1. Introduction

Alkali-free (AF) display glasses were commercially introduced to avoid alkali poisoning of the semiconductor display layer which is attached to it. Alkali metals, though being an excellent network modifier to tailor glass properties, are highly mobile and can diffuse into the underlying silicon layer especially when the device operating temperature rises. The selection of AF glasses based on borosilicates is due to their excellent properties of high thermal shock resistance, chemical inertness, high optical transparency, light weight and a thermal expansion coefficient matching that of silicon [1,2]. It is not surprising that these glasses formed a major platform in integrated photonics with the advent of the femtosecond laser inscription technique enabling low loss waveguides with high refractive index contrast [3–5]. Understanding the physical and chemical dynamics of waveguide formation is essential for the optimization of low loss and high refractive index contrast waveguides. Quite recently evidence of elemental migration in femtosecond laser written waveguides was identified and was successfully used to tune waveguide performance [6,7]. In this paper we demonstrate and identify the elemental and structural dynamics of AF borosilicate glass waveguide formation, and propose a solution to produce high refractive index change waveguides at higher feed rates (>500 mm/min). We conclude by proposing an empirical formula to produce laser written waveguides with positive refractive index change in glasses that are otherwise difficult to form.

Commercial AF borosilicate glasses have a SiO₂ content of about 60 wt%. Hence they have predominant silicate features in any materials characterizations techniques based on X-rays, electron beam or light. Addition of the glass former boron oxide (generally less than 16 wt % to avoid boron anomaly) to silica will provide most of the physical, thermal and chemical properties of a borosilicate glass viz low coefficient of thermal expansion, high thermal conductivity, high mechanical strength and chemical durability. Aluminum, being an intermediate, performs the role of network modifier and/or glass former. As a modifier it avoids spinodal separation into silica rich phase and boron rich phase by promoting the polymerization through B-O-Al-O-Si linkages [8]. In this work we have found that upon elemental migration due to waveguide formation, incoming aluminum prefers to assume the role of a glass former. An alkaline earth fraction comprises the final component of the glass, acting as a network modifier.

2. Waveguide fabrication

The composition of the three commercial glasses that were used in this study were determined by X-ray fluorescence analysis (XRF) and are provided in Table 1. Corning Eagle 2000 (E2K) glass which was superseded by an arsenic free (arsenic oxide is an excellent fining agent in glass melting but its usage makes the product fall outside RoHS regulations) and environmental friendly version Eagle XG (EXG) that has a similar composition to the latter; whereas AF32 glass from Schott has additional barium oxide incorporated to the matrix at the expense of the calcium oxide content.

Table 1. Nominal composition of the commercial borosilicate glasses used in this work (values in wt %).

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Waveguides were written using a 5.1 MHz high-repetition rate Ti:Sapphire chirped-pulse femtosecond oscillator (Femtosource XL500, Femtolasers GmbH) emitting 50 fs pulses and operating at a wavelength of 800 nm. Circularly polarized laser pulses were focused inside the glass using an Olympus UPLANSAPO 100× oil immersion microscope objective (NA = 1.4). Oil reduces the refractive index mismatch and thus mitigates spherical aberration. Waveguides were written transversely (sample translated perpendicular to the laser focusing direction) at a depth of 170 µm using a set of 3-axis computer-controlled high precision Aerotech air-bearing linear stages. The structures were inscribed at feed rates of 10, 20, 50, 100, 200, 500, 1000 and 2000 mm/min. At each feed rate the pulse energy was adjusted to result in a 30 µm wide structure. This means that, for each feed rate, the temperature at a distance of 15 µm away from the focal spot was insufficient to induce any refractive index modification. We define the quenching time as the time it takes for the glass to cool from the peak temperature at the focal spot to a temperature that does not result in any further refractive index modification. In our case, this corresponds to the time it takes for the sample to move by 15 µm. Hence, the resulting quenching times are 90, 45, 18, 9, 4.5, 1.8, 0.9 and 0.45 ms at a feed rate of 10, 20, 50, 100, 200, 500, 1000 and 2000 mm/min, respectively. It should be noted, that even at the largest feed rate of 2000 mm/min, the quenching time is more than one order of magnitude larger than for static exposure, which is typically around 10 µs for silicates [9]. The differential interference contrast microscope images of the E2K and AF32 waveguides are provided in Fig. 1. EXG was excluded to avoid redundancy as the waveguides look similar to E2K.

 

Fig. 1. DIC images of the waveguide cross sections with 30 µm diameter in E2K and AF32 glasses. The laser was incident from the top.

