1. Introduction

Direct laser writing is now a well known technique to induce very localized refractive index variation (Δn) in various materials [1, 2] including polymers, crystals and glasses, and it has been applied successfully to produce passive and active photonic devices [3].

However, the result of the light-matter interaction in term of Δn is still not predictable and thus the required photoinscription parameters are determined empirically from systematic studies. As an example, small changes in the glass composition can lead to positive Δn (and then guiding) or to negative Δn [4]. Then it is needed to understand the structural modifications of the glass that cause a positive or negative Δn.

Several studies have been carried out in this sense on various glasses. In particular, a higher concentration of 3-member rings has been observed in silicate glasses after femtosecond pulse irradiation with corresponding decrease of 4-member rings population. The resulting glass densification leads to a positive Δn [5–7]. In the case of zinc phosphate glass, the interaction causes the depolymerisation of the glass network [8]. For a review, the reader can refer to [9, 10].

Our study is focused on the glass network modification of ternary chalcogenide glass (80 GeS₂ − 20 Ga₂S₃) by femtosecond laser pulses in order to find the correlation with induced refractive index changes. Since chalcogenide glass are highly nonlinear, the laser beam experiences self-focusing and a light filament can easily be formed [11]. This particular condition of light propagation leads to Δn having a spatial extension along the beam propagation direction much longer than the Rayleigh length [12]. The resulting structure can have only positive Δn regions [13] or more complex features with negative and positive parts [12], depending on the repetition rate of the laser.

In our study, a 2D μ − Raman mapping of the region modified by the laser pulses is realized and the reorganization of chemical bonds is evidenced. The contribution to the Raman signal from each structural unit that composes the glass network, is determined in all the points of the mapping. Quantitative analysis of every contribution over more than 11,000 spectra is allowed by the constant detection conditions during the 2D scanning of the sample.

2. Experiments

The experiment consists in a static irradiation of 80 GeS₂ − 20 Ga₂S₃ glass and a 2D Raman mapping of the resulting Δn.

The light source used in the experiment is a high repetition rate (76 MHz) femtosecond Ti:Sa laser (Mira Coherent Inc.) delivering pulse of duration around ∼200 fs, 2.6 nJ energy and a central wavelength of 800 nm. The beam is focused in the bulk of the sample by a X5 (0.1 NA) microscope objective. The glass irradiation is performed in static conditions (without sample translation) and the exposure duration is set to 1 second. Further information on the writing procedure are given in [12] and the glass preparation is detailed in [14].

After the irradiation the sample is cleaved to bring the irradiated area near the surface. Raman spectra are recorded using a Jobin-Yvon Raman micro-spectrometer with a X100 objective. A He-Ne laser (λ = 632 nm) was used as excitation source. The laser power was limited to 1 mW to avoid the laser damage of the sample surface. The sample is translated with a resolution of 1 μm in the direction perpendicular to the beam propagation direction and 2 μm in the beam direction, to obtain a complete Δn mapping dimensions 326 × 68 μm². A special attention was paid to the sample alignement to ensure an invariant illumination and detection geometry.

3. Results and discussion

3.1. Fitting procedure

The main idea of the fitting is to identify contributions of different structural groups to the Raman spectra of the non-irradiated glass and to observe their evolutions in the irradiated zone along with the 2D scan. Direct qualitative and quantitative comparison between the spectra appears to be possible because the geometric factor, solid angle seen by the detector, detector efficiency are the same. The invariant detection conditions have been confirmed by the reproducibility between the spectra of non-irradiated matrix obtained for different positions.

In this paper we do not present a complete analysis of Ge-Ga-S glass structure that will be published elsewhere [15]. We are interested in the 2D evolution of the contribution from different structural groups. The groups to be considered are determined starting from a comparison of the Raman spectra of 80 GeS₂ − 20 Ga₂S₃ and 10 GeS − 90 GeS₂ glasses, as given in the Fig. 1.

 

Fig. 1 Raman spectra of the 80 GeS₂ − 20 Ga₂S₃ and 10 GeS − 90 GeS₂ glasses.

Download Full Size | PDF

The Ge-rich binary glass exhibits usual spectroscopic features for the g-Ge_xS_100−x glassy system at x > 33.3 (see for example [16–18] and references therein). The most intense line at 344 cm⁻¹ correspond to A₁ symmetric in-phase breathing of corner-sharing CS-GeS_4/2 tetrahedra [19–21], accompanied by an A_1c companion line at 372 cm⁻¹ [22] related to symmetric breathing of edge-sharing ES-GeS_4/2 units [20,21]. The broad asymmetric feature at 259 cm⁻¹ originates from Ge-Ge vibrations in S₃Ge-GeS₃ ethane like units [16, 18, 23]. Recent ab initio calculations [23, 24] have shown that the broad poorly resolved feature around 400 cm⁻¹ contains contributions from both CS and ES tetrahedra, but the peaks at 436 cm⁻¹ is due entirely to the highest mode in the ES tetrahedra [24].

