# A Review of Mid-Infrared Supercontinuum Generation in Chalcogenide Glass Fibers
## 4 Coherent SC Sources Based on ChG Fibers  
Many significant applications of SC sources require both an extraordinary bandwidth and a high average power as well as specific coherence properties. For instance, optical coherence tomography requires low coherence [155]. Meanwhile, applications in laser synchronization, frequency metrology and nonlinear microscopy require extremely high coherence [156; 157; 158]. Therefore, coherent MIR SC sources have attracted much attention because of their numerous application prospects. To quantitatively study the coherence degradation, the modulus of the complex degree of coherence is determined from the following equation [159; 2]:  
\[\left|g_{12}^{(1)}(\lambda,t_{1}-t_{2})\right|=\left|\frac{\left\langle E_{1}^ {*}(\lambda,t_{1})E_{2}^{*}(\lambda,t_{2})\right\rangle}{\sqrt{\left\langle \left|E_{1}(\lambda,t_{1})\right|^{2}\left|E_{2}(\lambda,t_{2})\right|^{2} \right\rangle}}\right|, \tag{3}\]  
Figure 10: Measured SC spectra generated from 12-cm-long As–S ChG tapered fibers with transition region lengths varying from 6.7 to 10.5 mm, pumped at 3.25 \(\upmu\)m.  
where \(E\) is the intensity of the electric field. The angular brackets represent an ensemble average over independently generated pairs of SC spectra, and \(t\) is the time measured on the resolution time scale of the spectrometer used to resolve these spectra. The modulus, \(\mid\!g_{12}^{(1)}\!\mid\), at \(t_{1}-t_{2}=0\) can be adopted in situations only concerning the wavelength dependence of the coherence. It is worth nothing that \(\mid\!g_{12}^{(1)}\!\mid\), a measure of the phase stability of two fields in the interval [0:1], is calculated over a finite bandwidth at each wavelength of the spectra. As expected, \(\mid\!g_{12}^{(1)}\!\mid\!=\!1\) over the entire bandwidth corresponds to perfect coherence, whereas \(\mid\!g_{12}^{(1)}\!\mid\!=\!0\) implies that the two spectral phases are completely irrelevant. The coherence property of MIR SC light depends on the parameters of pump light and the nonlinear processes involved in the spectral broadening mechanism [2; 159; 160; 161]. For the pump scheme, a laser light with short pulse width and high stability is necessary to reduce the coherence degradation caused by technical noise [2]. For the spectral broadening mechanism, the coherence degradation of SC sources is mainly caused by noise amplification which comes from SRS and modulation instability [162; 163]. In most of the studied cases, MIR SC generation based on ChG fibers always occurs with pump pulses in the anomalous dispersion regime of the fiber with a single ZDW. The SC broadening mechanisms are mainly soliton effects where higher order solitons break down into a series of fundamental solitons, accompanied by the emission of dispersive waves in the normal dispersion regime. This process produces a spectrum with a complex structure, which is sensitive to laser shot noise due to the increase in noise amplification through modulation instability gain, resulting in different spectral components [106; 159; 162]. There is low coherence across the bandwidth due to the fluctuations in the relative phase and intensity, limiting the resolution or precision for specific applications. However, SCs generated from fibers pumped with periodic and ultrashort pulse trains can exhibit strong correlations between different pulses when the spectral broadening mechanism is highly reproducible, even though these pulses may still have complex spectral intensity and phase profiles [20]. A commonly used method for generating coherent SCs is to pump fibers with optimized all-normal dispersion (ANDi) profiles by using ultrashort lasers [164; 165; 166]. These fibers have low and flattened normal dispersion over the entire spectral region of interest. The SC spectral broadening in these cases is mainly caused by SPM and OWB, which can maintain a deterministic phase relationship between the newly generated wavelengths and the pump pulse, eliminating noise-sensitive soliton dynamics [165; 166; 167].