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All waveguide structures were highly circular indicating good spherical aberration compensation. When the feed rate exceeded 100 mm/min the guiding region was highly circular which is generally a highly desirable feature in photonic device fabrication to facilitate efficient coupling to optical fibers. The waveguide morphology can be described as a core-shell structure. At feed rates greater than 100 mm/min, the core comprises of a bright positive index change region with a concentric dark negative index change region. For feed rates slower than 100 mm/min the appearance of the core is inverted with a central dark zone and a concentric bright ring. The shell is basically the heat affected zone which appears as a halo around the central core. The difference in morphology between AF32 and E2K is evident only at low feed rates of 10 and 20 mm/min.

3. Waveguide characterization and discussions

Refractive index measurements of these waveguides were carried out using a SID4HR camera from Phasics based on quadriwave lateral shearing interferometry [10]. The camera spatially resolves optical path length differences resulting from the laser induced refractive index modification. After waveguide inscription 1 mm thick slices were cut from the samples and then ground to a thickness of ∼400 µm followed by polishing to optical quality using colloidal silica. The samples then were turned over and the procedure was repeated to reach a final thickness of < 100 µm. The final thickness of the samples were carefully determined with ∼ 1 µm accuracy by confocally measuring the distance between the optical reflection from the front and back surface, respectively. The thickness was used to convert optical path length difference to refractive index change. All measurements were carried out using a quasi-monochromatic light source at 600 nm with 25 nm FWHM bandwidth under 64× magnification. This resulted in a spatial resolution of ∼0.5 µm. The refractive index change maps for E2K waveguides written at 10, 50, 100 and 2000 mm/min feed rates are provided in Figs. 2(a)–2(d). The morphology of the refractive index change matches the DIC images in Fig. 1. The consolidated results of the peak-to-valley index contrast and peak positive index contrast obtained for all three samples are provided in Figs. 2(e)–2(f). Positive index contrast is the increase in refractive index w.r.t the bulk glass, whereas peak-to-valley is the magnitude between the positive and negative index change within the waveguide structure. It is interesting to observe that there is a local minimum for all samples at 100 mm/min before the index contrast recovers at higher feed rates. It is also notable that though there are greater discrepancies between the peak positive index contrast values (Fig. 2(f)) between different glasses at extreme feed rates, they are less pronounced when the peak-to-valley index contrast is calculated. This indicates independent behavior of atomic species migrations rather than a one to one ion/elemental exchange.

 

Fig. 2. Refractive index map of E2K waveguides written at (a) 10 (b) 50 (c) 100 and (d) 2000 mm/min feed rates. (e) Peak-to-valley index contrast and (f) peak positive index contrast.

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To study the refractive index change dynamics and especially its collapse and recovery centered around 100 mm/min, electron probe micro analysis (EPMA) based on wavelength dispersive spectroscopy (WDS) was used [11]. SEM imaging and X-ray intensity mapping of constituent elements were carried out on a JEOL JXA-8500F field-emission EPMA. The results are shown in Fig. 3 and Fig. 4. Figures 3(a)–3(d) shows the backscattered images of waveguides inscribed in E2K glass at 10, 50, 100 and 2000 mm/min feed rates, respectively. The observed morphology under backscattered SEM agrees well with the observations under an optical microscope (Fig. 1). Figures 4(a)–4(c) and Figs. 4(e)–4(g) show the WDS X-ray maps in E2K for Si, Ca and Al at 10 and 2000 mm/min feed rate to highlight the compositional changes for the two distinctively different waveguide morphologies. These results are representative of trends found across all feedrates; similar results were observed for the other feedrates but with different magnitudes of compositional change. Across all feed rates, waveguide formation was due to the migration of elements, an increase in Si formed lower index regions while the positive index zones were formed due to an increase in Ca and Al concentrations. The EXG and AF32 results were very similar to E2K and hence are not shown. Due to the additional presence of ∼3 wt% magnesium oxide in AF32, Mg maps for this glass are also presented in Figs. 4(d) and 4(h), showing migration of Mg towards the positive index zone. The stimulus for migration of elements is considered to be purely thermal (thermomigration) [12,13] and the direction generally depends on the shape of the plasma [11,13].

 

Fig. 3. (a-d) Backscattered electron images of E2K glass waveguides written at 10, 50, 100 and 2000 mm/min feed rates.