Surprisingly, the stoichiometric 80 GeS₂ − 20 Ga₂S₃ glass exhibits rather similar Raman spectrum to the Ge-rich binary composition. As difference we note (i) a blue shift of the low frequency feature from 259 to 268 cm⁻¹, (ii) an asymmetric broadening of the A₁ line at low frequencies, and (iii) some decrease of the intensity of the vibration modes corresponding to ES-GeS_4/2 units, i.e., at 372 cm⁻¹ (A_1c mode) and 436 cm⁻¹. Similar changes were reported earlier for related Ga-Ge-S glasses compared to the Ge-S parents [25–28].

Since Ge and Ga have nearly the same atomic masses, the band at 268 cm⁻¹ indicates that 80 GeS₂ − 20 Ga₂S₃ glass should contain S₃Ga-GaS₃ and/or S₃Ge-GaS₃ ethane like units. However, pure Ge ethane like contribution seems to be unlikely in 80 GeS₂ − 20 Ga₂S₃ while the Ge-Ge vibrational mode appears only in Ge-rich compositions of g-Ge_xS_100−x glass (x > 33.3).

Taking into account the four-fold coordination of Ga [27] and the Ga₂S₃ stoichiometry, sulfur should exist in two- and three-fold coordination environments, i.e., as [GaS_1/3S_3/p]₃ tetrahedral triclusters where p = 2,3. Such tricluster contribution to the Raman spectra was found earlier for CsCl-Ga₂S₃ glass [29].

Consequently, the calculations performed in this study target four structural units: CS-GeS_4/2, ES-GeS_4/2, S₃Ga-GaS₃ ethane like units and [GaS_1/3S_3/p]₃ (p = 2,3) triclusters.

Theoretical calculations are performed using GAUSSIAN 03 [30] associated with its graphical user interface GaussView 03. In order to find a compromise between the cost of the calculations and the accuracy of the results, structural optimisations and harmonic vibrational frequency calculations are performed for size-limited clusters composed of Ga(SH)₄ and Ge(SH)₄ tetrahedral subunits. Calculations on Ga(SH)₄ clusters are described in details in Ref. [29]. In this study, density functional theory (DFT) harmonic frequency calculations for the Raman active vibrations of S₃Ga-GaS₃ ethane like group and tricluster formed of Ga/S are re-examined. DFT calculations are performed with the Becke [31] three parameters hybrid exchange functional and the Lee-Yang-Parr correlation functional (B3LYP) [32]. All the structures are optimised using the GDIIS convergence criteria ensuring adequate convergence and reliability of computed wavenumbers. Harmonic frequency calculations are performed with the method and basis set used for the optimisation. Using the 6-311G+(2d,p) basis set, the best quality of the wavenumber predictions is obtained with an optimum scaling factor close to 1 and a root-mean square standard deviation around 5 cm⁻¹ [29]. In order to obtain similar accuracies for the GeS₄ tetrahedron edge-sharing (ES) and corner-sharing (CS) dimers harmonic frequencies, an extension to the 6-311G++(3df,2p) basis set is required.

In the fitting procedure, every vibrational mode determined by the DFT calculations is represented by a Gaussian function. The non-irradiated glass (matrix) spectra has been fitted by fixing the frequency and the relative intensity of each vibration mode inside a group, according to the result of DFT calculation. The varying parameters are the Gaussian full width at half maximum and the relative amplitude of the contributions of the four groups. In Fig. 2 the Raman spectrum of the matrix and the fitting results are presented together with the residues.

 

Fig. 2 Raman spectra of the 80 GeS₂ − 20 Ga₂S₃ glass and the result of the fit. The contributions of each group are shown by the colored line. Residues are also shown on the bottom. An artist view of each structural group highlights the well-resolved contribution of the group.

Download Full Size | PDF

It can be seen in this figure that every group has a characteristic well resolved vibration mode from which the behaviour of the contribution of the groups can unambiguously be determined. The low frequency band centered at 275 cm⁻¹ is due to S₃Ga-GaS₃ ethane like group (ETH-Ga₂S_6/2). The edge sharing GeS₄ tetrahedron (ES-GeS_4/2) has a signature at 376 cm⁻¹ while the more intense peak at 341 cm⁻¹ is a contribution from the corner sharing tetrahedron (CS-GeS_4/2). The tricluster of tetrahedra possesses a marked contribution between the ETH and the CS bands and a larger one between 350 and 450 cm⁻¹.

Consequently, the contribution of each group in the Raman spectra is clearly identified in the spectra of the non-irradiated matrix. Then a complete mapping of the entire region is obtained by fitting the spectra in each point with only four relative amplitude of each contribution as fitting parameter. We note that for all the spectra, the R² coefficient changes between 0.9980 and 0.9996.

3.2. Raman mapping results

In Fig. 3, the mapping of the four contributions are shown. All the amplitudes are normalized to the mean value of the matrix. The influence of the femtosecond pulse is clearly seen on all contributions. On this figure, the laser beam propagates from the left to the right.

