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.

Nanoscale investigations of femtosecond laser induced nanogratings in optical glasses.

Femtosecond (fs) laser irradiation inside transparent materials has drawn considerable interest over the past two decades. More specifically, self-assembled nanogratings, induced by fs laser direct writing (FLDW) inside glass, enable a broad range of potential applications in optics, photonics, or microfluidics. In this work, a comprehensive study of nanogratings formed inside fused silica by FLDW is presented based on high-resolution electron microscopy imaging techniques. These nanoscale investigations reveal that the intrinsic structure of nanogratings is composed of oblate nanopores, shaped into nanoplanes, regularly spaced and oriented perpendicularly to the laser polarization. These nanoporous layers are forced-organized by light, resulting in a pseudo-organized spacing at the sub-wavelength scale, and observed in a wide range of optical glasses. In light of the current state of the art, we discuss the imprinting of nanoporous layers under thermomechanical effects induced by a plasma-mediated nanocavitation process.

Upper temperature limit for nanograting survival in oxide glasses: publisher's note.

This publisher's note contains corrections to Appl. Opt.62, 6794 (2023)APOPAI0003-693510.1364/AO.496351.

Upper temperature limit for nanograting survival in oxide glasses.

The thermal stability of self-assembled porous nanogratings inscribed by an infrared femtosecond (fs) laser in five commercial glasses (BK7, soda lime, 7059, AF32, and Eagle XG) is monitored using step isochronal annealing experiments. Their erasure, ascertained by retardance measurements and attributed to the collapse of nanopores, is well predicted from the Rayleigh-Plesset (R-P) equation. This finding is thus employed to theoretically predict the erasure of nanogratings in the context of any time-temperature process (e.g., thermal annealing, laser irradiation process). For example, in silica glass (Suprasil CG) and using a simplified form of the R-P equation, nanogratings composed of 50 nm will erase within ∼30m i n, ∼1µs, and ∼30n s at temperatures of ∼1250∘ C, 2675°C, and 3100°C, respectively. Such conclusions are expected to provide guidelines to imprint nanogratings in oxide glasses (for instance, in the choice of laser parameters) or to design appropriate thermal annealing protocols for temperature sensing.

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.

Volume nanogratings inscribed by ultrafast IR laser in alumino-borosilicate glasses.

Self-assembled nanogratings, inscribed by femtosecond laser writing in volume, are demonstrated in multicomponent alkali and alkaline earth containing alumino-borosilicate glasses. The laser beam pulse duration, pulse energy, and polarization, were varied to probe the nanogratings existence as a function of laser parameters. Moreover, laser-polarization dependent form birefringence, characteristic of nanogratings, was monitored through retardance measurements using polarized light microscopy. Glass composition was found to drastically impact the formation of nanogratings. For a sodium alumino-borosilicate glass, a maximum retardance of 168 nm (at 800 fs and 1000 nJ) could be measured. The effect of composition is discussed based on SiO2 content, B2O3/Al2O3 ratio, and the Type II processing window is found to decrease as both (Na2O + CaO)/Al2O3 and B2O3/Al2O3 ratios increase. Finally, an interpretation in the ability to form nanogratings from a glass viscosity viewpoint, and its dependency with respect to the temperature, is demonstrated. This work is brought into comparison with previously published data on commercial glasses, which further indicates the strong link between nanogratings formation, glass chemistry, and viscosity.

Tailoring chiral optical properties by femtosecond laser direct writing in silica.

An object that possesses chirality, that is, having its mirror image not overlayed on itself by rotation and translation, can provide a different optical response to a left- or right-handed circular polarized light. Chiral nanostructures may exhibit polarization-selective optical properties that can be controlled for micro-to-nano optical element engineering. An attractive way to induce such complex nanostructures in three-dimension in glass is femtosecond laser direct writing. However, the mechanism of femtosecond laser induced chirality remains to be unveiled due to complex physical and chemical processes occurring during the ultrashort light-matter interaction. Here, a phenomenological model is proposed and is built on two-layers phase shifters to account for this laser-induced optical chirality in an initially achiral material (silica glass). This model is based on the observation that femtosecond laser induced nanogratings own two principal contributions to its aggregate birefringent response: a form and a stress-related one. By refining this formalism, a multilayer approach is developed to imprint on demand optical rotation. Values up to +/-60° at 550 nm within an optimal 80 µm thickness in silica glass are possible, corresponding to the highest value in a glass to date. These results provide new insights of circular-optical control in micro-nano optical manufacturing and open new opportunities for photonics applications.

Femtosecond laser direct writing multilayer chiral waveplates with minimal linear birefringence.

