## 3 Results and Discussion  
A regeneratively amplified mode-locked femtosecond Ti: sapphire laser with a pulse width of 100 fs and a wavelength of 800 nm was used as a trigger source, the laser pulse energy was 97.5 \(\upmu\)J, and the bias voltage was \(\pm\)2.0 kV, according to the demand for the streak camera. The output waveform is shown in Figure 4.  
As shown in Figure 4, the peak voltage of negative output pulse is 1.329 kV, and the transmission efficiency is 66.45%. The rise time of the pulse is 164 ps, and the time of linear range constitutes 92 ps with the corresponding voltage range of 0.598 kV, which yields a slope of 6.5 kV/ns. The rise time of positive pulse and the fall time of negative pulse are 174 ps and 164 ps, respectively, the difference is about 10 ps, and the error is about 6%, which is within the margin of error, for a femtosecond streak camera. The error is mainly caused by the electrical elements (resistors and capacitors) in electrical circuits, because their values are not exactly the same for two corresponding elements in the symmetric sweep circuits in Figure 2. The rise time of the pulse is mainly decided by the photoelectric response time of the GaAs substrate and the time duration of pump laser, and the pulse width is mainly decided by the lifetime of carriers of GaAs substrate. Moreover, the performance of the device can be improved by optimizing device geometry parameters. For example, the impedance of device elements should be matched by optimizing the microstrip line.  
When the bias voltage is \(\pm\) 2.0 kV, the electric field is 11.4 kV/cm. In our previous research [14], an avalanche gain (G) for high-gain operation was proposed to demonstrate the level of avalanche  
Figure 4: The output waveform at a bias voltage of \(\pm\) 2.0 kV and a laser pulse energy of 97.5 \(\upmu\)J.  
Figure 3: Schematic diagram of the testing circuit.  
multiplication in the photoconduction process of a GaAs PCSS. The expression of G is shown in Equation (1):  
\[G=N_{G}/N_{L} \tag{1}\]  
where \(N_{G}\) is the number of photo-activated carriers in high-gain operation and \(N_{L}\) is the number of photons absorbed by SI-GaAs. However, the result shows that \(G\) is \(1\times 10^{-3}\), that is, the carriers can not generate multiplication in this experiment.  
When the GaAs PCSS operates in the linear mode, the jitter mainly comes from the instability of the laser performance [15; 16; 17]. In the previous research, the jitter time was 14.3 ps when GaAs PCSSs was triggered by the incident laser pulse with a time duration of 500 ps [1]. That is, the jitter time is much less when GaAs PCSS is triggered by a femtosecond laser pulse with a pulse duration of 100 fs. Now, the jitter time is so small that it cannot be measured by the 6 GHz oscilloscope. The 10 output waveforms measured at the same experiment condition are shown in Figure 5, and they overlap very well, which means the stability of our device is good. The relative standard deviation (RSD) of the output voltage can be defined as the stability of the PCSSs. Under each fixed bias voltage, one can obtain the stability of the PCSSs by calculating the RSD of the output voltage difference:  
\[RSD=\frac{\sqrt{\frac{\sum_{i=1}^{n}(U_{i}-\overline{U})^{2}}{n-1}}}{ \overline{U}}\times 100\% \tag{2}\]  
where RSD is the stability of the PCSSs, \(\overline{U}\) is the average of \(U_{i}\), and n is the number of trigger times. In this way, the RSD values were measured as 1.3% and 0.83%, when the bias voltages were +2.0 and \(-\)2.0 kV, respectively, which is within the error range.