Carrier-envelope phase-dependent electronic conductivity in an air filament driven by few-cycle laser pulses

The modulation of the electron conductivity in an air filament, which is produced by carrier-envelope phase (CEP) stabilized 7-fs laser pulses, is realized experimentally. Numerical results based on a coupled 3D+1 generalized nonlinear Schrödinger equation including the real electric-field dependent ionization model are in good agreement with those from the experiment. It is demonstrated that the CEP effect on the electron density originates from the CEP-induced modification of the electric field of the laser pulse, and this modification is amplified during nonlinear propagation. The results provide important information to help understand the physical mechanism of the filaments driven by few-cycle femtosecond laser pulses.

Figure 1

Schematic of the experiment. (a) The laser system includes an acousto-optical modulator (AOM) and chirped pulse amplification (CPA). The 0-to-f and f-to-2f interferometers are controlled by the fast and slow feedback loops through the AOM, respectively. (b) Schematic of the circuit system used to measure the electron conductivity in the laser induced filament. (c) The voltage signal detected by an oscilloscope.

Figure 2

Comparison of the maximum voltage signal with locked (a) and unlocked (b) CEP.

Figure 3

(a) Spatial distribution of the electron density in the filament from the solution of the nonlinear Schrödinger equation. (b) Distribution of on-axis electron density in the range $50<z\text{[mm]}<130$ for different CEP.

Figure 4

(a) On-axis electric field at different $z$ for ${\phi }_{\text{CE}}=0$ and (b) on-axis electric field at $z=109$ mm for four ${\phi }_{\text{CE}}$.

Figure 5

Comparison of the conductivities as a function of CEP under two conditions. After making the integration over space and time, the red curve with hollow rectangles ($C_{np}$) and the black curve with solid circles ($C_p$) are the calculated conductivity without and with propagation effects, respectively.