1. Introduction

Optical access to the mid-infrared (MIR) spectrum puts forward a strong interest for a range of photonic-based applications including astronomy and space sensing, organic tracing or thermal detection. The challenge of MIR accessibility and fabrication of adapted complex optical functions working in the MIR spectral domain puts forward chalcogenide technology as a promising solution [1–10]. Chalcogenide glasses (ChGs) represent an important class of materials for MIR applications particularly due to their transparency and nonlinear strength [11–15]. Equally, the requirements of embedded, mechanically stable miniature optical devices recommends laser fabrication as a technique of remarkable potential for developing miniaturized 3D embedded photonic micro-circuitries. The optical performance relies then on defining upgraded material characteristic and optical design, including a passage from two to three dimensions and, in this context, 3D ultrafast laser processing of transparent materials offers already interesting perspectives [16–19]. Highly contrasted refractive index domains within guiding structures can be obtained by localized laser-induced changes following laser scan; this allows creating light control functions inside bulk materials where the embedded nature assures for intrinsic phase stability. The performance of such light guiding structures (waveguides) in a given spectral range depends on the balance between index contrast, profile, and dimension, thus optimal material response to light interaction is determinant. This implies that the physical interaction, material response and the characteristic dimensional scale have to be accurately controlled for achieving desired mode transport.

Typically ChG materials show photosensitivity and intrinsic metastability, which marks the reaction to external radiation [20–26]. The structural flexibility allows tuning optical properties, namely gap and phonon energy, or nonlinearities, by elemental constituents. These features, coupled to a relatively high two photon absorption yield at current ultrafast laser radiation IR wavelengths can allow the development of efficient volume 3D photoinscription methods [27–35]. The induced refractive index change has a nonlinear nature and it is determined, depending on glass composition, by molecular, structural, and thermomechanical rearrangements [36–38]. Here we study the response of Ge₁₅As₁₅S₇₀ glass irradiated by high intensity ultrafast laser pulses in comparison to As₂S₃, and indicate the facility of generating positive index changes in the former. While asking the question which are the factors that enable the index change form a compositional and structural viewpoint, we discuss the possibility that photo-contraction, structural rearrangements, photo-expansion processes induced by carrier excitation via two-photon absorption and heat-induced mechanical relaxation play an important role in the photo-inscription process of this glass. We first discuss the conditions for type I positive index changes and the stability of the structural modifications. The index modifications are linked to a laser-induced re-structuring process and rearrangement of the glass matrix following bond softening. The rearrangement of the matrix depends on the initial degree of structural relaxation. The thermal history of the glass preparation fix the level of flexibility in rearranging the structure, where high fictive temperature glass allows for more efficiency in densely repacking the structure. Above a certain threshold we show that plasma generation and local laser heating, able to initiate hydrodynamic expansion, is important for the generation of highly contrasted type II void-like negative index changes. Single-pulse type II trace in this chalcogenide glass can be obtained significantly more efficiently by focusing non-diffractive Bessel laser beams due to their increased nonlinear stability. Using time-resolved microscopy on sub-ps and ps scales we confirm a thermomechanical scenario for the type II case, relaxing by pressure wave emission. The results are further confirmed by means of Raman analysis of type I regions photo-inscribed in irradiated and non-irradiated samples, indicating that significant structural changes are induced in the modified region.

2. Experimental conditions

An amplified Ti:Sapphire femtosecond laser system delivering 800 nm light pulses with a maximum power of 600 mW and a duration of 160 fs at a repetition rate of 100 kHz was employed as irradiation source. As₂S₃ and Ge₁₅As₁₅S₇₀ parallelepipedic samples with transparency cut-off respectively at 580 nm and 520 nm were irradiated and their response to laser radiation was studied. Exposure doses were controlled by electromechanical shutters. The beam was focused inside the target principally by large numerical aperture microscope objectives (NA = 0.42–0.45, effective NA due to truncation limited to NA = 0.4). The source is equipped with a pulse envelope control unit in time based on programmable spectral phase modulation in liquid crystal arrays so the response of the samples can be studied as a function of the temporal duration of the writing pulse [39]. Static and dynamic longitudinal writing configurations with translation parallel to the laser axis were used in direct focusing geometries. An Olympus BX41 positive optical transmission (OTM) and phase-contrast microscope (PCM) inserted in the irradiation setup was used to image the interaction region in side-view geometry. Positive refractive index changes relative to the background matrix are appearing dark on gray background, while white zones indicate negative index variations. The guiding properties of the photo-inscribed waveguides were verified upon injection with IR light. Time-resolved studies were conducted using an 800 nm amplified Ti:Sapphire femtosecond laser system delivering light pulses with a maximum power of 3 W and a duration of 50 fs at a repetition rate of 1 kHz allowing equally for extraction of single pulses or controllable pulse sequences. A Bessel-Gauss beam was used for excitation with the incoming irradiation pulse crossing an axicon lens. Details are given in [40]. The conical intersection image after the axicon (16° angle, tight focusing) was demagnified and imaged using a 4f afocal system inside the glass material. Non-diffractive excitation allows for a relatively lower yield of nonlinearities with respect to Gaussian propagation rendering thus stable excitation conditions.