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Fig. 4. Elemental migration map of E2K waveguides written at 10 mm/min (a-c) and 2000 mm/min (e-g) feed rate, respectively. The Mg maps (d-h) correspond to modifications in AF32 inscribed at identical feed rates.

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Figure 5 shows the percentage compositional change of Si, Ca and Al in E2K as function of feed rate. The increase in signal for Ca and Al corresponds to the positive index zones and for Si to the negative index zones. EXG and AF32 (not shown) also exhibited very similar results. The graph clearly shows that at low feed rates the index change is a result of strong migration of Ca, Al and Si. In contrast, at high feed rates the index change is dominated by the migration of Ca. Moreover, in particular Ca in Fig. 5 follows the same trend as the refractive index contrast in Figs. 2(e)–2(f) with a local minima observed at 100 mm/min feed rate. Miura's group recently carried out an analytical experiment based on non-equilibrium molecular dynamics (NEMD) simulation of a CaO-SiO₂ binary glass containing different molar volumes of SiO₂ [14]. The results were compared with a thermodynamical Kempers model and they came to the conclusion that there is a monotonic increase of the Soret coefficient of SiO₂ upon reducing its molar volume in the melt until it turns negative for fractions less than 20 wt% [14]. According to this, one should expect SiO₂ migrating towards hot zones at high molar volume (silicon rich melts) and cold zones for molar volumes less than 20%. This prediction is not consistent with our results, as we see the migration of silicon towards the center and away from it just by changing the feed rate in the same sample. Hence a plausible explanation might be the well-known mixed-modifier effect which attributes a nonlinear behavior to the transport (migration) related properties [15–17]. This might also explain the local minima seen in Figs. 2(e)–2(f). The dynamic structural model (energy landscape approach) states that the relaxation time required to overcome the site mismatch while modifiers are hopping between ionic sites is variable [15]. In other words, sites favorable for one type of cation in a glassy network are unfavorable for another type of cation. In such a case there should be a strong mismatch in cation modifier transport between calcium and aluminum which polymerize the network upon migration [17]. The specific role of modifiers depends on the type of network formers present in the glass and the relative free energies of modifier interactions with each type of the different network former sites. This variation of free energy with modifier speciation is responsible for the so-called mixed network former effect, i.e., the nonlinear scaling of property values in glasses having a fixed modifier concentration but a varying ratio of network formers [16].

 

Fig. 5. Magnitude of relative increase/reduction in EPMA signal counts of Ca, Al and Si in E2K. The increase in signal for Ca and Al corresponds to the positive index zones and for Si to the negative index zones.

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The initial evidence regarding the collapse and recovery of refractive index with increasing feed rate is directly observed from Fig. 5. In the zone of increased index, the migration of silicon and aluminum monotonically decreases with increasing feed rates from 11.6% to 1.7% and 6.0% to 1.6%, respectively. In contrast, calcium follows a similar trend from 10.0% to 2.7%, but surprisingly recovers when the feed rates exceed 200 mm/min. The enrichment of silicon in the negative index zone is almost linear for feedrates between 10-200 mm/min and then remains constant. Whereas in the positive index zone the reduction trend is similar to that of Ca and Al. An overall behavior for Si is difficult to predict at this stage as it is a highly polymerizable glass forming element and also has the capability to form 3 & 4-fold siloxane units, 2 & 3 non-bridging oxygen atoms and fully polymerized silicon. Relative signal variation for a particular element across positive and negative zones of the same structure need not necessarily be the same due to structural asymmetry, e.g. in Fig. 4(a) it has a large area of negative index region compared to positive, and non-linear dependence of density to elemental concentration. Thus the source of higher refractive index at faster feed rates stems from the migration of the relatively heavy alkaline earth metal calcium. To understand and explain this unique behavior, Raman spectroscopy was used to help understand the multicomponent glass network structure post migration/waveguide formation with respect to the pristine bulk.

