Investigation of the glass structure-property relationship
Enhancing a glass nonlinearity primarily involves increasing its nonlinear refractive index. From a chemical standpoint, this can be achieved by incorporating specific cations with particular electronic configurations, ranked in order of ability to increase the glass nonlinearity: alkali or alkaline-earth (e.g., K, Ba), d (e.g., Ga, Ge and In), d (e.g., Nb, Ti, Ta) and ns ions (e.g., Te and Pb). However, to preserve the high thermomechanical stability of gallate glasses, only a subset of these ions can be selected. While ns ions would be ideal for maximizing nonlinearity, their incorporation significantly compromises the glass thermomechanical properties. In contrast, d ions provide the optimal balance between increasing nonlinearity and maintaining the elevated thermomechanical properties of gallate glasses. Therefore, we have chosen tantalum oxide as a key element. Its +V oxidation state is chemically stable, and it has already been successfully incorporated in significant amounts into lanthano-gallate systems. Here, the influence of the germanium oxide substitution for tantalum oxide has been investigated from 0 up to 25 mol% of TaO. A summary of the glass nominal compositions and their properties is presented in Table 1. Note that up to 20 mol% of TaO, glasses did not lead to devitrification during casting. The EPMA chemical analyses did not reveal any variation of more than 1 mol% from the nominal compositions, consistent with a homogeneous glass synthesis without noticeable evaporation.
Bulk optical transmission spectra of all vitrified samples are shown in Fig. 1a. The transmission window spans from the UV up to the mid-infrared. Correlated with the photographs inserted in Fig. 1a, as the tantalum content increases, a new weak absorption band (<1 cm) appears around 450 nm giving a yellowish color to the glass. This results from the inadvertent incorporation of platinum ions from the platinum crucible. Meanwhile, as the tantalum content increases, the mid-infrared optical window shifts to longer wavelength, in agreement with theoretical expectations. Indeed, the substitution of Ge for Ta ions with both a weaker single bond strength (102 kcal and 72 kcal for Ge-O and Ta-O, respectively) and heavier mass (73 g mol and 181 g mol for germanium and tantalum, respectively) allows for minimizing the multiphonon absorption contributions of Ge-O bonds observed near 6 μm. Additionally, all glasses have an absorption band located at 3000 nm and 4300 nm, due to the presence of hydroxyl groups as the samples were synthetized in ambient air.
The glass structure has been investigated via Raman spectroscopy for the five glasses. All Raman spectra were normalized by their area, allowing for a good relative comparison of their Raman contributions (Fig. 1b). In gallate and germanate glass systems, three regions can be observed in the high (600-1000 cm), mid (400-600 cm) and low (200-400 cm) frequencies. The high frequency domain is attributed to symmetric and antisymmetric stretching modes of gallium and germanium tetrahedral units [TO]. The mid-frequency domain is characteristic of vibrational contributions of T-O-T bending with in-the-plane oxygen motions. Lastly, the low frequency contributions are assigned to network-modifying cations vibrating in large interstitial sites and T-O-T bending with out-of-plane oxygen motions. For glasses containing tantalum oxide, a single distinctive contribution appears at about 700 cm, characteristic of tantalate structural units in six-fold coordination ([TaO]). All Raman assignments are summarized in Table 2.
Raman signature of the tantalum-free composition presents two main bands peaking at 510 and 810 cm with a barely visible shoulder at 450 cm. Since the gallium content is 1.5 times larger than that of germanium, the alternation of gallium and germanium tetrahedral units within the glass network is expected to follow a similar trend. Consequently, the formation of two directly linked [GeO] units is likely rare, which explains the minimal band contribution at 450 cm, typically associated with Ge-O-Ge bridges. In contrast, the dominant response at 510 cm strongly aligns with a glass structure rich in [GaO] units. In the meantime, the amount of positive-charge compensators provided by Ba ions exceeds what is needed to stabilize the [GaO] units. As a result, the excess Ba ions, accounting for approximately one-third of the total barium content, contribute to the depolymerization of the glass network, leading to the formation of Ge∅O entities. These entities correspond to GeO tetrahedral units with three bridging oxygens (∅) and one non-bridging oxygen (O). The second most intense spectral contribution, peaking at 810 cm, is attributed to the presence of non-bridging oxygens (NBOs) within these Ge∅O units. With the increase of tantalum oxide at the expense of germanium oxide in our glasses, the contributions at 450 and 500 cm progressively decrease to give rise to strong bands at 650 and 710 cm. The tantalum cations are incorporated into the glass network predominantly in their preferred octahedral configuration as the 710 cm band increases linearly. The replacement of Ge ions for Ta ions suppresses progressively the last Ge-O-Ge bridges while keeping almost unaffected the Ge∅O units at 810 cm. In the meantime, the gallate tetrahedral units are impacted as the 650 cm band is indicative of non-bridging oxygens on [GaO] structural units. Indeed, the excess of Ba ions that were compensating the Ge∅O entities when the content of germanium was higher are now depolymerizing the gallate network by forming non-bridging oxygens on [GaO] structural units.