3. Comparison As₂S₃ – Ge₁₅As₁₅S₇₀

A very insightful observation appears from studying on a comparative basis the optical response of As₂S₃ and Ge₁₅As₁₅S₇₀ under femtosecond laser irradiation. In Fig. 1 we show typical photoinscription traces that can be obtained in the bulk by translating the sample in the longitudinal direction during laser irradiation. Depicted on the left (Fig. 1(a)) is the response of As₂S₃ and on the right (Fig. 1(b)) the response of Ge₁₅As₁₅S₇₀ for an averaged laser power of 2 mW at 100 kHz repetition rate and two different translation speeds: 100 µm/s (up) and 1000 µm/s (down).

 

Fig. 1 Comparison of the refractive index change results (PCM) of the waveguide laser photoinscription process in reference As₂S₃ (a) and Ge₁₅As₁₅S₇₀ (b) glasses by 2 mW (@100 kHz) and 160 fs laser pulses. The translation speeds of the samples are indicated on the left. A larger processing window for positive index changes is observed in the case of Ge₁₅As₁₅S₇₀. (c) Variation of the guided mode intensity (left axis) and waveguide index contrast (right axis) as a function of the translation speed of a reference Ge₁₅As₁₅S₇₀ sample, for energy of 4 mW (@100 kHz).

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As can be clearly seen, As₂S₃ and Ge₁₅As₁₅S₇₀ samples show almost an opposite response to the femtosecond laser flux, with an increased facility to photoinscribe positive index changes for the latter. By analyzing the response of both samples over a wide range of translation speeds and laser powers, three main conclusions can be given:

To characterize the optical properties, waveguides photo-inscribed in both samples were injected with 800 nm light. No guided light has been observed in the As₂S₃ sample within single traces. This is due to the fact that light cannot be guided in negative index type II structures and the refractive index contrast for type I structures is too weak to obtain a confined mode, with a reasonable normalized frequency value. This indicates that the index contrast for type I structures photo-inscribed in As₂S₃ is smaller than 10⁻⁴. However, an opposite behavior is observed in the Ge₁₅As₁₅S₇₀ sample. Here a very large processing window for type I structures permits obtaining well-guided single modes for different values of power and translation speed. This allows tuning the intensity and the diameter of the guided mode along the waveguide, as can be seen in Fig. 1(c).

A first conclusion can be drawn here. Doping with Ge allows creating glasses (as Ge₁₅As₁₅S₇₀) with a large window for type I modifications, starting from glasses (as As₂S₃) which have very narrow window for type I modifications under femtosecond laser beam irradiation and therefore can only give few and rather complex solutions to guiding light, like for example depressed cladding concepts. Controlling the induced refractive index variation via elemental composition gives an important flexibility in engineering materials for a large spectrum of needs and applications in photonics, by generating optimized optical functions. For example tuning the refractive index change values in the 10⁻³ – 10⁻⁴ domain is important for determining the guiding conditions and the single-mode or multimode performance, but equally in engineering the evanescently coupling coefficient in optical systems based on evanescently-coupled waveguide arrays [41].

4. Ultrafast photo-inscription of thermally-conditioned higher/lower-density Ge₁₅As₁₅S₇₀

In this section we make a comparison between the photo-inscription process in lower and higher density (higher and lower enthalpy respectively) chalcogenide glasses obtained by changing the annealing time during the preparation phase. We will discuss the role of the thermal history in the photo-inscription process.