 

Fig. 3 Mapping of the relative contribution of the four groups into the Raman spectra.

Download Full Size | PDF

First, the fs-laser irradiation increases the tricluster population and decreases the fraction of S₃Ga-GaS₃ ethane-like units, (see Figs. 3d and 3c). We should note that this trend is observed for both positive and negative Δn regions (see Fig. 4b); however the magnitude of changes are distinctly different. Regions with the highest |Δn| changes (called hereafter the head) are characterised by a two-fold increase of triclusters, while the tricluster fraction in the positive Δn domains (called hereafter the tail) does not exceed +30 − 40% compared to the non-irradiated matrix (see Fig. 4b). The tricluster formation is not just a conversion of S₃Ga-GaS₃ ethane-like units into triclusters. The related changes in the S₃Ga-GaS₃ population are significantly smaller (−15%) compared to triclusters (+100%). However, the decrease of the CS- and ES-GeS₄ population is consistent with the formation of mixed triclusters [TS_1/3S_3/p]₃ where p = 2 or 3, and T = Ga and/or Ge, Figs. 3a and 3b.

 

Fig. 4 (a) Photography of Δn. (b) Δn measurement according to quantitative phase imaging technique and Abel inversion [35] (see text). (c) Integrated intensity of the Raman spectra.

Download Full Size | PDF

3.3. Correlation with the refractive index variation

The intensity of the Raman scattered light is proportional to the number of scattering units, N, in the sample volume being probed by the Raman instrument [33, 34]. In our conditions of identical instrument efficiency and geometric factor, the enhanced or reduced Raman integrated intensity reflects the increased average number density in sample regions with Δn > 0 or the diminished average number density for regions with Δn < 0.

In the Fig. 4 we compare the mapping of Δn and the integrated Raman intensity, and also a photography of Δn (Fig. 4a). The Δn mapping (Fig. 4b) is obtained by quantitative phase imaging followed by an Abel inversion [35]. This procedure can be used if Δn possess an axial symmetry and it results in a Δn(r,y) where r is the distance to symmetry axis. Therefore the image 4b has an other meaning than the Fig. 4c where the Raman mapping is represented in the (x,y) plane. This mapping represents the total intensity of the Raman signal in each point.

It is clear from these two figures that an increase of the refractive index is associated to an increase of the Raman signal while a negative Δn is related to a decrease of the Raman intensity. Positive refractive index changes are closely related to the tricluster population simply because the efficient packing of triclusters gives higher density and number density, thus increasing the refractive index. Crystalline references clearly show the effect of triclusters on network densification. The density of α − and β − Ga₂S₃ (2/3 of triclusters: 3.67–3.69 g · cm⁻³, 4.70 × 10⁻² atoms Å⁻³) is significantly higher (+25%) compared to low temperature GeS₂ (CS-GeS_4/2: 2.99 g·cm⁻³, 3.94 × 10⁻² atoms Å⁻³) or high temperature GeS₂ (CS-GeS_4/2 and ES-GeS_4/2: 2.89–2.94 g·cm⁻³, 3.87 × 10⁻² atoms Å⁻³).

The question arises why the regions with negative Δn and having higher triclusters population compared to the non-irradiated glass, exhibit lower number density. In silica glass, such difference in the Δn sign between the head and the tail has already been observed [36, 37]. The negative Δn sign is associated with the formation of nanoporous region [37] located where the density of electron generated inside the laser filament, is the highest [38]. In 80 GeS₂ − 20 Ga₂S₃, free carrier accumulation effect due to the high repetition rate of the laser is dominating over the heat accumulation [13, 39]. Correspondingly, we can assume that the negative Δn region is also due to the formation of nanopores arising from Coulombian micro-explosions.

4. Conclusion

A 2D μ-Raman analysis of refractive index variation of 80 GeS₂ − 20 Ga₂S₃ glass due to femtosecond laser filament has been carried out. This study evidences the reordering of chemical bonds from S₃Ga-GaS₃ ethane like group into triclusters of [GaS_1/3S_3/p]₃. We also note the decrease of the CS- and ES-GeS_4/2 tetrahedra population leading to the formation of mixed triclusters [TS_1/3S_3/p]₃, where T = Ga and/or Ge.

This structural modification is uniform over the irradiated zone whereas Δn reverses its sign between the head and the tail of the structure. Positive Δn in the tail is shown to be due to the higher efficiency of the tricluster tetrahedral packing leading a higher density and number density. Where the free carrier density generated during laser filamentation is high enough to induce Coulombian micro-explosion, the formation of nanovoids leads to negative Δn.

The obtained Raman results show that gallium is a key element for photo-inscription in Ga-containing chalcogenide glasses caused by its labile coordination simplifying the formation of triclusters and ethane-like units as well as a favourable conversion of a loose network organisation into a dense spatial arrangement.