## 4 Experimental Results  
Based on the above numerical results, we have carried out experiments to demonstrate the efficiency of our dispersion-engineered tellurite fibers for mid-IR SC generation in the case of femtosecond pumping with moderate energy. First, we describe the experimental setup shown in Figure 10. A Ti:Sapphire laser is used to pump an optical parametric oscillator (OPO) that delivers 200-fs pulses at a repetition rate of 80 MHz with an average power about 200 mW (i.e., 2.5 nJ per pulse) in the wavelength window from 2.2 to 2.4 \(\upmu\)m (idler output). Our fibers were cleaved with a scalpel blade, and the quality of the interfaces was carefully checked under a microscope. A half-wave plate was also inserted in the light path to control the orientation of the linear polarization of the beam and excite the fiber under test along one of its polarization eigenaxes. Light coupling into the fundamental mode of the tellurite fibers was obtained by means of a silica microscope objective lens and the analysis of the output beam profile with an IR camera. The output of tellurite fiber was directly butt-coupled to a 0.5 m long multimode fluoride (InF\({}_{3}\)) fiber with high transmission over the 0.35-5.5 \(\upmu\)m spectral range. SC spectrum was then analyzed with an optical spectrum analyzer (OSA) covering the range 1.2-2.4 \(\upmu\)m and a FTIR spectrometer for the range of 1-6 \(\upmu\)m. In the following, we show the results obtained with three step-index tellurite fibers with the following core diameters: 3, 3.5, and 4 \(\upmu\)m (i.e., corresponding to the three distinct SC regimes shown in Figure 5). Our coupling efficiency varies from 25 to 35% as a function of the fiber core diameter, so that SC generation can be investigated here for all the fibers with a maximum input peak power of roughly 3 kW (i.e., 600 pJ per pulse). Figure 10: Experimental set-up used for mid-IR supercontinuum generation. OPO: optical parametric oscillator. HWP: half-wave plate. OBJ: 20 \(\times\) microscope objective lens. FTIR: Fourier-transform infrared spectrometer. OSA: optical spectrum analyzer. Figure 9: **(a)** Evolution of the average SC spectrum. The pump wavelength is now fixed at 2500 nm with 200-fs pulses and 3 kW peak power. The fiber length is 12 cm. (**b**) Corresponding evolution of the modulus of the complex degree of first-order coherence. (**c**) Corresponding soliton number calculated at pump wavelength. Figure 11 shows the impact of fiber length or input peak power on the generated SC spectrum when using the tellurite step-index fiber with a core diameter of 3.5 \(\upmu\)m (i.e., with two ZDWs) pumped at 2300 nm between the two ZDWs. We can note that the maximum spectral broadening is reached after 12 cm of propagation for a fixed input power (see Figure 11a). In particular, we observe the emergence of mid-IR dispersive waves around 3500 nm for the power fixed here at 2.2 kW (in agreement with simulations presented in Figures 5 and 7). After 12 cm, the SC bandwidth saturates due to higher fiber losses around 4 \(\upmu\)m. To reach wavelengths located further in the mid-IR, one has to use higher pump powers (i.e., higher values of \(N\)) to decrease the fiber length required for the frequency conversion mechanisms [26] before loss-induced limitations. Next, Figure 11b depicts the SC evolution as a function of input peak power for the optimized fiber length of 12 cm. We clearly retrieve the SC bandwidth predicted by numerical simulations (see Figure 5e), which almost extends from 1.5 to 4.5 \(\upmu\)m for the maximum input power of 3 kW. We also investigated the impact of pumping wavelength on the SC bandwidth in Figure 12. Again we confirm the general behaviour expected from numerical simulations (see Figures 8 and 9), namely that spectral broadening is slightly enhanced when increasing the pump wavelength (here from 2250 to 2350 nm) as shown in Figure 12a.