4.1 The role of thermal history

After observing the role of Ge in establishing a wide positive index change, a question relies on the as-generated structural flexibility of the glass matrix. How does the connectivity driven by Ge relates to the structural flexibility designed by the thermal history of the glass? Several levels of structural arrangements and rigidity can be obtained by the thermal history during glass preparation and we have opted to compare two distinct regimes; a short annealing close to the glass transition temperature T_g (in the following called the “reference sample”), and a long re-annealing (in the following called “re-annealed sample”), both followed by a slow ramped cooling. This provides respectively a high and low value of enthalpy (see Fig. 2).

 

Fig. 2 Schematic of the thermal history of annealed chalcogenide glasses and its influence on the enthalpy of the microscopic glass structure.

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In detail, the Ge₁₅As₁₅S₇₀ is obtained by mixing elements in a furnace at a temperature of 800 °C for 15 hours and rapid cooling to Tg–15 °C. An annealing of 30 minutes allows a partial removal of constraints, followed by a slow cooling at room temperature. This process generates unrelaxed glasses (the reference sample) with characteristic volumes higher than the volume corresponding to relaxed glasses, and therefore a lower density. The re-annealed sample follows an additional temperature treatment. A long annealing (70 h) at Tg–15 °C allows to erase the previous history and determines a rather complete relaxation of the glass. Typical relaxation times in this range below T_g are in the order of tens of minutes, significantly smaller than the heat treatment cycle. Thus a relaxed glass with a minimal volume (low enthalpy) and higher density is obtained. Two samples with different intrinisic relaxation degrees and therefore densities are thus obtained.

In conclusion a process that does not allow structural relaxation generates a glass sample with high enthalpy and volume, i.e. lower density. Re-annealing enables a structural relaxation process that corresponds closely to a structural equilibrium at the annealing temperature, little affected by the cooling time as the relaxation times becomes prohibitively long [49]. In other words, from a standard normal thermodynamic behavior of a chalcogenide glass, the longer the annealing time at temperatures under T_g, the lower its final volume, i.e. higher its density [42]. The glass refractive index, which depends on its density, will depend therefore on its thermal history. A glass annealed long time at a temperature close to T_g will have therefore a higher refractive index than a glass annealed during a short time; global refractive index variations of the order of 10⁻⁴ to 10⁻³ can be reached by annealing [43, 44]. The enthalpy represents a first evaluation of structural flexibility allowing evaluating the strength of additional laser-induced modification on a structure with different degrees of relaxation, up to the point where in principle no further structural changes and relaxation can be induced. The structural state reached by controlled annealing will play therefore a role in additional laser-assisted processes as the laser excitation can relaunch a heating-cooling cycle or additional molecular reorganization. In re-annealed samples, where the glass structure is relaxed, it should be much harder to induce photo-contraction, and furthermore the opposite effect of photo-expansion should be observed, especially at higher intensities [45].

4.2 Measurement

In order to verify this point, we performed ultrafast laser photoinscription of type I waveguides in a reference Ge₁₅As₁₅S₇₀ sample, annealed only 30 min at T_g–15 °C and then slowly cooled to room temperature, and in one re-annealed during 72 hours at T_g −15 °C and then slowly cooled to the room temperature.

The photoinscription process was performed in both samples under the same experimental conditions (numerical aperture of the focusing objective, laser pulse duration, and an averaged laser power of 2 mW) and the response of the two samples was evaluated by injecting IR light in the waveguides and checking the guided modes in the near-field. As can be seen in Fig. 3 the response of the reference and re-annealed samples was significantly different. The reference sample (Figs. 3(a) and 3(c)) showed the expected response of index increase, very similar to that described in [41]. On the contrary the photoinscription of efficient type I waveguides in the re-annealed sample was more difficult to perform and only lower index contrast type I traces could be photo-inscribed inside; this is demonstrated by the fact that it was impossible to obtain a confined guided mode for the waveguides photo-inscribed in the re-annealed sample (Figs. 3(b) and 3(d)), which normally indicates a low refractive index contrast. In Figs. 3(g) and 3(h) we plot the contrast profile (grey level) of type I waveguides photo-inscribed in the reference sample and in the re-annealed sample, in the same experimental conditions indicated in Figs. 3(a-d)). As can be seen, the region where the laser pulse is more intense (the center of the pulse) corresponds always to a negative refractive index variation (indicated with an arrow in the figures) when the sample is re-annealed, and this effect is more pronounced at higher intensities and higher laser doses, as expected (Fig. 3(g)). This behavior is in good agreement with the results reported in [45], i.e. irradiating the surface of high enthalpy chalcogenide glass with low intensity laser pulses results in a large photocontraction, while high intensity irradiation can generate the exactly opposed effect, i.e. photoexpansion, in low enthalpy samples. In Figs. 3(e) and 3(f) we also reported, for comparison, the response in terms of index change of a reference As₂S₃ sample exposed to a photo-inscription process where 2 mW laser pulses and low 60 µm/s (3e) and high 1000 µm/s (3f) scanning speeds are used. We can clearly see that laser-induced densification in As₂S₃ glass is hard to obtain, as if the molecular arrangement of this sample was already relaxed in a configuration of very low enthalpy. By comparing Figs. 3(c), 3(e), 3(d) and 3(f), we can see that the response of the re-annealed Ge₁₅As₁₅S₇₀ and the response of the reference As₂S₃ are similar in a certain respect. We can qualitatively conclude that, when re-annealed during long time the response of Ge₁₅As₁₅S₇₀ glasses to laser irradiation tends to match the response of reference As₂S₃ glasses (not re-annealed).