The Vickers hardnesses are reported in Fig. 1c. From 0 up to 20 mol% of TaO, the glass hardness is significantly increased by 25% reaching 6.0 GPa, but this increase is not linear with the tantalum content. Typically, glass hardness is primarily influenced by two factors: free volume and bond strength. As observed in the Raman spectra, germanium cations predominantly form tetrahedral units, while tantalum cations adopt an octahedral configuration. The substitution of germanium with tantalum reduces the glass free volume, as confirmed by the evolution of oxygen packing density (Supplementary Fig. 1), which aligns with the overall increase in glass hardness. However, since the Ta-O single bond is weaker than the Ge-O bond, it partially counteracts the hardness improvement induced by the free volume reduction. Additionally, the gallate glass network becomes more depolymerized due to the formation of non-bridging oxygens (NBOs) on gallate structural units, which could also minimize the hardness improvement. These competing effects contribute to the nonlinear increase in glass hardness. As a comparison, the Vickers hardness of tellurite (<3 GPa), lead-germanate (<3 GPa), and fluoride glasses (<2 GPa) remains significantly lower than the 5-6 GPa range shown for our tantalo-gallate glasses, particularly when considering compositions suitable for fiber drawing.
Chemical durability of gallate glasses immersed in deionized water is reported in Fig. 1d. Thanks to the addition of tantalum oxide in the gallate glasses, a clear improvement of the chemical durability is observed. Indeed, even after being exposed for one week, the 20Ta sample is still completely undamaged on the surface, while the composition free of tantalum became slightly opaque. This difference of chemical sensibility is demonstrated by the huge change in terms of corrosion rate, evaluated at 0.126 mg cm h and 0.003 mg cm h, for the glass without and with 20 mol% of TaO, respectively. Additionally, to push even further the experiment on our glass compositions, both samples with 15 and 20 mol% of tantalum oxide, were immersed in deionized water now heated at 50 °C for several days. While the 15Ta sample presents a low corrosion rate of 0.017 mg cm h, the glass with the highest amount of tantalum still degrades extremely slowly at a rate of 0.004 mg cm h. Already studied in barium gallo-germanate and indium-containing germanate glasses, both the decrease of germanium content and the addition of octahedral structural units have been reported to increase the glass durability by decreasing the free volume. Replacing the germanium ions with highly coordinated Ta cations thus noticeably increases the gallate glass durability.
The differential scanning calorimetry (DSC) analyses were carried out on the gallate glasses on powder (Fig. 2a) and bulk (Fig. 2b) forms. Glass transition temperatures (T), onsets of crystallization (T) and glass stabilities (ΔT), calculated from the difference between T and T for the powder were extracted from Fig. 2a and plotted in Fig. 2c. Through the introduction of tantalum ions in the glass compositions, the T increases nonlinearly from 710 to 780 °C which is consistent with the decrease of free volume and increase of cross-linking brought by the tantalum ion in octahedral configuration. In the meantime, the T firstly drops with the introduction of 5 mol% of TaO from 905 to 865 °C, then slightly increases up to 15 mol% of TaO, to finally re-decreasing down to 880 °C. The ΔT is maintained above 100 °C except for the 20Ta glass composition. As a general rule of thumb, an ideal ΔT above 100 °C is preferred to consider fiber drawing from the preform-to-fiber technique. By monitoring the difference of maximal crystallization temperature (ΔT) extracted from the DSC performed on bulk and powder forms, the main type of crystallization can be determined. Indeed, with a large surface area, DSC performed on glass powder favors surface crystallization, while DSC performed on glass bulk favors volume crystallization.
