Formation mechanism of element distribution in glass under femtosecond laser irradiation

Usable Analytical Expressions for Temperature Distribution Induced by Ultrafast Laser Pulses in Dielectric Solids

This paper focuses on the critical role of temperature in ultrafast direct laser writing processes, where temperature changes can trigger or exclusively drive certain transformations, such as phase transitions. It is important to consider both the temporal dynamics and spatial temperature distribution for the effective control of material modifications. We present analytical expressions for temperature variations induced by multi-pulse absorption, applicable to pulse durations significantly shorter than nanoseconds within a spherical energy source. The objective is to provide easy-to-use expressions to facilitate engineering tasks. Specifically, the expressions are shown to depend on just two parameters: the initial temperature at the center denoted as T00 and a factor Rτ representing the ratio of the pulse period τp to the diffusion time τd. We show that temperature, oscillating between Tmax and Tmin, reaches a steady state and we calculate the least number of pulses required to reach the steady state. The paper defines the occurrence of heat accumulation precisely and elucidates that a temperature increase does not accompany systematically heat accumulation but depends on a set of laser parameters. It also highlights the temporal differences in temperature at the focus compared to areas outside the focus. Furthermore, the study suggests circumstances under which averaging the temperature over the pulse period can provide an even simpler approach. This work is instrumental in comprehending the diverse temperature effects observed in various experiments and in preparing for experimental setup. It also aids in determining whether temperature plays a role in the processes of direct laser writing. Toward the end of the paper, several application examples are provided.

Ultra-high temperature Soret effect in a silicate melt: SiO2 migration to cold side

The Soret effect, temperature gradient driven diffusion, in silicate melts has been investigated intensively in the earth sciences from the 1980s. The SiO2 component is generally concentrated in the hotter region of silicate melts under a temperature gradient. Here, we report that at ultra-high temperatures above ∼3000 K, SiO2 becomes concentrated in the colder region of the silicate melts under a temperature gradient. The interior of an aluminosilicate glass [63.3SiO2-16.3Al2O3-20.4CaO (mol. %)] was irradiated with a 250 kHz femtosecond laser pulse for local heating. SiO2 migrated to the colder region during irradiation with an 800 pulse (3.2 ms irradiation). The temperature analysis indicated that migration to the colder region occurred above 3060 K. In the non-equilibrium molecular dynamics (NEMD) simulation, SiO2 migrated to the colder region under a temperature gradient, which had an average temperature of 4000 K; this result supports the experimental result. On the other hand, SiO2 exhibited a tendency to migrate to the hotter region at 2400 K in both the NEMD and experimental study. The molar volume calculated by molecular dynamics simulation without a temperature gradient indicates two bends at 1650 and 3250 K under 500 MPa. Therefore, the discontinuous (first order) transition with coexistence of two phases of different composition could be related to the migration of SiO2 to colder region. However, the detailed mechanism has not been elucidated.

Optical and structural characterization of femtosecond laser written micro-structures in germanate glass

We report on direct femtosecond laser writing in zinc barium gallo-germanate glasses. A combination of spectroscopic techniques allows to progress in the understanding of the mechanisms taking place depending on the energy. In the first regime (type I, isotropic local index change) up to 0.5 µJ, the main occurrence is the generation of charge traps inspected by luminescence, together with separation of charges detected by polarized second harmonic generation measurements. At higher pulse energies notably at the threshold corresponding to 0.8 µJ or in the second regime (type II modifications corresponding to nanograting formation energy domain), the main occurrence is a chemical change and re-organization of the network evidenced by the appearance of molecular O₂ seen in the Raman spectra. In addition, the polarization dependence of the second harmonic generation in type II indicates that the organization of nanogratings may be perturbed by the laser-imprinted electric field.

