# Online Measurement of Internal Parameters in a Quasi-CW Diode-Pumped Nd:YAG Laser
## 4 Results and Discussion
The absorption coefficient \(\alpha\) of the laser crystal of 0.0028 cm\({}^{-1}\), obtained by applying the fitted-data value of 0.0336 to Equation (8), falls within the scope of the Nd:YAG datasheet values and thus has a better agreement with the values in the datasheet. The total optical loss \(\delta_{T}\) of 0.2611 was determined by applying the results of \(t_{2}\) and \(\delta\) to Equation (18). Upon rotating PL2 to make the laser just cease to oscillate, an oscillation-stop \(\theta_{m}\) of about \(43^{\circ}\) was recorded. Applying the measurement results of \(\theta_{m}\) and \(\delta_{T}\) and the calibrated \(\delta_{i}\) to Equation (17) and Equation (16), the small-signal gain coefficient \(g_{0}\) of 0.1993 cm\({}^{-1}\) was obtained. The influence of the measured errors of \(\delta\) on the small-signal gain coefficient \(g_{0}\) was investigated. Figure 8a illustrates the small-signal gain coefficient \(g_{0}\) with respect to different values of \(\delta\). The measured \(g_{0}\) is 0.1993 cm\({}^{-1}\) at the fitted-data value \(\delta\) of 0.0366, and the maximum deviation of \(g_{0}\) is less than 1.7%. Therefore, the measurement of \(g_{0}\), influenced by the measured deviation of \(\delta\), must be ignored in a high pump power laser. We also investigated the influence of the measurement errors of the oscillation-stop angle \(\theta_{m}\) on the measurement of \(g_{0}\). The maximum measured deviation of \(g_{0}\) produced by a rotating angle error of approximately \(1^{\circ}\) is less than 1% as shown in Figure 8b. Thus, the accuracy of the measurement cell meets the measurement requirement of \(g_{0}\). Applying the measurement results of \(\delta\), \(g_{0}\), and \(t_{2}\) to Equations (10) and (11), the saturation parameter \(I_{S}\) of 2.83 kW/cm\({}^{2}\) was determined. The saturation parameter \(I_{S}\) as a function of the rotating angle \(\theta\) of the measurement cell is shown in Figure 9. The measured \(I_{S}\) has a minor fluctuation around the mean value of 2.83 kW/cm\({}^{2}\) as the rotating angle \(\theta\) varies from \(5^{\circ}\) to \(40^{\circ}\). The maximum difference in measured \(I_{S}\) was calculated to be approximately 0.2 kW/cm\({}^{2}\) with an oscillation wavelength of 1064 nm and at a room temperature of 25 \({}^{\circ}\)C. For a homogeneously broadened four-level system that employs the Nd:YAG active medium, the saturation parameter \(I_{S}\) is given by [13] as \(I_{S}=ln\
u/\big{(}\sigma\tau_{f}\big{)}\). The saturation parameter is only a function of the transmission cross-section \(\sigma\), the laser transmission frequency \(\
u\), and the fluorescence lifetime \(\tau_{f}\) between the laser transmission levels. Therefore, the saturation parameter \(I_{S}\) will remain a constant value as the intra-cavity loss varies. The saturation parameter value obtained in our experiments agrees with the theoretical value of 2.9 kW/cm\({}^{2}\) in the data sheets. Figure 8: Measured deviation of the small-signal gain coefficient \(g_{0}\). (**a**) Small-signal gain coefficient \(g_{0}\) with respect to different values of \(\delta\). (**b**) Small-signal gain coefficient \(g_{0}\) influenced by the measured oscillation-stop angle \(\theta_{m}\). A validity investigation is usually done by comparing the laser output experimental data with the predictions of a suitable laser model using the measurement results of gain, losses, and the saturation parameter.