In Fig. 2d ΔT is plotted over the concentration of tantalum oxide. At low concentration of tantalum oxide, the glass preferentially crystallizes from the surface, while above 15 mol%, the glass devitrifies preferentially from its volume. This change in crystallization behavior is consistent with a strong restructuration in the glass network induced via the incorporation of tantalum oxide. In the meantime, it is observed that from 15 mol% of TaO in Fig. 2b, the bulk crystallization peak is intense and sharp, indicative of aggressive crystallization. Hence, considering the overall glass thermal stability in terms of ΔT and crystallization behavior, the fiber drawing of our tantalum-containing gallate glasses is expected to be feasible up to at least 10 mol% of TaO from the preform-to-fiber technique. As a first demonstration of fiber drawing viability in this glass system, we report the drawing of a 50 m-long 250 μm-diameter coreless fiber of the glass composition containing 10 mol% of TaO (Supplementary Fig. 2). Cut-back loss measurement were performed and presented in Fig. 6e. No devitrification was observed either at the fiber surface or in its volume. Additionally, various robust fiber tapers with a 1:10 ratio were shaped by means of the common heat-and-stretch technique (Vytran GPX3800), thus demonstrating the ease of thermal post-processing of such glass fibers (Supplementary Fig. 3).
The linear and nonlinear refractive indices were measured on all five glasses. In Fig. 3a, the linear refractive index is strongly increasing with the increase of tantalum content, with Δn in excess of 0.1 from 0 up to 20 mol% of TaO. The linear optical susceptibility χ is plotted in inset and shows a clear linear evolution. Here, due to the high electron density of the Ta ions, there is no doubt that these ions are mainly driving the linear increase of the refractive index, as reported in similar lanthano-gallate glass systems.
Determined from Z-scan measurements, the nonlinear refractive indices at 1030 nm, normalized to the measured n value of an F300 silica sample (2.8 × 10 m W), are presented in Fig. 3b. In the absence of tantalum oxide, the glass exhibits an n value more than five times higher than that of silica glass. As the tantalum content increases, n follows a linear trend, ultimately exceeding an order of magnitude compared to silica glass, similar to some commercial tellurite and lead silicate glass compositions.
As presented in the Introduction, heavy-metal oxide glasses based on ns elements, such as tellurites and lead-germanates, exhibit high nonlinear refractive indices (up to 100 times the n value of silica) and broad mid-infrared bulk transmission (up to 6 μm). However, these advantages are offset by low glass transition temperatures (<400 °C) and poor mechanical strength (Vickers hardness below 3 GPa), intrinsic to the presence of ns lone-pair electrons. A similar trade-off is observed in chalcogenide glasses, where the heavy chalcogen anions responsible for high n (up to 1000 times the n value of silica) and extended MIR bulk transparency (up to 25 μm) also significantly reduce Tg (often below 200 °C), limiting mechanical property (Vickers hardness below 2 GPa). Fluorine-based glasses, such as fluoroindate, offer excellent MIR bulk transparency (up to 9 μm) and high rare-earth solubility due to their unique combination of heavy-metal cations and fluorine. Nevertheless, the inherently weak ionic bonding in fluoride glasses results in low thermomechanical performance, with Tg and hardness typically below 300 °C and 2.2 GPa, respectively, and pronounced sensitivity to moisture. Across all these MIR glass families, a persistent limitation has been their poor ability to produce robust, easy-to-handle optical fibers, particularly in unjacketed configurations. In this context, the development of tantalo-gallate glasses represents a significant advancement, offering a compelling balance of extended MIR bulk transparency (> 5.8 μm), high nonlinearity (one order of magnitude higher than silica), and superior thermomechanical properties (Tg at 750 °C with Vickers hardness of 5.6 GPa) conducive to the fabrication of durable and practical MIR fiber devices. Key properties of main MIR glass fiber systems are summarized in Table 3.
Here, we present two demonstrations of supercontinuum generation (SCG) using our glasses: one in a laser-inscribed waveguide and another in a tapered fiber. To summarize the key experimental parameters for the supercontinuum generation in both demonstrations, the latter are denoted in Table 4.