Composition-dependent sign inversion of the Soret coefficient of SiO2 in binary borosilicate melts

Using a laser-induced local-heating experiment combined with temperature analysis, we observed the composition-dependent sign inversion of the Soret coefficient of SiO2 in binary silicate melts, which was successfully explained by a modified Kempers model used for describing the Soret effect in oxide melts. In particular, the diffusion of SiO2 to the cold side under a temperature gradient, which is an anomaly in silicate melts, was observed in the SiO2-poor compositions. The theoretical model indicates that the thermodynamic mixing properties of oxides, partial molar enthalpy of mixing, and partial molar volume are the dominant factors for determining the migration direction of the SiO2 component under a temperature gradient.

Femtosecond laser induced thermophoretic writing of waveguides in silicate glass

Here in, the fs-laser induced thermophoretic writing of microstructures in ad-hoc compositionally designed silicate glasses and their application as infrared optical waveguides is reported. The glass modification mechanism mimics the elemental thermal diffusion occurring in basaltic liquids at the Earth's mantle, but in a much shorter time scale (108 times faster) and over a well-defined micrometric volume. The precise addition of BaO, Na2O and K2O to the silicate glass enables the creation of positive refractive index contrast upon fs-laser irradiation. The influence of the focal volume and the induced temperature gradient is thoroughly analyzed, leading to a variety of structures with refractive index contrasts as high as 2.5 × 10-2. Two independent methods, namely near field measurements and electronic polarizability analysis, confirm the magnitude of the refractive index on the modified regions. Additionally, the functionality of the microstructures as waveguides is further optimized by lowering their propagation losses, enabling their implementation in a wide range of photonic devices.

Space-Selective Control of Functional Crystals by Femtosecond Laser: A Comparison between SrO-TiO2-SiO2 and Li2O-Nb2O5-SiO2 Glasses

We report on space-selective crystallization of congruent and polar Sr2TiSi2O8 crystals in a stoichiometric SrO-TiO2-SiO2 glass induced by (1030 nm, 300 fs) femtosecond laser irradiation. This allows us to compare with non-congruent laser-induced crystallization of polar LiNbO3 in non-stoichiometric Li2O-Nb2O5-SiO2 glass and gain information on the mechanism of nanocrystals orientation with the laser polarization that we pointed out previously. Using scanning electron microscopy (SEM), second harmonic generation (SHG), and electron backscattered diffraction (EBSD), we studied the laser-induced crystallization according to the laser processing parameters (pulse energy, pulse repetition rate, scanning speed). We found (1) a domain where the laser track is filled with crystals not perfectly textured (low energy), (2) a domain where an amorphous volume remains surrounded by a crystallized shell (high energy). This arises from Sr out-diffusion and may give rise to the crystallization of both SrTiO3 and Sr2TiSi2O8 phases at low speed. In the one-phase domain (at higher speed), the possibility to elaborate a tube with a perfect Fresnoite texture is found. A significant difference in size and morphology whereas the crystallization threshold remains similar is discussed based on glass thermal properties. Contrarily to Li2O-Nb2O5-SiO2 (LNS) glass, no domain of oriented nanocrystallization controlled by the laser polarization has been found in SrO-TiO2-SiO2 (STS) glass, which is attributed to the larger crystallization speed in STS glass. No nanogratings have also been found that is likely due to the congruency of the glass.

Response of glassy liquids to thermal gradients

The Soret effect, i.e., the flow of matter caused by a temperature gradient, is studied in a glass-forming binary Lennard-Jones (LJ) mixture, using nonequilibrium molecular dynamics computer simulation. The transport processes associated with this effect are thermal diffusion and interdiffusion. While interdiffusion processes exhibit a drastic slowing down when approaching the glass transition, thermal diffusion appears to be a fast process even in the glass. We show that the Soret effect becomes more pronounced in the vicinity of the glass transition, due to the decoupling between thermal diffusion and interdiffusion as well as the chemical ordering in the considered LJ mixture. This is reflected in the occurrence of large concentration gradients, nonlinear concentration profiles, and long-lived nonstationary structures.

