 2009, 16, 053106. [Google Scholar] [CrossRef]
  42. Couairon, A.; Kosareva, O.G.; Panov, N.A.; Shipilo, D.E.; Andreeva, V.A.; Jukna, V.; Nesa, F. Propagation equation for tight-focusing by a parabolic mirror, Opt. Express 2015, 23, 31240–31252. [Google Scholar] [CrossRef] [PubMed]
  43. Stratton, J.A.; Chu, L.J. Diffraction Theory of Electromagnetic Waves,” Phys. Rev. 1939, 56, 99. [Google Scholar] [CrossRef]
  44. Zhukov, V.P.; Fedoruk, M.P. High efficient method for calculation of Stratton-Chu integral in problems of interaction of laser radiation with materials. Computational Technologies 2021, 26, 42–60. [Google Scholar] [CrossRef]
  45. Bulgakova, N.M.; Zhukov, V.P.; Sonina, S.V.; Meshcheryakov, Y.P. Modification of transparent materials with ultrashort laser pulses: What is energetically and mechanically meaningful? J. Appl. Phys. 2015, 118, 233108. [Google Scholar] [CrossRef]
  46. Zavedeev, E.V.; Kononenko, V.V.; Gololobov, V.M.; Konov, V.I. Modeling the effect of fs light delocalization in Si bulk, Laser Phys. Lett. 2014, 11, 036002. [Google Scholar] [CrossRef]
  47. Liu, V. I.; Petit, S.; Becker, A.; Aközbek, N.; Bowden, C.M.; Chin, S. L. Intensity clamping of a femtosecond laser pulse in condensed matter, Opt. Commun. 2002, 202, 189–197. [Google Scholar] [CrossRef]
  48. Sun, Q.; Liang, F.; Vallee, R.; Chin, S.L. Nanograting formation on the surface of silica glass by scanning focused femtosecond laser pulses, Opt. Lett. 2008, 33, 2713–2715. [Google Scholar] [CrossRef]
  49. Ultrafast Laser Nanostructuring: The Pursuit of Extreme Scales; Stoian, R.; Bonse, J. (Eds.) Springer Series in Optical Sciences; Springer: Cham, 2023. [Google Scholar] [CrossRef]
  50. Schultze, M.; Bothschafter, E.M.; Sommer, A.; Holzner, S.; Schweinberger, W.; Fiess, M.; Hofstetter, M.; Kienberger, R.; Apalkov, V.; Yakovlev, V.S.; Stockman, M.I.; Krausz, F. Controlling dielectrics with the electric field of light. Nature 2012, 493, 75–78. [Google Scholar] [CrossRef]
  51. Derrien, T.J.-Y.; Tancogne-Dejean, N.; Zhukov, V.P.; Appel, H.; Rubio, A.; Bulgakova, N.M. Photoionization and transient Wannier-Stark ladder in silicon: First-principles simulations versus Keldysh theory, Phys. Rev. B 2021, 104, L241201. [Google Scholar] [CrossRef]
  52. Borrelli, N.F.; Smith, C.; Allan, D.C.; Seward, T. P. Densification of fused silica under 193-nm excitation, J. Opt. Soc. Am. B 1997, 14, 1606–1615. [Google Scholar] [CrossRef]
  53. Brückner, R. Properties and structure of vitreous silica. I. J. Non-Cryst. Solids 1070, 5, 123–175. [Google Scholar] [CrossRef]
  54. Kazansky, P.G.; Shimotsuma, Y.; Sakakura, M.; Beresna, M.; Gecevičius, M.; Svirko, Y.; Akturk, S.; Qiu, J.; Miura, K.; Hirao, K. Photosensitivity control of an isotropic medium through polarization of light pulses with tilted intensity front. Opt. Express 2011, 19, 20657–20664. [Google Scholar] [CrossRef] [PubMed]
  55. Zhang, F.; Xie, X.; Zhao, X.; Ma, L.; Lei, L.; Qiu, J.; Nie, Z. Polarization-dependent microstructural evolution induced by a femtosecond laser in an aluminosilicate glass, Opt. Express 2021, 29, 10265–10274. [Google Scholar] [CrossRef] [PubMed]
  56. Sakakura, M.; Yoshimura, K.; Kurita, T.; Shimizu, M.; Shimotsuma, Y.; Fukuda, N.; Hirao, K.; Miura, K. Condensation of Si-rich region inside soda-lime glass by parallel femtosecond laser irradiation. Opt. Express 2014, 22, 16493–16503. [Google Scholar] [CrossRef] [PubMed]
  57. Macias-Montero, M.; Muñoz, F.; Sotillo, B.; del Hoyo, J.; Ariza, R.; Fernandez, P.; Siegel, J.; Solis, J. Femtosecond laser induced thermophoretic writing of waveguides in silicate glass. Sci. Rep. 2021, 11, 8390. [Google Scholar] [CrossRef] [PubMed]
  58. Meshcheryakov, Y.P.; Shugaev, M.V.; Mattle, T.; Lippert, T.; Bulgakova, N.M. Role of thermal stresses on pulsed laser irradiation of thin films under conditions of microbump formation and non-vaporization forward transfer. Appl. Phys. A 2013, 113, 521. [Google Scholar] [CrossRef]
  59. Gleason, A.E.; Bolme, C.A.; Lee, H.J.; Nagler, B.; Galtier, E.; Milathianaki, D.; Hawreliak, J.; Kraus, R.G.; Eggert, J.H.; Fratanduono, D.E.; Collins, G.W.; Sandberg, R.; Yang, W.; Mao, W.L. Ultrafast visualization of crystallization and grain growth in shock-compressed SiO2. Nat. Commun. 2015, 6, 8191. [Google Scholar] [CrossRef]
  60. Vailionis, A.; Gamaly, E.G.; Mizeikis, V.; Yang, W.; Rode, A.V.; Juodkazis, S. Evidence of superdense aluminium synthesized by ultrafast microexplosion, Nat. Commun. 2011, 2, 445. [Google Scholar] [CrossRef]
