## 3 Results
### Temporal Characteristics of Air Breakdown  
After determining the air breakdown threshold condition from different pulse shapes, the laser was operated to output modulated pulses with high peak power intensity that can 100% induce plasma signal for studying the temporal dynamics. Figure 4a depicts the temporal characteristics for the incident pulse, residual pulse, and the radiation of induced plasma after carefully calibrating time delay from the optical path difference. The temporal profiles of the incident and residual pulse reveal that the air molecules absorb only partial energy from the excitation pulse at the initial stage before the plasma is triggered. When the power intensity exceeds the threshold for air breakdown; however, most of the energy for the excitation pulse is depleted to build up the radiation of plasma with a rising time of about 2 ns. In addition, when the decaying instantaneous power of the excitation pulse is insufficient to sustain the buildup of plasma, plasma radiation begins to decay with a decaying time of a few tens of nanoseconds. Intriguingly, there were small peaks on the radiation pulse shape of induced plasma, corresponding to the mode-locked modulation subpulses of the incident laser pulse. It implied that the ionization process and correspondent plasma core density might be modulated rapidly, too. However, due to the long decay time of radiation, the fast dynamics cannot be seen through radiation directly. The fast dynamics was observed by the self-scattering method in the coming section.  
By replacing the HR-1064 nm filter with a band-pass filter at 1064 nm in front of the photodiode--PD2, we found that the 1064 nm pulse laser was scattered by the plasma induced by the laser itself. Here, we called the phenomenon'self-scattering'. The temporal characteristic of the scattered 1064 nm pulse in the above experiment was illustrated in the  
Figure 4: (**a**) Temporal characteristics for the 1064-nm incident pulse, 1064-nm residual pulse, white-light radiation of induced plasma. (**b**) Temporal characteristics for the 1064-nm incident pulse, the 1064-nm scattered pulse and the calculated scattering rate.  
upper part of Figure 4b. Dividing the temporal trace of scattered pulse to the incident pulse, we defined the above temporal result as scattering rate, which was shown in the lower part of Figure 4b. With the self-scattering method, the time-dependent scattering ability of induced plasma was obtained without additional probe light. Notice that when the signal of the scattered pulse was small, the calculated result of the scattering rate showed plenty of noise, which was ignored in the lower part of Figure 4b.  
Furthermore, the start-up time of scattering rate was matched the third subpulse that can induce initial breakdown with the power exceeding threshold power, and was 0.25 ns before the plasma emission observed. It implies that the self-scattering method could be useful for studying the plasma formation after comparing quantitatively with the method of interferometry, shadowgraphy, or high-speed photography using ns intensified CCD.  
Finally, the time-averaged radiation spectrum of the induced plasma was further measured, as shown in Figure 5. The peaks of the experimental spectrum were found to correspond to the excited levels of the gas molecules in the air [36] well. In addition, the envelope of the radiation spectrum is confirmed to be in good consistence with the reported result in previous literature [41].