Chirality transfer from femtosecond laser direct writing in achiral transparent materials mainly originates from the interplay between anisotropic nanogratings and mechanical stress with non-parallel and non-perpendicular (oblique) neutral axes. Yet, the laser fabrication simultaneously induces non-negligible linear birefringence. For precise manipulation of circular polarization properties, as well as to unlock the full functionality, we report here a geometry-inspired multilayer method for direct writing of chiral waveplates with minimal linear birefringence. We perform a theoretical analysis of both circular and linear properties response for different multilayer configurations and achieve strong circular birefringence of up to -2.25 rad with an extinction ratio of circular birefringence to total linear birefringence of up to 5.5 dB at 550 nm. Our strategy enables the precise control of circular properties and provides a facile platform for chiral device exploration with almost no linear property existence.

On the Formation of Nanogratings in Commercial Oxide Glasses by Femtosecond Laser Direct Writing.

Nanogratings (NGs) are self-assembled subwavelength and birefringent nanostructures created by femtosecond laser direct writing (FLDW) in glass, which are of high interest for photonics, sensing, five-dimensional (5D) optical data storage, or microfluidics applications. In this work, NG formation windows were investigated in nine commercial glasses and as a function of glass viscosity and chemical composition. The NG windows were studied in an energy-frequency laser parameter landscape and characterized by polarizing optical microscopy and scanning electron microscopy (SEM). Pure silica glass (Suprasil) exhibits the largest NG window, whereas alkali borosilicate glasses (7059 and BK7) present the smallest one. Moreover, the NG formation windows progressively reduced in the following order: ULE, GeO2, B33, AF32, and Eagle XG. The NG formation window in glasses was found to decrease with the increase of alkali and alkaline earth content and was correlated to the temperature dependence of the viscosity in these glasses. This work provides guidelines to the formation of NGs in commercial oxide glasses by FLDW.

Lifetime prediction of nanogratings inscribed by a femtosecond laser in silica glass.

This paper is dedicated to the lifetime prediction of Type II modifications (i.e., nanogratings) written in silica glass using an infrared femtosecond laser. Herein we report accelerated aging experiments of such nanogratings through the monitoring of their characteristic linear birefringence signature. Based on the master curve formalism, we demonstrate that these laser-induced nanostructures can survive for 200 hours at 1100°C. Under the reported processing conditions and after a dedicated passivation treatment, the estimated lifetime of the birefringent optical elements is beyond 10 years at 800°C with a minor erasure of 7%.

Thermal Stability of Type II Modifications by IR Femtosecond Laser in Silica-based Glasses.

Femtosecond (fs) laser written fiber Bragg gratings (FBGs) are excellent candidates for ultra-high temperature (>800 ºC) monitoring. More specifically, Type II modifications in silicate glass fibers, characterized by the formation of self-organized birefringent nanostructures, are known to exhibit remarkable thermal stability around 1000 ºC for several hours. However, to date there is no clear understanding on how both laser writing parameters and glass composition impact the overall thermal stability of these fiber-based sensors. In this context, this work investigates thermal stability of Type II modifications in various conventional glass systems (including pure silica glasses with various Cl and OH contents, GeO2-SiO2 binary glasses, TiO2- and B2O3-doped commercial glasses) and with varying laser parameters (writing speed, pulse energy). In order to monitor thermal stability, isochronal annealing experiments (Δt⁓ 30 min, ΔT⁓ 50 ºC) up to 1400 ºC were performed on the irradiated samples, along with quantitative retardance measurements. Among the findings to highlight, it was established that ppm levels of Cl and OH can drastically reduce thermal stability (by about 200 ºC in this study). Moreover, GeO2 doping up to 17 mole% only has a limited impact on thermal stability. Finally, the relationships between glass viscosity, dopants/impurities, and thermal stability, are discussed.

A Comparison between Nanogratings-Based and Stress-Engineered Waveplates Written by Femtosecond Laser in Silica.

This paper compares anisotropic linear optical properties (linear birefringence, linear dichroism, degree of polarization) and performances (absorption coefficient, thermal stability) of two types of birefringent waveplates fabricated in silica glass by femtosecond laser direct writing. The first type of waveplate is based on birefringence induced by self-organized nanogratings imprinted in the glass. One the other hand, the second design is based on birefringence originating from the stress-field formed around the aforementioned nanogratings. In addition to the provided comparison, the manufacturing of stress-engineered half waveplates in the UV-Visible range, and with mm-size clear aperture and negligible excess losses, is reported. Such results contrast with waveplates made of nanogratings, as the later exhibit significantly higher scattering losses and depolarization effects in the UV-Visible range.

Stress-induced optical waveguides written by an ultrafast laser in Nd3+, Y3+ co-doped SrF2 crystals.

In this paper, we report on the ultrafast laser-induced birefringence, refractive index changes, and enhanced photoluminescence properties in the volume of neodymium (Nd), yttrium (Y) co-doped strontium fluoride (SrF2) and Nd, Y co-doped calcium fluoride (CaF2) crystals. The optical waveguides written with 500 kHz repetition rate provided lowest propagation loss of 1.63±0.21 dB cm-1 for transverse magnetic (TM) polarization at 632.8 nm in Nd,Y:SrF2 crystal. The measured retardance can be interpreted by stress-induced birefringence related to the permanent volume expansion, photo induced by a non-spherical irradiated zone. The absorption, steady-state, and time-resolved photoluminescence properties are also carried out in and out of the laser irradiated zone, enabling the local changes of the Nd and Y network in Nd,Y:SrF2, as well as well-preserved Nd fluorescence in the written optical waveguides.