Ultrashort laser induced spatial redistribution of silver species and nano-patterning of etching selectivity in silver-containing glasses

Femtosecond laser-induced spatial redistribution of silver species (ions, clusters, and hole centers) in a silver-containing phosphate glass is investigated by correlative means of near-field scanning optical microscopy (NSOM) images, numerical simulations, chemical micro-probe analysis, and nanoscale spatial profiles after soft etching. In particular, we found that the chemical etching selectivity for nanoscale patterning is strongly dependent upon the irradiation of femtosecond laser due to the spatial redistribution of silver species within the affected area. These results strongly indicate that controlling the distribution of silver species by femtosecond laser irradiation may open new routes for surface nanoscale chemical and/or spatial patterning for the fabrication of 2D surface photonic crystals.

Role of partial molar enthalpy of oxides on Soret effect in high-temperature CaO-SiO2 melts

The Soret effect or thermodiffusion is the temperature-gradient driven diffusion in a multicomponent system. Two important conclusions have been obtained for the Soret effect in multicomponent silicate melts: first, the SiO₂ component concentrates in the hot region; and second, heavier isotopes concentrate in the cold region more than lighter isotopes. For the second point, the isotope fractionation can be explained by the classical mechanical collisions between pairs of particles. However, as for the first point, no physical model has been reported to answer why the SiO₂ component concentrates in the hot region. We try to address this issue by simulating the composition dependence of the Soret effect in CaO–SiO₂ melts with nonequilibrium molecular dynamics and determining through a comparison of the results with those calculated from the Kempers model that partial molar enthalpy is one of the dominant factors in this phenomenon.

Femtosecond laser writing of photonic devices in borate glasses compositionally designed to be laser writable

The design and performance of borate glass samples compositionally pre-designed to be femtosecond laser writable via laser-induced ion migration is reported in this Letter. It is demonstrated that borate glasses modified on purpose with small amounts of La₂O₃ and Na₂O can be straightforwardly used to produce high-index contrast (Δn) waveguides by femtosecond-laser-assisted ion migration. The positive Δn of the waveguides is caused by the local enrichment of La₂O₃ in the guiding region with a slope of 8·10^-3(mol.%)^-1. The value of this is consistent with numerical aperture measurements of the waveguides and local compositional measurements at the guiding region performed by energy-dispersive x-ray micro-analysis. The maximum achievable Δn values can be controlled through the initial La₂O₃ content of the glass. Maximum Δn values >10^-2 for samples with just 5.5 mol. % of La₂O₃ have been produced. This compositional design approach could be potentially used to produce highly efficient femtosecond laser writeable glasses in other glass families.

Compositional redistribution in CaO-Al2O3-SiO2 glass induced by the migration of a steel microsphere due to continuous-wave-laser irradiation

A high-power continuous-wave (CW) laser was used to move a steel microsphere through a CaO-Al₂O₃-SiO₂ glass block at room temperature along a trajectory toward the laser source. A compositional analysis revealed that the CaO concentration in the glass decreased at the center of the microsphere's trajectory but increased in the area adjacent to it; the SiO₂ concentration showed an opposite trend while the Al₂O₃ concentration did not change. Further, the compositional difference between the center and the area adjacent to the microsphere trajectory depends on the velocity of the microsphere, which is controllable by tuning the laser power.

Evolution of polarization dependent microstructures induced by high repetition rate femtosecond laser irradiation in glass

We report the observation of an anomalous polarization dependent process in an isotropic glass induced by long time stationary irradiation of a high repetition rate near-infrared femtosecond laser. Two distinctive types of polarization dependent microstructures were induced at different irradiation stages. At early stage (a few seconds), a dumbbell-shaped structure elongated perpendicularly to the laser polarization formed at the top of the modified region, which was later erased by further irradiation. At later stage (above 30 s), bubbles filled with O₂ formed by the irradiation, which were distributed along the laser polarization at a distance far beyond the radius of the laser beam. Based on a simple modeling of light reflection on boundaries, a thermal accumulation process was proposed to explain the formation and evolution of the dumbbell-shaped microstructure. The possible factors responsible for polarization dependent distribution of bubbles are discussed, which needs further systematic investigations. The results may be helpful in the development of femtosecond laser microprocessing for various applications.