 

Fig. 3 Comparison of the index change results (PCM) of the waveguide photoinscription process with two different scan speeds in the reference (a, b) and longtime re-annealed Ge₁₅As₁₅S₇₀ (c, d) samples by 2 mW (@100 kHz) and 160 fs laser pulses. For comparison, parts (e) and (f) show the photoinscription traces in a reference As₂S₃ sample. Figures (g) and (h) show the variation of the transverse relative refractive index profile (in grey levels) of the traces corresponding to the couple of figures (a, c) and (b, d) respectively. The decrease in the gray level correspond to index increase. Note the higher contrast obtained in the reference Ge₁₅As₁₅S₇₀.

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Based on the scenario depicted above, this gives an indication about the role of Ge doping. As₂S₃ in fact present a quite planar structure; the insertion of Ge introduces a 3D connectivity and new degrees of freedom, allowing for higher flexibly and so a higher relaxation potential. We could think that is more difficult to relax a planar structure such as As₂S₃ than a 3D connected structure such as Ge₁₅As₁₅S₇₀. In this kind of photo-inscription process the index variation can be totally or partially erased by re-annealing at a temperature close to the glass transition temperature, which for our sample has been measured as T_g = (204 ± 2) °C. However, the thermal stability of the waveguide obtained in our study has been evaluated at different temperature and no significant changes within the light mode transport have been observed until one hour annealing at 190 °C, indicating a quite good thermal stability.

4.3 Discussion

We have therefore observed that the laser effect depends on the degree of relaxation, the more relaxed the glass the more difficult is to obtain high contrast positive index changes. This indicates that the laser role is to locally trigger states with a different degree of relaxation with respect to the pristine sample, namely to foster further relaxation in unrelaxed or partially relaxed matrices (with a result in index increase) or to induce structural constraints in relaxed matrices up to thermomechanical effects. The question is then how the laser pulse is able, via the deposited energy/excitation to trigger molecular mobility and structural rearrangement [46]. We discuss below two paths, an electronic driven softening process in the presence of low temperature yields, and later in the text we will discuss the probability of thermal drives for molecular reorganization.

In our experimental conditions, laser pulses are focused into the sample and reach peak intensities for which high two-photon absorption takes place; where two photon absorption coefficient lies usually in the 1-2 cm/GW range [47]. Carrier plasma is therefore locally generated, i.e. a number of electrons is promoted from the valence band to the conduction band by two-photon absorption. When electrons are excited to the conduction band, bonds of the glass matrix are potentially weakened and molecular mobility is allowed even at room temperatures where normally it is prohibited by slow kinetics. The lifetime of the electron plasma generated by a single pulse (few tens of nanoseconds [32]) is too short to induce an efficient molecular mobility with only one laser pulse, however, laser pulse after laser pulse, a relaxation channel is generated through which the glass structure is allowed to rearrange even at room temperature The irradiation process can be seen therefore as a way to remove the kinetic constraint to the thermodynamically driven relaxation.

These results are in agreement with previous works reported in the literature. Hisakuni and Tanaka [48, 49] reported on photo-induced glass softening effect in amorphous As₂S₃. They have shown the possibility of athermally photo-induced fluidity, i.e. the possibility of introducing degrees of freedom and structural mobility via paths which are not exactly temperature driven in the glass matrix under laser irradiation. More recently Lucas and King [46] reported on the observation of fast light-activated relaxation in GeSe₉ chalcogenide glass illuminated with sub-band-gap light from a Ti-Sapphire laser.