Pulse energy dependence of refractive index change in lithium niobium silicate glass during femtosecond laser direct writing.

Femtosecond laser-induced refractive index changes in lithium niobium silicate glass were explored at high repetition rate (300 fs, 500 kHz) by polarized light microscopy, full-wave retardation plate, quantitative birefringence microscopy, and digital holographic microscopy. We found three regimes on energy increase. The first one corresponds to isotropic negative refractive index change (for pulse energy ranging 0.4-0.8 µJ/pulse, 0.6 NA, 5µm/s, 650µm focusing depth in the glass). The second one (0.8-1.2 µJ/pulse) corresponds to birefringence with well-defined slow axis orientation. The third one (above 1.2 µJ/pulse) is related to birefringence direction fluctuation. Interestingly, these regimes are consistent with crystallization ones. In addition, an asymmetric orientational writing effect has been detected on birefringence. These topics extend the possibility of controlling refractive index change in multi-component glasses.

Study of femtosecond laser-induced circular optical properties in silica by Mueller matrix spectropolarimetry.

Transmission Mueller-matrix spectroscopic ellipsometry is applied to femtosecond laser-induced modifications in silica glass in the spectral range of 450-1000 nm. Within a type II regime, the modifications exhibit not only circular dichroism, but also circular birefringence. We suggest that the laser polarization orientation with respect to pulse front tilt determines the amplitude and the sign of the circular properties. By using differential decomposition of the Mueller matrix, optical rotation is revealed for the first time, to the best of our knowledge. A maximum value of the effective optical activity of 143°/mm at 550 nm is found.

Radiation hardening of sol gel-derived silica fiber preforms through fictive temperature reduction.

The impact of fictive temperature (Tf) on the evolution of point defects and optical attenuation in non-doped and Er3+-doped sol-gel silica glasses was studied and compared to Suprasil F300 and Infrasil 301 glasses before and after γ-irradiation. To this aim, sol-gel optical fiber preforms have been fabricated by the densification of erbium salt-soaked nanoporous silica xerogels through the polymeric sol-gel technique. These γ-irradiated fiber preforms have been characterized by FTIR, UV-vis-NIR absorption spectroscopy, electron paramagnetic resonance, and photoluminescence measurements. We showed that a decrease in the glass fictive temperature leads to a decrease in the glass disorder and strained bonds. This mainly results in a lower defect generation rate and thus less radiation-induced attenuation in the UV-vis range. Furthermore, it was found that γ-radiation "hardness" is higher in Er3+-doped sol-gel silica compared to un-doped sol-gel silica and standard synthetic silica glasses. The present work demonstrates an effective strategy to improve the radiation resistance of optical fiber preforms and glasses through glass fictive temperature reduction.

Form birefringence induced in multicomponent glass by femtosecond laser direct writing.

We demonstrate a new kind of form birefringence in lithium niobium silicate glass induced by femtosecond laser direct writing. By combining electron backscatter diffraction and transmission electron microscopy, we reveal a self-assembled nanostructure consisting of periodic phase change: nonlinear optical nanocrystals embedded in a network of "walls" in a vitreous phase. These "walls" are aligned perpendicular to the laser polarization direction. This self-organized nanostructure may successfully explain the origin of the laser-induced birefringence in this multicomponent glass quite differently from pure silica. These findings highlight a spectacular modification of glass, and enable construction of a high contrast three-dimensional refractive index and birefringent structures at the micrometer scale in multicomponent glasses.

Femtosecond laser written nanostructures in Ge-doped glasses.

We report on nanostructures induced by femtosecond laser pulses in the bulk of Germanium-doped silica glasses. For studying structural properties of the nanostructure constituents small-angle x-ray scattering and SEM served to map pore size, filling factor and periodicity. Our results show that with increasing the Ge doping concentration, the aspect ratio (transverse to inscribing laser) of nanometric pores rises while they arrange in a smaller period in contrast to nanogratings in pristine fused silica. Consequently, higher optical retardance can be obtained demonstrating the pronounced glass decomposition due to the changing network structure.

Parity violation in chiral structure creation under femtosecond laser irradiation in silica glass?

The paper addresses the creation of circular optical properties from a femtosecond laser light beam with a linear polarization in an achiral material (glass) under an orthogonal incidence. In this situation, all aspects of the experiment are achiral and therefore should not give rise to chiral property creation. From that observation, we propose an interpretation that involves the action of a light-induced torque on the matter carrying a light-induced dielectric moment. We found that a direct current (DC) electric field could be produced in the lattice by the femtosecond laser in our conditions and that a non-collinear dielectric moment is created by a nonlinear effect between the DC electric field and the stress field due to the transformation of the material. We reveal that it is possible to break the chiral symmetry of glass using an intense, ultrashort laser light pulse.

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.