## 5 Conclusions  
In this work, we have reported the first experimental demonstration of an octave spanning supercontinuum generation in a compact TiO\({}_{2}\) optical waveguide. Following soliton-based nonlinear dynamics, the spectral broadening of femtosecond pulses at 1.64 \(\upmu\)m leads to the generation of new wavelengths from the visible up to 1.92 \(\upmu\)m, that is, this involves spectral components covering more than an octave. Both experiments and simulations also stress the crucial importance of the geometrical parameters of the waveguide structure that governs the dispersion properties and ultimately the supercontinuum extent. This study therefore confirms the strong potential of TiO\({}_{2}\) for nonlinear applications. With further reduction of the propagation losses combined with more advanced dispersion engineering of the waveguide and optimization of the device length, noticeable enhancements of the resulting SC source are expected and decade spanning SC could potentially be reached. Using TiO\({}_{2}\) in amorphous phase can also be a source of improvement. The use of wideband coupling grating structures such as reported in [42] that are able to handle femtosecond pulses could also improve the stability of the source and increase the power coupled within the waveguide.  
Compared to other widely used materials, its transparency in the visible also makes TiO\({}_{2}\) appealing for pumping with cost-efficient fibre laser sources operating around ytterbium typical wavelength (1.06 \(\upmu\)m) as well as the versatile titanium-sapphire ultrashort lasers. Other intrinsic advantages of TiO\({}_{2}\) such as the absence of TPA and its thermal stability are also critical to enable the efficient generation of continuum from sources delivering longer picosecond or nanosecond pulses, which paves the way for future theoretical and experimental investigations.  
This work is financially supported by PARI PHOTCOM Region Bourgogne, by Carnot Arts Institute (PICASSO 2.0 project), by the Institut Universitaire de France, by FEDER-FSE Bourgogne 2014/2020 and by the the French \"Investissements d'Avenir\" program, project ISITE-BFC (contract ANR-15-IDEX-0003). The research work has benefited from the PICASSO experimental platform and the ARCEN-CARNOT nanofabrication facilities of the University of Burgundy.  
[PERSON], [PERSON], [PERSON] and [PERSON] conceived, designed and performed the experiment of supercontinuum generation; [PERSON], [PERSON], [PERSON] and [PERSON] fabricated and took part in the characterization of the optical waveguides. [PERSON], [PERSON] and [PERSON] were involved in the numerical modelling and design of the  
Figure 6: (**a**) Dispersion profiles of the fundamental TE\({}_{0,0}\) mode of the waveguide for different widths (1.4, 1.5 and 1.8 \(\upmu\)m). (**b**) Experimental spectra (blue lines) and corresponding numerical simulations (red lines) for (**b1**) 1.4 \(\upmu\)m and (**b2**) 1.8 \(\upmu\)m. For the clarity of the figure, the various spectra were vertically offset.  
component. All the authors contribute to the analysis of the results and to the writing of the manuscript. [PERSON] supervised the project.  
**Conflicts of Interest**: The authors declare no conflict of interest.