## 2 Experimental Set Up  
The schematic of the laser setup is shown in Figure 1.  
Here, the MgO:PPLN crystal is a step-chirped structure with poling periods increasing from 10.1 to 10.3 \(\upmu\)m in steps of 0.1 \(\upmu\)m, and the length is 21 mm with three equivalent segments and intended to fulfill the phase-matching condition of the SFG process. We used the standard electric poling technique to fabricate the step-chirped QPM device on a 1 mm-thick z-cut MgO:LN crystal as reported in Reference [27]. After poling, the crystal was cleaned and wet etched in hydrofluoric acid (HF) to reveal the domain structure, and the end faces were optically polished. However, no anti-reflection coating was performed. It is important to note the difficulty in achieving the same QPM grating as the initially designed QPM mask because of fabrication errors which are expected to significantly affect the efficiency profile and bandwidth. By setting up a temperature gradient along the MgO:PPLN crystal, a chirp is induced in each section, henceforth, extending the input wavelength acceptance range. The pump (P1), was a laser diode (LD) at 974 nm (\(\lambda_{1}\)) of 0.20 nm spectral width, while the signal (P2) was a C-band (1525-1565 nm) amplified spontaneous emission (ASE) source (\(\lambda_{2}\)). Using a 50:50 wavelength division multiplexer (WDM) coupler, we combined the output of C-band ASE and collimated with a C-lens before focusing at the center of nonlinear MgO:PPLN crystal with a 125 mm focal length plano-convex lens. The QPM period of the SFG grating, which combines \(\lambda_{1}\) and \(\lambda_{2}\) to yield \(\lambda_{3}\) in the 600 nm spectral region, was calculated using the Sellmeier expression for MgO-doped lithium niobate crystal at 25 \({}^{\circ}\)C [28].  
We measured the maximum input powers to be P1 = 229 mW and P2 = 200 mW. The output power and bandwidth were evaluated using a laser power meter (PM100D, Thorlabs, Newton, NJ, USA) and a fiber spectrometer (BIM-6001, Brolight, Hangzhou, China), whereas the M2 factor was measured using knife-edge method with Beamgage (Ophir-Spiricon, Inc., Jerusalem, Israel) laser beam analyzer. At the output, the rest of the pump and signal wavelengths including other harmonics from the MgO:PPLN were filtered. Our device was set to attain a temperature gradient by specifically attaching the hot and cold temperature-controlled thermoelectric ovens (model TCS-100, CTL photonics, Fuzhou, China) with a precision of \(\pm\)0.1 \({}^{\circ}\)C near the input and output faces of the crystal, respectively, subsequently forcing the heat flow through it. We set the thermal contacts at both ends of the MgO:PPLN crystal to be around 5 mm and measured the actual temperature of the MgO:PPLN crystal using a thermal camera (FLIR-E64501, FLIR Systems, Tallin, Estonia). \(\Delta\)T = T1 \(-\) T2 represents the temperature difference between the two ends of the crystal, where T1 and T2 are the temperatures at the input and output faces of the MgO:PPLN crystal, respectively. Once different points along the crystal length attain distinctive temperatures (temperature gradient), perfect phase matching of various incoming wavelengths of the ASE can be achieved at those points by constantly changing the temperature limits as desired.