However it will be seen below that, in conditions of type I writing, the single shot level of excitation is rather low, with carrier densities presumably below 10¹⁹ cm⁻³, keeping thus the single shot effect in molecular reorganization low, and, at the same time, a low accompanying thermal yield, improbable to sustain molecular reorganization.

All these results suggest nevertheless that ultrafast optically induced relaxation processes are possible at room temperature under ultrafast laser irradiation or generally where laser-induced heat yield is low, and this process is much efficient in chalcogenide glasses with a glass matrix quenched in a configuration of high enthalpy (or high fictive temperature). The verification of a low temperature yield will be given later in the text.

5. Static and Time resolved imaging of photo-written type I/type II changes

5.1 Static results: type I and type II permanent changes in single and multi-shot regimes

We study here the photo-inscription of type I and type II permanent changes induced by focusing ultrashort non-diffractive (Bessel) beams into the sample. We choose Bessel beams because they are quasi-non-propagative self-healing beams and therefore they allow locally deposing higher energy densities with reduced nonlinear effect due to propagation, as observed for example with Gaussian laser beams. Experimental observations show that when high energy and low energy laser pulses are focused into the sample, no permanent type I local changes are observed in single shot regime both with femtosecond and picosecond Bessel beams; type I modification are observed only with low energy Bessel pulses (femtosecond or picosecond) after several laser shots (see Fig. 4(b)). In Fig. 4(b) we can clearly see for example that for 100 nJ - 80 fs Bessel pulses one needs a number of laser shots equal to N = 100 before starting to observe a very low contrasted type I change (threshold), and the index contrast increases with the number of laser shots. This indicates that, in femtosecond or in picosecond regime, an efficient photo-induced densification at low energy can be observed only after many laser shots (cumulative effect), and it is a further indication of the fact that local densification observed in correspondence to type I modified regions has not a thermomechanical origin. This is supported by numerical simulations, which are discussed in the next paragraph. Type II permanent change, on the contrary, can be observed in single shot regime and is associated with the generation of relatively dense electron plasmas as showed and discussed in the paragraph 5.3.

 

Fig. 4 (a) Type II change produced in single-shot regime by a 1 µJ, 4 ps Bessel laser pulse focused into Ge₁₅As₁₅S₇₀. (b) Type I changes produced in multi-shots regime by low energy 100 nJ, 80 fs Bessel laser pulses focused into Ge₁₅As₁₅S₇₀. Type I changes can be produced only in multishots regime.

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5.2 Numerical simulations

In order to support the above conclusions based on experimental observations, we have tried to estimate the level of energy deposition via numerical simulations of the interaction between Bessel laser beams and our chalcogenide sample. The simulation used a NLSE approach. The numerical code used for simulations is described in ref [40], but in our case the sample is ionized by two photon absorption (two-photon absorption coefficient: $\beta =0.8\times {10}^{-9}{\text{cm}}_{}{\text{W}}^{\text{-1}}$). The other sample parameters are: $n=2.2$ (refractive index), $E_g={2.4}_{}\text{eV}$ (band-gap), $n_2=1.6\times {10}^{-14}{\text{cm}}^{\text{2}}{}_{}{\text{W}}^{\text{-1}}$ (nonlinear index).

The calculation of the integrated deposited energy density (electronic energy accumulated via Bremsstrahlung) here was performed for the two cases studied experimentally (shown in Fig. 4); the results for high energy femtosecond and low energy picosecond laser pulses can then be extrapolated. In Fig. 5 we show the result for the case of a 100 nJ – 80 fs Bessel beam (corresponding to Fig. 4(b)) and the case of a 1 µJ – 4 ps Bessel beam (corresponding to Fig. 4(a)), focused in Ge₁₅As₁₅S₇₀. These results have been used to estimate the local temperature reached by the glass matrix after carrier relaxation and vibrational excitation. In order to estimate the temperature elevation we use the relation: $\Delta T=E/\rho C_p$, where $E$ is the peak integrated deposited energy density, $\rho =2.795\times {10}^{-3}{\text{kg}}_{}{\text{cm}}^{\text{-3}}$is the density of the chalcogenide sample and $C_p={500}_{}{\text{J}}_{}{\text{kg}}^{\text{-1}}{\text{K}}^{\text{-1}}$is an estimated reasonable value of the specific heat capacity at constant pressure for sulfur rich chalcogenide glasses [50]. The calculation gives a matrix local temperature which is about 990 °C in the case corresponding to Fig. 4(a) (high negative index contrast type II change) and about 180°C in the case corresponding to Fig. 4(b) (positive index contrast type I change). For comparison, the glass transition temperature of Ge₁₅As₁₅S₇₀ has been measured as T_g = (204 ± 2) °C.