One-step photoinscription of asymmetrically oriented fresnoite-type crystals in glass by ultrafast laser

Oriented fresnoite-type crystals (Sr(2)TiSi(2)O(8)) were photoinduced directly in bulk silica-based glass by femtosecond laser irradiation at high repetition rate (typ. 300 kHz). Unlike related results obtained from other researchers, asymmetrical polar-axis orientation of those nonlinear crystals in transverse direction of the cross section has been demonstrated by electron backscattered diffraction and micro-second-harmonic generation (SHG). The nonlinear optical property of laser lines has been further characterized by SHG measurement. We found that the preferential directions of the polar axis were in the laser motion direction with a small dispersion in part of the heated volume. The other part of the crystallized volume shows an axis perpendicular to the writing direction. The mechanism of asymmetric orientation of femtosecond-laser-induced crystallization also is discussed.

Condensation of Si-rich region inside soda-lime glass by parallel femtosecond laser irradiation

Local melting and modulation of elemental distributions can be induced inside a glass by focusing femtosecond (fs) laser pulses at high repetition rate (>100 kHz). Using only a single beam of fs laser pulses, the shape of the molten region is ellipsoidal, so the induced elemental distributions are often circular and elongate in the laser propagation direction. In this study, we show that the elongation of the fs laser-induced elemental distributions inside a soda-lime glass could be suppressed by parallel fsing of 250 kHz and 1 kHz fs laser pulses. The thickness of a Si-rich region became about twice thinner than that of a single 250 kHz laser irradiation. Interestingly, the position of the Si-rich region depended on the relative positions between 1 kHz and 250 kHz photoexcited regions. The observation of glass melt during laser exposure showed that the vortex flow of glass melt occurred and it induced the formation of a Si-rich region. Based on the simulation of the transient temperature and viscosity distributions during laser exposure, we temporally interpreted the origin of the vortex flow of glass melt and the mechanism of the formation of the Si-rich region.

Shape control of elemental distributions inside a glass by simultaneous femtosecond laser irradiation at multiple spots

The spatial distributions of elements in a glass can be modulated by irradiation with high repetition rate femtosecond laser pulses. However, the shape of the distribution is restricted to being axially symmetric about the laser beam axis due to the isotropic diffusion of photo-thermal energy. In this study, we describe a method to control the shape of the elemental distribution more flexibly by simultaneous irradiation at multiple spots using a spatial light modulator. The accumulation of thermal energy was induced by focusing 250 kHz fs laser pulses at a single spot inside an alumino-borosilicate glass, and the transient temperature distribution was modulated by focusing 1 kHz laser pulses at four spots in the same glass. The resulting modification was square-shaped. A simulation of the mean diffusion length of molten glass demonstrated that the transient diffusion of elements under heat accumulation and repeated temperature elevation at multiple spots caused the square shape of the distribution.

Three-dimensional temperature distribution and modification mechanism in glass during ultrafast laser irradiation at high repetition rates

We experimentally determined the three-dimensional temperature distribution and modification mechanism in a soda-lime-silicate glass under irradiation of ultrafast laser pulses at high repetition rates by analyzing the relationship between the morphology of the modification and ambient temperature. In contrast to previous studies, we consider the temperature dependence of thermophysical properties and the nonlinear effect on the absorbed energy distribution along the beam propagation axis in carrying out analyses. The optical absorptivity evaluated with the temperature distribution is approximately 80% and at most 3.5% smaller than that evaluated by the transmission loss measurement. The temperature distribution and the strain distribution indicate that visco-elastic deformation and material flow play important roles in the laser-induced modification inside a glass.