## 4 Results and Discussion  
### Power Dependence  
The maximum input fundamental powers were measured before Crystal 1 to be 418 mW (\(P_{1}\)) at 1545.7 nm (\(\lambda_{1}\)) and 229 mW (\(P_{2}\)) at 975.2 nm (\(\lambda_{2}\)). We estimated the beam waist radii of \(\lambda_{1}\) and \(\lambda_{2}\) to be \(\sim\)68 \(\upmu\)m and \(\sim\)43 \(\upmu\)m inside the crystals, respectively. A comparison of the resulting maximum output powers and corresponding conversion efficiencies with expected calculated values are summarized in Table 1. Perhaps, the total orange output power can be enhanced by anti-reflection (AR) coating the end faces of each crystal in order to minimize Fresnel reflection losses. We can infer from Table 1 that, in comparison to single crystals, the conversion efficiency is higher in the cascaded module  
Figure 1: Schematic of the experimental setup. The beams are focused into single-pass cascaded module to generate orange output by sum frequency generation (SFG). EDFA: erbium-doped fiber amplifier; WDM: wave division multiplexer; CL: collimator; L\({}_{1}\) and L\({}_{2}\): lenses; PM: power meter; OSA: optical spectrum analyzer; TLS, tunable laser source; LD, laser diode.  
although lower than the expected conversion efficiency. We attribute the losses to the relative phase offset between the fundamental and SFG beams primarily due to dispersion in air and focusing lenses. The refractive nature of the lens causes color aberration since the focusing lengths for both fundamental wavelengths are different and consequently different beam waist radii results in the second crystal. In order to optimize the conversion efficiency, these limitations can be overcome by focusing the fundamental sources separately into the second crystal. Other possible reasons for the discrepancy between experimental and calculated values may originate from uneven temperature distribution within the crystals and/or poling imperfections in the QPM structure.  
Figure 2a shows the CW orange power as a function of the total input power incident on the two individual crystals and for the cascaded case. The TLS power, \(P_{1}\) was fixed at 418 mW (maximum) and the LD power, \(P_{2}\) was increased steadily to a maximum value of 229 mW by varying the operating current. Figure 2b shows the measured beam profiles when \(P_{1}\) and \(P_{2}\) were 418 mW and 229 mW, respectively. For all the cases, the SFG beam was nearly identical in the horizontal direction with \(M_{x}^{2}\sim 2.1\) at 595.9 nm, 597.3 nm, and 596.9 nm for Crystal 1, Crystal 2, and the cascaded module, respectively. In the vertical direction, we measured \(M_{y}^{2}\sim 1.9\), \(M_{y}^{2}\sim 2.0\), and \(M_{y}^{2}\sim 4.1\) for Crystal 1, Crystal 2, and the cascaded module, respectively.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Crystal**} & \multicolumn{2}{c}{**P\({}_{\text{SFG }}\)(mW)**} & \multicolumn{2}{c}{**Conversion Efficiency (\% W\({}^{-1}\))**} \\ \cline{2-5}  & **Calculated a  & Experiment \\ \hline Crystal 1 & 38.2 & 7.1 & 39.9 & 7.4 \\ Crystal 2 & 15.2 & 4.3 & 15.9 & 4.5 \\ Cascaded module & - & 10.0 & 23.4 & 10.4 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Calculated and experimental comparison of output powers and conversion efficiencies in single crystals and cascaded module.  
Figure 2: _Cont._