 

Fig. 5 Integrated deposited energy density calculated using an NLSE code in the case of the interaction between a 100 nJ – 80 fs Bessel beam (a), and a 1 µJ – 4 ps Bessel beam (b).

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These results are in good agreement with the previous conclusions based on experimental observations. In fact in the case of low energy femtosecond laser pulses the temperature reached by the glass matrix is leveled below T_g; this means very long thermodynamic relaxation times if compared with the heat diffusion time (local cooling of the glass structure), which in our case is estimated as ${\tau }_c\approx w_0^2/D\approx 10\text{µs}$, where$w_0\approx 1_{}\text{µm}$ is the waist of the focused Bessel beam and $D\approx {10}^{-7}{\text{m}}^{\text{2}}{}_{}{\text{s}}^{\text{-1}}$ is a typical value of the diffusivity of a chalcogenide glass. The observed relaxation of the glass structure therefore cannot have a pure thermodynamic origin and we believe it is improbable also for multiple thermal cycles of this level; the structure however is allowed to relax towards type I changes during the lifetime of the electron plasma generated by the laser pulse because the glass bonds are weakened. This becomes a main factor in initiating molecular mobility and structural relaxation. This process is more efficient in multi-shots regime because of cumulative effects and no changes are observed with a single shot. In the case of high energy picosecond laser pulses, the glass structure can reach temperatures largely higher than T_g. In this case thermodynamic relaxation can become comparable with or even shorter that the diffusivity time and the glass structure can rapidly go in a liquid-like phase. Moreover in the liquid-like phase characterized by low viscosities and temperature in excess of T_g, the elevation of the temperature can generate pressure increase accompanied by strong local expansion. The expansion and the related rarefaction can lead in turn to cavitation. The stress is unloaded by launching pressure waves as we observed in the time-resolved experiment discussed in the next paragraph. The competition between the local fast thermodynamic relaxation of the structure (cooling) and the local mechanical expansion can bring to the achievement of voids-like type II structures with very high negative refractive index contrast.

5.3 Time resolved study and plasma dynamics: observation of a pressure wave

In order to clarify the role of two-photon absorption and ionization in the ultrafast laser photo-inscription process of bulk Ge₁₅As₁₅S₇₀, we performed a time-resolved study of the relaxation for the carrier plasma generated by focusing Bessel laser beams. Both optical transmission and phase contrast imaging were performed; the first allows for detecting the plasma density generated by the laser pulse by its absorption signature, the second allows for detecting relative local refractive index variations via transient phase shifts. Experiments were performed for irradiation conditions in the vicinity of type I and type II domains. The excitation yield in type I range was too low to observe carrier densities, leading to believe that they may be below 10¹⁹ cm⁻³. The situation described below concerns therefore the single-shot induced type II regimes.

