## 2 PPLN Design and Fabrication  
In order to realize multiple nonlinear processes in the same crystal, it is necessary to simultaneously fulfill their phase matching conditions. For SFG and SHG processes involving three interacting waves, a pump (\(\omega_{1}\)), signal (\(\omega_{2}\)), and an idler (\(\omega_{3}\)), their respective wave vector mismatches due to material dispersion are [17]  
\[\Delta k_{SFG}\ =\ k_{1}\ +\ k_{2}\ -\ k_{3}\ -\ 2\pi/\Lambda_{SFG} \tag{1}\]  
\[\Delta k_{SHG}\ =\ k_{SHG}\ -\ 2k_{2}\ -\ 2\pi/\Lambda_{SHG} \tag{2}\]  
where \(k_{j}\ =\ 2\pi n_{j}/\lambda_{j}\) is the wave vector at the corresponding frequency \(\omega_{j}\), \(j\ =\ 1\), 2, 3, \(\lambda_{j}\) is the wavelength in vacuum, \(n_{j}\) is the refractive index (extraordinary) at that wavelength that can be calculated using the Sellmeier equation [18]. \(\Lambda_{SFG}\) and \(\Lambda_{SHG}\) are the QPM poling periods of SFG and SHG respectively given by  
\[\frac{1}{\Lambda_{SFG}}\ =\ \frac{n_{1}}{\lambda_{1}}\ +\ \frac{n_{2}}{\lambda_{2}}\ -\ \frac{n_{3}}{\lambda_{3}} \tag{3}\]  
\[\frac{1}{\Lambda_{SHG}}\ =\ \frac{n_{SHG}}{\lambda_{SHG}}\ -\ \frac{2n_{2}}{\lambda_{2}} \tag{4}\]  
The two processes can occur simultaneously if \(\Lambda_{SFG}\ =\ m\Lambda_{SHG}\) where \(m\) is an integer. For a given material, Equations (3) and (4) can be satisfied for a specific pump and signal wavelengths and one periodicity. In this work, \(\lambda_{1}\) is an LD source emitting 974 nm and \(\lambda_{2}\) is a C-band ASE source at 1525-1565 nm. Using standard electric poling technique, we fabricated a single period QPM device on a 1 mm-thick z-cut MgO:LN crystal as reported in [19]. The device length is 50 mm. To realize efficient SHG and SFG processes simultaneously, we are seeking the condition \(\Delta k_{SFG}\ =\ \Delta k_{SHG}\ =\ 0\). Using SNLO (AS photonics) [20], we calculated the required periodicities as \(\Lambda_{SFG}\ =\ 10.2\ \upmu\)m at 60 \({}^{\circ}\)C and \(\Lambda_{SHG}\ =\ 5.1\ \upmu\)m at 110 \({}^{\circ}\)C based on Sellmeier equations with \(m\ =\ 2\). We fabricated the PPLN to have a period of 10.2 \(\upmu\)m for perfect quasi-phase-matched SFG and the second-order quasi-phase-matched SHG processes, and at the same time utilize the broadband nature of the ASE source. In this regard, we have coincidental phase matching for SHG of \(\lambda_{1}\) but a decreased efficiency is expected because of the second-order phase matching [21]. It is worth noting that, the SHG conversion efficiency can be enhanced by a factor of 4 theoretically by using first-order QPM period. The orange laser output is obtained by frequency mixing \(\lambda_{1}\) and \(\lambda_{2}\) whereas the blue laser is generated by frequency doubling of \(\lambda_{1}\). Theoretically, the maximum SHG power can be calculated using the relation \(P_{SHG}=8\pi d_{eff}^{2}P_{1}^{2}L^{2}/n_{SHG}n_{1}^{2}\epsilon_{0}\lambda_{1}^{2} \omega_{f}^{2}\)[22] and the corresponding conversion efficiency is given as \(\eta~{}=~{}P_{SHG}/P_{1}^{2}\). Similarly, the theoretical sum frequency output power can be estimated using the relation \(P_{SFG}~{}=~{}32\pi^{2}d_{eff}^{2}P_{1}P_{2}L/n_{SFG}\epsilon_{0}\lambda_{SFG}^ {2}c(n_{1}\lambda_{1}~{}+~{}n_{2}\lambda_{2})\)[23], and the corresponding conversion efficiency can be given as \(\eta~{}=~{}P_{SFG}/P_{1}P_{2}\), where \(c\) is the speed of light in vacuum, \(\epsilon_{0}\) is the permittivity in vacuum, and \(d_{eff}~{}=~{}2d_{33}/\pi\) is the effective nonlinear coefficient of MgO:PPLN. \(n_{SHG}\), \(n_{SFG}\), \(n_{1}\), and \(n_{2}\) are refractive indices at \(\lambda_{SHG}\), \(\lambda_{SFG}\), \(\lambda_{1}\), and \(\lambda_{2}\), respectively, while \(\omega_{f}\) (~43 \(\upmu\)m) is the confocal beam waist. Our design is well suited for Type-0 QPM interaction (\(e~{}+~{}e~{}\to e\)) in MgO:PPLN in order to take advantage of the largest nonlinear coefficient. We chose MgO:LN as the nonlinear material due to its low susceptibility to optical damage photo-refraction and visible induced infrared absorption [24].