Raman spectroscopy was carried out on a Renishaw inVia Raman Microscope with 514 nm laser excitation using a 100× objective operated in confocal mode to achieve a spatial resolution of ∼0.5 µm. Figure 6 depicts the Raman spectrum of unmodified E2K glass. To understand such a complex spectrum we divided it into three regions, 300-700 cm⁻¹, 700-1250 cm⁻¹ and 1250-1550 cm⁻¹. The strong peak at 478 cm⁻¹ and shoulder at 590 cm⁻¹ correspond to the well-known defect bands D1 and D2 of the siloxane rings [18]. Presence of alkaline earth metal can produce a cation band vibration near 350 cm⁻¹, but this is not manifested in the E2K spectrum as the alkaline earth metal concentration is well below ∼20 wt% [19]. The broad peak present at 353 cm⁻¹ is attributed to the Si-O-Si bond rocking and bending vibrations in SiO₄ tetrahedra [20]. The 674 cm⁻¹ peak correspond to the vibrations from the ring structured metaborate groups [21,22]. The second region between 700-1250 cm⁻¹ is quite important in our case because it is very sensitive to the addition of aluminum which acts as a perturbing source on those bands [23]. The spectral band at 790 cm⁻¹ is attributed to two different sources in the literature, one is that it is a manifestation of Al-O stretching [24] and the second hypothesis is that the band is predominantly Si-O in nature with aluminum acting as a perturbation [23]. Following this band there are three overlapping vibrational peaks at 932, 1042 and 1155cm⁻¹ that are commonly be attributed to the well-known Q² (2 non-bridging oxygen atoms per silicon), Q³ (3 non bridging oxygen atoms per silicon) and Q⁴ (fully polymerized SiO₄) Si-O– stretching vibrations. However, due to the presence of aluminum these are revised/analogous peaks corresponding to symmetric stretching vibrations of silicate tetrahedral with four, three and two oxygens bound to aluminum respectively [25,26]. The bands between 1250 and 1550 cm^–1 can be assigned to borate groups [20].

 

Fig. 6. Raman spectrum of unmodified E2K glass

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The 2D mapping of waveguides written in E2K reveal structural changes due to the laser modification. The waveguides written with 50, 200 and 2000 mm/min feed rates were chosen. The Raman maps are 40 µm x 40 µm in size. Only the images of peak shifts and variations in bandwidth having a definite characteristic resemblance to the DIC image are shown. In Fig. 7, the bandwidth of the 353 cm⁻¹ peak shows a well-defined change for all feed rates. The bandwidth increases for the positive index change zone irrespective of feed rate. The variation of bandwidth as a function of feed rate follows the trend of calcium migration as seen in Fig. 5 and thus signifying the Ca influence on the refractive index modification. The 353 cm⁻¹ peak was observed shifting to a lower value by 3.5 - 4 cm⁻¹ across the entire 30 µm structure independent of the feed rates (data not shown). A decrease in frequency of the SiO₄ tetrahedral bending and rocking vibrational peak generally indicates either a less strained glass matrix or an increase in long range order (onset of crystallization).

 

Fig. 7. 2D Raman mapping of the E2K glass waveguides.

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The four membered siloxane ring vibration at 478 cm⁻¹ shows a monotonic increase in vibrational frequency across the entire waveguide cross section, thus indicating Si-O bond shortening. The magnitude of frequency shift with respect to the bulk glass is 2-3 times larger in the positive refractive index region compared to the negative index region, it suggests a strong influence of calcium atom migration as observed using EPMA. The bandwidth of the 478 cm⁻¹ peak (not shown) is featureless but shows an overall strong monotonic increase in its magnitude with increasing feed rate. This is suspected to be due to an increase in short range order. While the 478 cm⁻¹ does not show any signs of long range ordering, it could be inferred that the shift to lower wavenumber of the 353 cm⁻¹ peak is an onset of crystallization. The onset of long-range ordering affects the low frequencies first before it starts perturbing higher wavenumber peaks as the crystals grow. Crystallization is not surprising given the absence of a highly mobile alkali network modifier in the glass compositions that helps to avoid crystallization. However, the increase in bandwidth for the 353 cm⁻¹ peak suggests a perfect dispersion of such nuclei, making the network even more random. Additionally it could be deduced that the migrated aluminum fails to depolymerize the extensive silicon network and hence it may preferably assume the role of a glass former rather than a modifier.

The three-membered siloxane ring vibration (D2) at 590 cm⁻¹ follows a peak shift congruent to the migration of calcium rather than of silicon or aluminum. This is expected, as it has been reported earlier that D2 is sensitive to density variations and the shift to higher wavenumbers correspond to densification. The 590 cm⁻¹ peak shift to higher wavenumbers in the high index region exactly follow the trend of refractive index vs feed rate with a local minima for speeds around 200 mm/min. Counterintuitively, the low index regions do also show a shift to higher wavenumbers with even larger magnitude. This is due to the formation of relatively large numbers of three membered siloxane rings compared to four membered rings resulting from an increase in silicon concentration and a decrease of calcium and aluminum. This suggests that the frequency of the D2 band is more sensitive to density changes caused by a concentration change in three-membered siloxane rings than density changes caused by the migration of Ca. [18,27]. Its bandwidth variation around the waveguide structure is negligible or almost zero for all feed rates.