The result shown in Fig. 6 corresponds to the plasma generated by focused single-shot 4ps-long laser pulses with energy of about 1 µJ. The plasma relaxation detected by optical transmission as a variation of local transmissivity (and therefore an absorption signature) is shown in the Fig. 6(a), while the relative optical phase variation detected by phase contrast microscopy is shown in Fig. 6(c). The electron density N_e (Fig. 6(b)) normalized to the critical density value N_c can be estimated after Abel inversion of the results in Fig. 6(a). The Abel inversion delivers the central absorptivity value and, within a Drude formalism, the value of the electron density can be extracted with certain approximations on the electronic scattering time (1 fs). The variation of the average electron density (relative to the critical density at 800 nm incident wavelength) as function of the delay time, τ_d, between the pump and the probe beams is reported in Fig. 6(d). The over-threshold plasma density generated in corresponding type II permanent change domains can be estimated by means of this technique. We observe a long-living plasma, up to the ns scale, with values around 10% of the critical density (in the range of 10²² cm⁻³. This graph allows estimating the detecting threshold of this technique to about 10¹⁹ electrons/cm³ (about three orders of magnitude below the critical electron density N_c in bulk glass). A second aspect concerns the optical phase dynamics, relating to a local transient change of the refractive index. The results permit to link the transient index to a hydrodynamic behavior. The hydrodynamics initiated by laser heating is shown in the Fig. 6(c). A pressure wave is clearly visible in time moments corresponding to a delay time of sub-ns and ns. The presence of this pressure wave indicates a thermo-mechanical relaxation of an initially hot region and a hydrodynamic expansion due to laser heating. This reinforces the scenario based on rarefaction and the associated negative index change observed corresponding to type II modified regions (white traces observed through a phase contrast microscope). The high negative refractive index contrast (high rarefaction, almost voids) obtained in this case in single shot regime (see Fig. 6(e)) indicates a cavitation regime, which is reached after thermodynamic expansion in liquid phase. This suggests therefore that in this case temperatures largely higher than T_g are reached locally in the sample.

 

Fig. 6 (a) Time-resolved optical transmission microscopy imaging of the relaxation of the carrier plasma produced by a single-shot 1 µJ, 4ps Bessel laser pulse focused into Ge₁₅As₁₅S₇₀. (b) Time-resolved imaging of plasma electron density with spatio-temporal excitation profiles. (c) Time-resolved phase contrast microscopy imaging; a pressure wave is clearly visible around 6ns. The time frame is the same for the figures (a), (b) and (c). (d) Averaged plasma electron density dynamics as function of the delay time between pump and probe. (e) Type II change produced in single-shot regime by a 1 µJ, 4 ps Bessel laser pulse focused into Ge₁₅As₁₅S₇₀.

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The behavior of the irradiated sample at lower energies however is completely different. No plasma is detected and no pressure-waves are observed in correspondence of generated type I permanent positive refractive index changes (black traces observed through a phase contrast microscope, see Fig. 4(b)). This indicates that in this case the electron density is under the detecting threshold, and the local temperature of the glass matrix after carrier relaxation and vibrational excitation is not high enough (below Tg) to initiate a local hydrodynamic expansion, as observed for type II permanent changes.

6. Raman analysis of irradiated samples

Local modifications of the refractive index induced by focused laser pulses are generally accompanied by important local structural changes of the glass matrix. Normally these local changes present Raman signatures, which can be quite strong in some cases, as for example in fused silica [51]. In our experiment, Raman spectroscopy has been performed on non-irradiated and irradiated Ge₁₅As₁₅S₇₀ samples. The analysis of Raman spectra shows several laser-driven structural changes in the irradiated region.

Specifically, in Fig. 7 we underline the comparison between two Raman spectra detected for a non-irradiated (black line) and an irradiated (grey line) sample. The effect of the boson peak at low frequencies is minimized by calculating reduced Raman intensities as defined in [52].

 

Fig. 7 Raman shift of non-irradiated (red line) and irradiated (black line) Ge₁₅As₁₅S₇₀ samples.

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The Raman spectra of the S-rich Ge₁₅As₁₅S₇₀ (1:1) glass samples have a major band at about 345 cm⁻¹. This band has shoulders on the high wavenumbers side at approximately 367 and 420 cm⁻¹. Really weak bands are also apparent in the spectra of these samples at about 150, 218 and 237 cm⁻¹ and broad small band between 476 and 496 cm⁻¹.

Considering the contribution of Ge-S entities vibrational modes to Raman spectra, main vibration bands are expected to be present at about 341, 370, 399 and 437 cm⁻¹ in agreement with Lucovsky et al. and Sugai et al. considering Ge_xS_1-x glasses [53, 54]. The most intensive at 341 cm⁻¹ can be associated with the ν₁(A₁) symmetric stretching mode of [GeS_4/2] tetrahedra and 370 cm⁻¹ ν_1c(A_1c) usually called “companion peak” albeit an origin that remains controversial. This “companion band” is often related to [GeS₄] edge-sharing. The two other shoulders, usually related to the medium range order structure of GeS₂, have been attributed to the vibration of Ge-S bonds in tetrahedral units linked by corners. For As₂S₃ glass, there are two active modes a symmetric one at 345 cm⁻¹ and an antisymmetric mode at 309 cm⁻¹ of lower intensity compared to what can be permitted in IR spectroscopy. They are characteristic of As-S vibrations in [AsS_3/2] pyramidal sites [55, 56] leading to a really broad band. Thus in non-irradiated Ge₁₅As₁₅S₇₀ glass, the principal band around 344 cm⁻¹ is composed of overlapping bands associated with the symmetric stretching modes of [AsS_3/2] pyramids and [GeS_4/2] tetrahedral [57, 58]. The shoulders at 367, 399 and 430 cm⁻¹ can also be related to Ge-S vibrational modes. The broad band at 400-500 cm⁻¹ that is clearly observed in the spectra of S-excess glasses is mainly related to the formation of S-S bonds in chains-rings and Ge(As)-S-S-As(Ge) entities [53, 59].

