# Online Measurement of Internal Parameters in a Quasi-CW Diode-Pumped Nd:YAG Laser
## 4 Results and Discussion  
We performed online measurements of the internal parameters of a Nd:YAG solid-state laser employing the method of introducing variable polarization reflective loss. The experimental arrangement for the measurements is shown in Figure 3. The laser outputs were recorded by an EPM2000 energy detector. We used a quasi-CW pump and an incident pump current of 45 A, which corresponds to single-pulse incident pump energy of 500 mJ. The results of the measurement of the parameters are listed in Table 1.  
Under quasi-CW pumping, the recorded single-pulse outputs \(E_{o}\) from mirror M2 and \(E_{Mo}\) from the measurement cell as functions of the variable polarization reflective loss \(T(\theta)\) and the polarization reflective loss \(T(\theta)\) with respect to the rotating angle of \(\theta\) are illustrated in Figure 6. \begin{table}
\begin{tabular}{l c c} \hline \hline
**Parameters** & **Measurement Results** & **Datasheets** \\ \hline Transmittance of M2, \(t_{2}\) & 22.45\% & 23.8\% \\ Round-trip net optical loss of the laser crystal, \(\delta\) & 0.0366 & — \\ Absorption coefficient of the laser crystal, \(\alpha\) (cm\({}^{-1}\)) & 0.0028 & (2\(\sim\)3) \(\times\) 10\({}^{-3}\) \\ Total optical losses, \(\delta_{T}\) & 0.2611 & — \\ Small-signal gain coefficient, \(g_{0}\) (cm\({}^{-1}\)) & 0.1993 & — \\ Saturation parameter, \(I_{S}\) (kW/cm\({}^{2}\)) & 2.83 & 2.90 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Results of the measurement of internal parameters (calibrated \(\delta_{i}\) = 0.008). Figure 5: Schematic of the experimental setup for the comparison and the optimization. The laser outputs \(E_{o}\) and \(E_{Mo}\) have the same value of 63.5 mJ, which corresponds to a polarization reflective loss \(T(\theta_{r})\) of 21.65% as shown in Figure 6. A transmittance \(t_{2}\) of mirror M2 of 22.45% is obtained by applying the measured \(T(\theta_{r})\) and calibrated \(\delta_{i}\) to Equation (14). Comparing the measured value of 22.45% with the calibrated transmittance value of 23.8% of mirror M2, the measurement error is around 1.35%. Figure 6 shows that the curve of \(T(\theta)\) has a linear zone from 20% to 60%, which corresponds to the rotating angle \(\theta\) from 20\({}^{\circ}\) to 38\({}^{\circ}\). There is a nonlinear zone in the curve at \(T(\theta)<20\%\) and a near oscillation stop zone (also a nonlinear zone in the curve) at \(T(\theta)>60\%\). Applying the transmittance \(t_{2}\) of 22.45% and the recorded outputs of \(E_{o}\) and \(E_{Mo}\) within the linear zone of the curve to Equation (13), the round-trip net optical loss \(\delta\) of 0.0336 was determined as shown in Figure 7.  
Figure 7 shows the measured round-trip net optical loss \(\delta\) as a function of the rotating angle \(\theta\), and the rotating angle \(\theta\) with respect to the polarization reflective loss \(T(\theta)\). The measured data of \(\delta\) have a better convergence at the fitted-data value of 0.0336 between the rotating angles \(\theta\) of 23\({}^{\circ}\) and 32\({}^{\circ}\) and some divergence at the values of 0.043 and 0.0262 corresponding to the rotating angles of  
Figure 6: The laser outputs \(E_{o}\) and \(E_{Mo}\) as a function of the variable polarization reflective loss \(T(\theta)\), and the variable polarization reflective loss \(T(\theta)\) with respect to the rotating angle \(\theta\). Figure 7: The round-trip net optical loss \(\delta\) as a function of the rotating angle \(\theta\), and the rotating angle \(\theta\) with respect to the polarization reflective loss \(T(\theta)\). \(20^{\circ}\) and \(35^{\circ}\), which are near the nonlinear region and the oscillation stop zone, respectively. In the nonlinear region, the indication error of the measurement cell is the main factor in the measurement of \(\delta\). In the near oscillation stop zone, the measurement error of \(E_{MO}/E_{O}\) is the main factor due to the unstable output of the laser.