## 3 Experimental Setup  
The experimental setup is sketched in Figure 2. The pulse pump is generated from an all-fibre femtosecond laser source delivering fs pulses at a central wavelength of 1.56 \(\upmu\)m and operating at a repetition rate of 80 MHz (OneFive GmbH, Origami 15-SP). The maximum available peak power is about 16 kW (maximum pulse energy of \(\sim\)1.5 nJ). Then, the fs-pulses passed through an inline polarization controller (Lefevre loops) in order to optimize the energy launched into the fundamental TE mode of the waveguide. Indeed, given the noticeable difference in the values of effective area between TE and TM modes, the broadest SC can only be achieved for a proper TE linearly polarized wave. The total power injected into the waveguide can be adjusted by means of a set of calibrated fixed optical attenuators (OA). The injection of light into our TiO\({}_{2}\) waveguides is ensured by a butt coupling technique through lensed fibres (Figure 2b1) characterized by a working-distance of 14 \(\upmu\)m. To reduce the insertion losses through such butt-coupling of light, the component design includes 1 mm-long tapers (Figure 2b2) at both ends of the waveguide. Note that the nonlinear propagation of the initial pulse, equivalent to a near fundamental soliton pulse (N-1) [43], within the segment of standard anomalous dispersion SMF 28 fibre between the fs-laser output and the TiO\({}_{2}\) waveguide leads to the tuning of the central wavelength of the initial pulse from 1.56 \(\upmu\)m towards 1.64 \(\upmu\)m through Raman soliton self-frequency shift (see Figure 2c).  
The injecting conditions are optimized thanks to a visible camera (providing a top view of the sample) as well as a second infrared camera implemented at the waveguide output in such a way to image the far-field modal profile. The typical injection losses are around 11 dB (per facet) while the propagation losses are estimated to around 5.5 dB/cm, thus leading to an effective length below 1 cm, similar to the results available in the literature [25; 40]. As a consequence, we believe that for the present experiment, the finite length of the device is not the main limiting effect. Note that a different process of fabrication avoiding etching could decrease drastically such losses down to around 1 dB/cm [44].  
Figure 2: (**a**) Experimental setup involved for generation of supercontinuum in TiO\({}_{2}\) waveguides. (**b1**) Sketch of the waveguide and butt-coupling thanks to lensed fibres and (**b2**) the corresponding optical microscope image of the taper used for the coupling. (**c**) Spectrum of the injected soliton pulse centred at 1640 nm compared with the spectrum of a 90 fs sech\({}^{2}\) pulse (**c**).  
Once the input conditions are properly adjusted, the output camera is replaced by a second single-mode lensed fibre connected to an optical spectrum analyser (OSA) operating in the near-infrared range (Anritsu MS9740A). For analysis beyond 1.7 \(\upmu\)m, the output silica lensed fibre is replaced by a fluoride multimode fibre and the injection in this collecting fibre is now achieved through a free-space setup involving two microscope objectives. Note that in this case, the OSA is also switched to another one operating up to 2.4 \(\upmu\)m (Yokogawa AQ6375B) that includes a built-in cut filter to eliminate higher order diffracted light. However, despite this filter, some residual contribution of spurious double-order mode may eventually contribute to the spectrum recorded between 2200 and 2400 nm.