## 1 Introduction  
Mid-infrared (mid-IR) light sources from 2 to 20 \(\upmu\)m are of key importance for applications in molecular sensing, medicine, security and defense, and in free-space communication [1]. The mid-IR spectrum covers important atmospheric windows, and numerous features of molecular gases, toxic and explosive agents, water, and pollutants. Bright, coherent and broadband radiations bring numerous practical advantages for some applications such as spectroscopy and frequency metrology, and this can be conveniently obtained by means of fiber-based supercontinuum light generated from femtosecond mode-locked lasers [2; 3], thus surpassing thermal infrared sources and challenging quantum cascade lasers. In the last decade, strong efforts have been made to transfer robust supercontinuum (SC) fiber sources from near-infrared into the mid-IR spectral range, mainly driven by the purpose of covering the largest spectral region possible [4; 5]. Recent developments now focus on satisfying the user needs for mid-IR SC application such as compact and high repetition rate sources, single-mode behavior, all-fiber systems, high power spectral density, and coherent emission across the SC spectrum [6; 7; 8; 9; 10; 11]. In the context of infrared spectroscopy and identification of organic molecules, the mid-IR spectra consist of the absorption bands mainly related to fundamental vibrations [12; 13]. There are two regions in such absorption spectra, namely the functional group region (2-6 um) that contains the characteristic bands of specific individual bonds and functional groups (i.e., mainly stretching vibrations) and the fingerprint region (6-20 um) that usually contains a large complex set of absorption bands (i.e., bending vibrations), unique to each molecule and making it difficult to interpret. The common route toward practical mid-IR SC generation in the important functional group region is the implementation of ps-pumped SC generation in commercially-available fluoride fibers [14; 15; 16], in particular fluoroindate fibers wherein Watt-level SC spanning from 1 to 5 um can be reached at the expense of the SC coherence properties. The recent development of step-index tellurite glass fibers appears as a possible alternative to fluoride glass fibers for comparable SC source features, in particular due to their similar spectral transmission window (in general 0.4-5 um) [17; 18]. Other important advantages from tellurite glasses have to be noticed, such as higher nonlinearity and zero-dispersion wavelength (ZDW) around 2.1-2.3 um, highly suitable for pumping with novel fiber lasers beyond 2 um (based on thulium-doped silica fibers, erbium- or holmium-doped fluoride glass fibers) [17; 19; 20; 21]. Note that they also offer a large flexibility in the chemical compositions that are compatible with fiber drawing. To date, high-power supercontinuum generation covering the 1-5 um spectral range has been also demonstrated in robust step-index tellurite fibers by using picosecond or femtosecond pulses [17; 22]. Mid-IR SC studies in the coherent regime remain less investigated in fluoride and tellurite fibers, this requires the use of a femtosecond pulse pump and a careful tailoring of fiber dispersion [22; 23; 24]. In a previous work [25], we already demonstrated the ability to control four-wave-mixing-based frequency conversion and continuum generation around 2 um in step-index tellurite fibers, more particularly in the long-pulse (picosecond) pumping regime. Nevertheless, the route to coherent SC generation is typically based on the use of all-normal dispersion (ANDi) fibers, but not exclusively; coherence-preserving nonlinear wavelength conversion with pumping into the anomalous dispersion regime is still possible with femtosecond pump pulses [26]. In this article, we numerically and experimentally demonstrate the possible control of SC features in the 1.5-4.5 um spectral range with a simple step-index tellurite fiber pumped by femtosecond pump pulses.