The first demonstration employed a laser-inscribed waveguide embedded in a 4 cm-long bulk sample of gallate glass containing 17.5 mol% of TaO (the reader is referred to the Experimental section for details on the laser irradiation conditions). This tantalum concentration was selected because it yields an n value roughly one order of magnitude higher than that of silica, still allowing fabrication in a long bulk form. A similar demonstration could likely have been achieved using the 20 mol% TaO composition. Yet, it was not explored in this work. In the second demonstration, a tapered gallate glass coreless fiber containing 10 mol% of TaO was used. This composition was chosen to enable the drawing of crystal-free fibers via the preform-to-fiber technique while maintaining high n. It was preferred over higher tantalum concentrations (e.g., 15Ta and 20Ta), which exhibit lower glass stability. However, it is worth noting that no fiber drawing attempts were reported for these richer compositions. Also, the coreless fiber was preferred over conventional core-clad designs due to its ease of fiber fabrication while providing the strong light confinement suitable for the SCG. The SCG setup is presented in Fig. 4 and detailed in the Experimental section.
Owing to the nonlinear nature of its absorption, ultrafast lasers are now widely recognized as a reliable tool for microscale processing of complex three-dimensional structures within the bulk of materials. This capability enables the fabrication of three-dimensional waveguides and compact integrated photonic devices. In this work, a usual one-dimensional waveguide was inscribed in a 4 cm-long 17.5Ta glass sample (Fig. 5a) and optimized to achieve a near-circular transverse profile with a refractive index change Δn of the order of 1 × 10. As for the waveguide diameter, it was established as a trade-off between easing pump coupling and reducing the number of transverse modes. Accordingly, the following laser inscription parameters were selected: scanning speed of 5 mm s, pulse energy of 190 nJ, and a repetition rate of 5 MHz. The resulting laser-inscribed waveguide cross-section, shown in Fig. 5b, exhibits a cross-section with an aspect ratio of 1:1.4 and a diameter of 30 μm. The refractive index change, inferred from phase contrast imaging (Fig. 5c), is slightly above 1 × 10, enabling the propagation of 5 transverse modes near 1.9 μm. The resulting experimental SCG spectra are presented in Fig. 5d.
Considering both material and waveguide contributions, we estimated the properties of the fundamental guided mode LP of the inscribed waveguide through numerical solutions of the dispersion equation for cylindrical step-index geometries. The calculation employed fitted refractive index curves for both the core and cladding, incorporating a refractive index contrast of the order of 1 × 10. At a pump wavelength of 1755 nm, the waveguide exhibits normal dispersion (β~0.025 ps m), with a zero-dispersion wavelength (ZDW) around 1.94 µm. Due to the low laser repetition rate (1 kHz), the average output power from the waveguide remains low, on the order of tens of µW. Consequently, the peak power values used in simulations align with experimentally measured average power levels, assuming free-space to fiber coupling losses exceeding 10 dB in agreement with estimated experimental coupling losses. Figure 5e presents simulated spectra for different peak powers. At lower power levels, spectral broadening is primarily driven by self-phase modulation (SPM) and optical wave breaking, resulting in a nearly symmetric spectrum centered around the pump wavelength (1.6-2.0 µm). At the highest peak power (P = 500 kW), symmetry breaks upon reaching the ZDW, leading to an SC spectrum spanning 1.4-2.3 µm at -20 dB. In fact, as the pump wavelength approaches the ZDW, some energy is transferred into the anomalous dispersion regime. As a result, both normal dispersion and soliton-related dynamics coexist, leading to an asymmetric spectral broadening. A good agreement is observed between the numerical and experimental results, particularly in spectral shape at high peak power and in the ZDW crossing near 1.9 µm. To further illustrate SCG dynamics, Fig. 5f shows the spectral evolution along the waveguide at 500 kW peak power. Most of the broadening occurs within the first few centimeters of propagation, consistent with previous laser-inscribed SCG waveguides in tellurite and chalcogenide glasses, where comparable pulse energies yielded spectra spanning several hundred nanometers. The combination of high peak power, a pump wavelength near the ZDW, and the high nonlinearity of the glass promotes substantial spectral broadening. Even broader SC spectra could be achieved by pumping in the anomalous dispersion regime (i.e., above 2 µm), where higher-order soliton fission, dispersive wave emission, and Raman-induced soliton self-frequency shift (SSFS) can further extend the spectrum. Additionally, optimizing the waveguide diameter and increasing the refractive index contrast would further enhance SCG dynamics.