Regarding the 790 cm⁻¹ vibration, we believe that its origin is predominantly Si-O perturbed by aluminum, and as reported by McMillan et al., [24] increasing the aluminum content decreases its frequency. The variation of the positive index change region follows the aluminum migration where it shifts by -3.1 cm⁻¹ (higher Al content) and -2.5 cm⁻¹ (low Al content) relative to the bulk as the feed rate is increased.

The 932 cm⁻¹ peak is considered to be the modified Q2 due to the presence of aluminum. Of the Q2-Q4 peaks, Q3 never showed any sign of variation in its peak shift, bandwidth or peak intensity (Figs. 8(b), 8(e), and 8(h)). Therefore, this confirms the role of migrated aluminum as a glass former rather than a modifier, because the 3⁺ charge of aluminum should produce strong modification to the Q3 upon migration. Migration of calcium is evident as it is the strongest perturbation to the Q2 peak due to its 2⁺ charge. The vibration is observed shifting to higher frequency where the calcium content increases. A bandwidth increase suggests the increase in short range order due to depolymerization and finally the intensity of the peak is seen increasing in the calcium rich zones irrespective of feed rates (Fig. 8(a), 8(d), and 8(g)). The final proof of aluminum assuming the role of glass former comes from the increase in the intensity of Q4, which is a direct result of the extended polymerization of SiO₄ units in an aluminum rich zone (Fig. 8(c), 8(f), and 8(i)). The role of incoming aluminum as a modifier not only would have hindered this, it would have depolymerized the existing Q4 in the glass matrix. Hence the mixed modifier effect neither explains the nonlinear behavior of refractive index as a function of feed rates nor does it account for the observed calcium migration.

 

Fig. 8. Vertical line scans of relative intensities of Q2, Q3, Q4 peaks across the waveguide. Red arrows show the laser writing direction and DIC images in the insets with broken arrow shows the line scan direction.

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A reasonable explanation based on the discrepancy of coefficient of diffusivity between Ca, Al and Si can be put forward. Though calcium has a comparatively large ionic radius it has a lower cationic charge (2⁺) in comparison to Al (3⁺) and Si (4⁺). Since doubling the charge results in an effectively higher drop in diffusivity than doubling the ionic radius, the discrepancy in diffusivity could be used to explain the calcium migration. It is well known that solidification of glass happens with a higher glass transition temperature when the quenching rate is higher. That is, the deviation from the Arrhenius to non-Arrhenius behavior on a log η vs log 1/T plot (η being the viscosity) [28] or simply a deviation from the supercooled liquid which is in equilibrium to a non-equilibrium solid state (glass) happens quicker at a faster quench rate [29]. So one could infer that solidification happens at a higher viscosity for faster feed rate (fast quench) compared to a slow feed rate (slow quench). At 1000 °C, there is a strong discrepancy in the diffusivity of calcium and silicon for any silicate composition with more than 50 wt% SiO₂ [30]. Calcium has a higher diffusivity by several orders of magnitude and this discrepancy grows as the silica content is increased at the same temperature. Despite the viscosity increasing due to higher silica content, the mobility of calcium remains several orders of magnitude higher. In summary, we believe that the selective migration of calcium at faster feed rates stems from the fact that solidification happens at high viscosity where calcium is several orders more mobile than silicon or aluminum. For very slow feed rates the difference in diffusivity between silicon, aluminum and calcium is much lower since the melt stays at low viscosity for a longer period of time before solidification occurs.

The arguments of fast and slow quenching and solidification at high and low viscosities due to different feed rates are validated by two observations. Firstly, waveguides written with 10 and 20 mm/min show signs of crystallization in E2K. Figures 9(a)–9(b) shows high resolution images of Fig. 3(a). Crystallization was observed only for those two feed rates. This supports our proposition that slower feed rates translate slow enough for the atoms to find a long range order. The crystallization was identified only in the waveguides of E2K and not in EXG indicating that increasing the MgO (223% relative) and Al₂O₃ (8% relative) in the latter might be to avoid crystallization either during glass melting or subsequent processing at elevated temperatures. Secondly, even though the observation of a heat diffused zone is evident for all feed rates in the DIC images (Fig. 1), this was not the case for BSE images (Figs. 3(a)–3(d)). The heat diffused zone was completely absent in the BSE images for feed rates slower than 100 mm/min, whereas it was seen gaining contrast between 100-2000 mm/min. This trend was directly observed in both the refractive index maps of Fig. 2 and the width of the 478 cm⁻¹ peak in the Raman spectra. The heat diffused zone gave a positive refractive index value of 1.17 × 10⁻³ for 10 mm/min but for 100 mm/min it rose to 1.75 × 10⁻³ and eventually reached a value of 1.90 × 10⁻³ for 2000 mm/min. Similarly, in the Raman spectra the 478 cm⁻¹ peak widened in bandwidth by 5.8 cm⁻¹ for 50 mm/min, 7.5 cm⁻¹ for 200 mm/min and 8.5 cm⁻¹ for 2000 mm/min. Thus indicating an increase in short range order.