The Raman spectra of all S-deficient Ge-As-S glasses are dominated by the appearance of bands between 210 and 250 cm⁻¹ associated with metal-metal bonds which grow in intensity with decreasing S content [60]. Lucovsky et al. [54] suggested that a feature at 250 cm⁻¹ in Ge_xS_1-x is associated with Ge-Ge bonds. In the samples studied here, there is no distinct 250 cm⁻¹ feature. In the 1:1 Ge:As samples, the intensity appears to increase equally for 220 cm⁻¹ and 240 cm⁻¹. The attribution of 218 cm⁻¹ is always less clear than 238 cm⁻¹ and is probably related also to As-As bonds. Bands at similar frequencies (238 cm⁻¹) in As₂S₃ have been assigned to the vibrations of As-As bonds [60]. Thus, the other very weak bands at 218 cm⁻¹ and 236 cm⁻¹ could presumably be due to the formation of metal-metal bonds. However, the band at 155, (linked with 234 and 474 cm⁻¹ bands) has been assigned to vibrations of S₈ rings in S-rich glass and can be associated to the observed vibrations modes.

In the irradiated sample, there is a strong effect on the main broad band initially peaking at 344 cm⁻¹: the band is shifted to lower wavenumbers around 341cm⁻¹, the band-width is widened and the ratio between ν₁(A₁)/ν_1c(A_1c) is reduced. It was reported that the ratio is decreasing in case of sulfur diminution in Ge_xS_1-x or increase of As contents [54, 57]. This ratio change can be interpreted as an increase in the number of edges-sharing tetrahedra. The enlargement of the main band indicates an increased disorder. In detail, the small bands associated to vibrations of S₈ rings and As-As bonds almost disappeared in the range of 125-250 cm⁻¹ and also the vibration at 496 cm⁻¹ increased. We can conclude that the irradiation seems to reduce the number of As-As bonds and S₈ rings and small chains are probably partially replaced by S-S bonds connecting AsS_3/2 and/or GeS_4/2 entities [59].

Raman measurements on re-annealed samples showed qualitatively the same behavior; the observed changes in the Raman spectrum after laser exposure where present but less intense than in the case of fresh samples, in agreement with the difference observed in the refractive index change.

It is not clear how the observed structural changes can be relied to the photo-induced densification. Further analyses are required in order to conclude. However we can propose that the structural changes observed by Raman spectroscopy indicate features of a local structural disorder, which could be the signature of local densification with formation of edge-sharing tetraedra of [GeS_4/2] in higher amount and presence of S-S dimers connecting [AsS_3/2] and/or [GeS_4/2] entities decreasing the proportion of As-As bonds and S₈ and long sulfur chains. Furthermore the observed structural changes are the confirmation of the fact that molecular bonds of the microscopic glass structure are modified by photo-ionization.

7. Conclusions

In conclusion, Ge-doping increases the metastability flexibility in S-based glasses, allowing for a larger processing window of type I positive index changes, via structural disorder via photocontraction. This is accentuated by the thermal treatment of the sample, a short annealing time corresponding to a reduced packaging, allowing for a more efficient response. Time-resolved observation of the excitation-relaxation cycles suggest low density generated plasmas in the case of type I changes, and higher but sub-critical excitation densities and onset of thermomechanical phenomena for type II modifications. Raman inspection indicates the presence of structural changes and the insight of a local desorder in correspondence of type I modified regions, which could be linked to the observed densification; however at least it confirms that the microscopic glass structure is weakened during photo-ionization. Structural changes are found stronger in short time annealed samples (microscopic structure quenched in a high enthalpy state) than in long time re-annealed samples (microscopic structure quenched in a low enthalpy state).