  61. McCoy, C.A.; Gregor, M.C.; Polsin, D.N.; Fratanduono, D.E.; Celliers, P.M.; Boehly, T.R.; Meyerhofer, D.D. Shock-wave equation-of-state measurements in fused silica up to 1600 GPa, J. Appl. Phys. 2016, 119, 215901. [Google Scholar] [CrossRef]
  62. Zukas, J.A. Shock waves in solids. In Studies in Applied Mechanics; Chapter 3; Elsevier, 2004; Vol. 49, pp. 75–102. [Google Scholar] [CrossRef]
  63. Sakakura, M.; Shimotsuma, Y.; Miura, K. Observation of stress wave and thermal stress in ultrashort pulse laser bulk processing inside glass, J. Laser Micro Nanoeng. 2017, 12, 159–164. [Google Scholar] [CrossRef]
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Figure 1. (a) Optical microscope images of volumetric modifications by the Gaussian and DS laser pulses with energies of 39 and 3 µJ. (b) Comparison of modification level for the Gaussian and DS laser pulses at the high E p values of 32 and 19 µJ. (c) The same as in (b) for relatively low pulse energies of 5 and 1.5 µJ. The modification level is a dimensionless quantity evaluated from the optical microscope images of the modified areas in the planes of the highest modification contrast (the grayscale in the classical transmission imaging mode).
Figure 1. (a) Optical microscope images of volumetric modifications by the Gaussian and DS laser pulses with energies of 39 and 3 µJ. (b) Comparison of modification level for the Gaussian and DS laser pulses at the high E p values of 32 and 19 µJ. (c) The same as in (b) for relatively low pulse energies of 5 and 1.5 µJ. The modification level is a dimensionless quantity evaluated from the optical microscope images of the modified areas in the planes of the highest modification contrast (the grayscale in the classical transmission imaging mode).
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Figure 2. The peak values of the absorbed energy density as a function of the pulse energy E p . Red and black curves correspond to the DS and Gaussian pulses respectively.
Figure 2. The peak values of the absorbed energy density as a function of the pulse energy E p . Red and black curves correspond to the DS and Gaussian pulses respectively.
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Figure 3. The absorbed energy density distributions obtained in simulations for the Gaussian (upper row) and DS laser pulses (bottom row) at different pulse energies. The pulse propagates from the bottom to the top. The geometric focus is at z = 400 µm.
Figure 3. The absorbed energy density distributions obtained in simulations for the Gaussian (upper row) and DS laser pulses (bottom row) at different pulse energies. The pulse propagates from the bottom to the top. The geometric focus is at z = 400 µm.
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Figure 4. Experimental data on the transmitted energy of the single Gaussian (black curve) and DS (red curve) ultrashort laser pulses in the energy range E p = 0.1–26 µJ.
Figure 4. Experimental data on the transmitted energy of the single Gaussian (black curve) and DS (red curve) ultrashort laser pulses in the energy range E p = 0.1–26 µJ.
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Figure 5. Top: The spatial profiles of the laser intensity of the Gaussian (left) and DS (right) laser beams before the focusing lenses. Curves 1 and 2 correspond respectively to the shapes used in the simulations and measured experimentally. Bottom: Laser beam cross-sectional images recorded with a laser beam profiler.
Figure 5. Top: The spatial profiles of the laser intensity of the Gaussian (left) and DS (right) laser beams before the focusing lenses. Curves 1 and 2 correspond respectively to the shapes used in the simulations and measured experimentally. Bottom: Laser beam cross-sectional images recorded with a laser beam profiler.
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Figure 6. The dynamics of the double shock wave structure created in fused silica as the result of the action of the DS pulse with the energy of 2 µJ for the conditions of laser excitation reported in Ref. [28].
Figure 6. The dynamics of the double shock wave structure created in fused silica as the result of the action of the DS pulse with the energy of 2 µJ for the conditions of laser excitation reported in Ref. [28].
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