In a final set of experiments, we investigated supercontinuum generation in a tapered gallate coreless fiber. Initial SCG results were obtained in non-dehydrated tapered fibers (Supplementary Fig. 3), however, due to the high hydroxyl (OH) content in the glass, the SC spectra were limited to below 2.7 μm (Supplementary Fig. 3). To overcome this limitation, we synthesized the same 10 mol%-TaO gallate glass composition (Fig. 6), ensuring rigorous dehydration following the optimized protocol reported in a previous work. The dehydrated 10 mol%-TaO gallate glass exhibits even better thermal stability with a ΔT of 180 °C (Fig. 6d), leading to crystal-free fibers (Supplementary Fig. 3). The fiber had an initial diameter of 125 µm, tapering down to a waist diameter of 15 µm. The taper transition lengths were both 12.5 mm long, separated by a waist length of 20 mm (Fig. 7a). Fiber propagation losses were measured to be below 5 dB m in the 1-3.6 μm region, with a minimum below 1 dB m around 2 μm (Fig. 6e). For a 5 cm-long taper, such losses are actually negligible. Similarly to the inscribed waveguide, we investigated the properties of the fundamental guided mode LP. We consider the taper to have a step-index profile with an infinite air cladding (n = 1). We made use of the fitted curve of the refractive index shown in Fig. 3 for the 10Ta as the core composition. For a pump wavelength of 1900 nm, the fiber exhibits normal dispersion (β~0.006 ps m) at a diameter of 125 µm, and anomalous dispersion (β~-0.01 ps m) in the 15 μm-waist section. The coupled peak powers were estimated from the average output power measured at the fiber exit. The maximum average power reached approximately 200 µW, corresponding to a peak power of ~ 3 MW. Assuming equivalent coupling conditions, we applied attenuation ratios based on the filter optical densities, leading to estimated peak powers of 300 kW and 30 kW.
Experimental results and corresponding numerical simulations of the SC spectra under these conditions are shown in Fig. 7b, c. At the lowest peak power, the SCG remains limited, with broadening primarily driven by self-phase modulation (SPM). However, at the highest peak power, the tapered fiber produces a broad supercontinuum spanning from 0.6 µm up to the CO absorption band at 4.3 µm, with a 40 dB dynamic range. This result can be attributed not only to the high peak power injection but also to the strong optical confinement and enhanced nonlinearity in the waist region compared to the initial 125-µm diameter section. As illustrated in Fig. 7d, the most pronounced spectral broadening occurs within the first 15 mm of propagation, particularly near the transition between the down-taper and the fiber waist. In this region, soliton fission takes place, leading to the formation of multiple soliton-like pulses that undergo soliton self-frequency shift (SSFS), while short-wavelength components may originate from dispersive wave emission. Considering the simulation of the fundamental mode only, the soliton order N () for a peak power of 3 MW, is approximately 9 for a diameter of 125 µm, and 55 for a diameter of 15 µm. This underlines the strong nonlinear regime achieved in the waist region, where complex soliton dynamics, including fission and Raman-induced self-frequency shifts, are expected to play a dominant role.
Experimental and numerical results show a good agreement in terms of spectral bandwidth across all peak powers. However, differences in spectral shape can be attributed to the highly multimode nature of the tapered fiber and initial coupling conditions, as evidenced by the residual pump energy in the experimental spectrum, whereas in simulations, all pump energy is redistributed across new wavelengths. The numerical SC simulations were based on the generalized nonlinear Schrödinger equation (GNLSE) model, which only considers the fundamental mode propagation. However, in practice, the high refractive index contrast between the coreless fiber and the air-cladding makes the fiber highly multimode. For short pulses (<10 ps), fundamental-mode-only simulations generally provide a good approximation of SCG dynamics and spectral bandwidth, as higher-order modes contribute less to spectral broadening. This experimental demonstration, achieving SCG from the visible to 4.5 µm, is the first of its kind in gallate glass. While this spectral range does not extend as far as 5 µm, as achieved in some fluoride-based compositions, it remains comparable to tellurite fiber-based SC sources. This result underscores the strong potential of tantalo-gallate glass fibers. Moreover, given their excellent thermomechanical properties, further dispersion engineering (e.g., step-index or W-type fiber designs) could enable high-power SCG (tens of watts or more) across the 1-5 µm range, comparable to what is achievable in ZBLAN or fluorotellurite fibers.