## 2 Experimental Setup  
The schematic diagram for the experimental setup is shown in Figure 1. A Xe flash lamp with an arc length of 70 mm, normal pressure 450 Torr, and a maximum energy output of 20 J at 850 volts was used as the pump source. A 1.1 at %-doped Nd:YAG rod with a length of 50 mm and a diameter in 3 mm was used as the gain medium. Both surfaces of the gain medium were coated with anti-reflection (AR, R \(<\) 0.01%) at 1064 nm and wedged with 2 degrees to prevent the parasitic pulse and the unwanted etalon effect. The Nd:YAG rod and the flash lamp were placed inside a pumping enclosure consisting of reflectors coated with silver on the inside surface to improve the pump efficiency. The laser resonator was designed as a convex-concave cavity to enlarge the laser mode volume for achieving high pulse-energy output with good beam quality [32]. The radius of curvature of the convex front mirror was \(-\)500 mm, and the surface was coated for high reflection (HR, R \(>\) 99.9%) at 1064 nm. For the concave output coupler, the radius of curvature for the resonant surface was 600 mm, and the coating was partially reflective (R \(=\) 55%) at 1064 nm. The 1064 nm anti-reflective coated outer surface of the output coupler was designed to be convex with a curvature of \(-140\) mm to reduce the output divergence. A Cr\({}^{4+}\):YAG crystal with initial transmittance of 35% was employed as the saturable absorber. The effective cavity length was chosen to be 90 mm. With a weak thermal lensing effect, the laser was operated in a stable region [32; 34]. The output pulse energy was able to be stabilized around 21 mJ with one-sigma stability of 1% under continuous-firing operation at a repetition rate of 0.2 Hz after warm-up. However, under the randomly single-shot operation, the one-sigma energy stability was up to 3%, coinciding with an increased energy fluctuation of \(\pm 10\%\). For varied incident energy for the air breakdown, an attenuator was placed behind the laser cavity to adjust the pulse energy by utilizing the polarization given by the Brewster plate. The Q-switched pulses were able to be attenuated with a range from 0 to 11 mJ.  
A focusing unit composed of a beam expander with 10 times magnification and a triplet focusing lens with a 12 cm focal length is exploited to tightly focus the Q-switched pulses for inducing breakdown in atmospheric air. The focused laser beam waist of 7 um in radius was measured through the knife-edge method. We also measured the beam radius within 1-3 mm before and after the focal point to verify the beam size at focal point through the curve fitting with Gaussian-beam propagation theory. High-speed photodetectors with a silicon base (PD2, EOT Inc., ET-2030 with rising time 300 ps) and an InGaAs base (PD1, PD3, EOT Inc. (Traverse City, MI, USA), ET-3500 with rising time 25 ps) were respectively employed to detect the temporal characteristics of the induced plasma as well as the incident and residual laser pulses. The output signal of the photodetectors was connected to a digital oscilloscope (Agilent DSO 80,000) with 10 GHz electrical bandwidth and a sampling interval of 25 ps. The time-averaged radiation spectrum of the induced plasma is measured by a compact spectrometer (UVisIR Inc. (Traverse City, MI, USA), FullScan-LR) with a resolution \(<5\) nm.