 

Fig. 9. Crystallite formation in E2K waveguide inscribed with (a) 10 mm/min feed rate with (b) low and (c) high resolution BSE images.

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A backscattered electron image is based on Z-contrast (atomic number) and the basic process behind image formation is the measurement of primarily back scattered incident-beam-electrons at any given point in the scanned area. This scattering is effectively proportional to the Coulombic field of the constituent atoms in the material, which is related to the number of protons (i.e., average atomic number). An area with relatively larger constituent atoms has a higher average atomic number, thereby generating more backscattered electrons and higher Z-contrast. With this in mind, a localized change of density in a glassy material as a result of the stress during waveguide writing could bring the constituent atoms closer to each other, thereby causing the incident electron beam to interact with more nuclei (protons) compared to the unirradiated zones. In our case this could explain why at higher feed rates and more rapid quenching, these stress-induced localized density variations are frozen-in whereas at slower feed rates this effect is reduced due to annealing. This supports the argument of solidification at different melt viscosities due to different feed rates as previously suggested.

During the analysis of diffusivity of elements we were able to derive an empirical relationship between the field strength (FS) of the elements [31], the ratio Z²/r (where Z is the common valence charge on the element and r is the ionic radius) and the glass composition producing smooth positive refractive index modification (type-1 waveguides) [32]. Instead of using the radius of a neutral atom we have used the crystal ionic radii, which is reported to be closer to the physical size of ions in solids, and the charge associated with it reported by Shannon [33]. Comparing the field-strength values of main elements that were used to form positive refractive index change waveguides, it could be concluded that if the main glass forming element is matched with its field strength preferably by a second glass former or an intermediate, there is a high probability of obtaining waveguides with a positive refractive index. Tellurite glass with Te having a FS of 14 failed to produce positive refractive index until it was modified with phosphate having a FS of 15.5 [34]. ZBLAN glass with Zr having 18.6 FS had a similar outcome until it was modified with hafnium (HZBLAN) having 18.8 FS to produce positive refractive index contrast [35,36]. A similar trend was also found for boro-aluminosilicates (Si=29, B=21, Al=16.8) where fused silica couldn’t produce a practically useful waveguide with positive refractive index change. Aluminum phosphate glasses (P=15.5, Al=13) also demonstrated similar behavior [7]. In such a case alkalis are generally the outliers with a valence of +1 and hence the field strength will be less than or equal to 1. It should also be noted that the diffusivity of alkalis are higher and invariant with respect to melt viscosity compared to other elements [31]. We have reported the unique behavior of alkalis in the past [37], whose migration does not follow a relationship with that of the laser energy or fluence used to modify the material and might be able to fit this behavior being the outlier among the elements categorized by their field-strengths.

4. Conclusion

To conclude, femtosecond laser inscribed waveguides formed in commercial borosilicate glasses were in-depth studied. It was found that structural changes along with ion migration were responsible for waveguide formation. Calcium and aluminum migration were found to be responsible for positive index formation and silicon migration for forming the negative index change. 30 µm diameter modifications, that were inscribed at different feed rates, demonstrated behavior corresponding to different quenching rates. Crystallization was found in waveguides with the slowest feed rates, whereas high index change was found in the heat diffused zones of those created at the fastest feed rates due to frozen-in shock diffusion. These points were validated using refractive index mapping by a camera that employs quadriwave lateral shearing interferometry, electron micro probe analysis to uncover compositional changes and Raman spectroscopy. The role of calcium in positive refractive index change at fast feed rates/high quenching rates was attributed to the high diffusivity of Ca at higher melt viscosities relative to Al and Si. Ultimately, an empirical analysis reveals that if the main glass forming element is matched with its field-strength preferably by a glass former or an intermediate, there is a high probability to obtain waveguides with positive refractive index change by femtosecond laser inscription.