Controllable Terahertz Radiation from a Linear-Dipole Array Formed by a Two-Color Laser Filament in Air

We demonstrate effective control on the carrier-envelope phase and angular distribution as well as the peak intensity of a nearly single-cycle terahertz pulse emitted from a laser filament formed by two-color, the fundamental and the corresponding second harmonics, femtosecond laser pulses propagating in air. Experimentally, such control has been performed by varying the filament length and the initial phase difference between the two-color laser components. A linear-dipole-array model, including the descriptions of both the generation (via laser field ionization) and propagation of the emitted terahertz pulse, is proposed to present a quantitative interpretation of the observations. Our results contribute to the understanding of terahertz generation in a femtosecond laser filament and suggest a practical way to control the electric field of a terahertz pulse for potential applications.

Figure 1

(a) Schematic presentation of the experimental setup in a polar coordinate ($z$, $\theta$), where the origin $O$ corresponds to the geometric focus of the lens. The $z$ axis corresponds to the propagation axes of the laser beam as well as the THz radiation. $\theta$ and $r$ are used to describe the transverse propagation direction of the THz radiation. (b) Evolution of a THz wave front (red dashed curves) while a THz wave passes through different layers of a plasma channel. $W_0,W_1,W_2,\dots$ are typical points on one trace of a THz wave. The inset shows a dipole formed by charge separation inside a laser-plasma filament.

Figure 2

The pictures of the plasma columns obtained with a laser energy of (a) 0.2, (b) 1.4, and (c) 2.4 mJ, respectively. $T$ is the transmittance of the beam before reaching the CCD camera. The length of the plasma column is 3 mm for (a), 20 mm for (b), and 30 mm for (c). The corresponding measured THz waveforms vs the initial phase difference between the FW and its SH are given in (d)–(f), while the simulation results are shown in (g)–(i). Typical THz waveforms obtained when $\mathrm{\Delta }{\varphi }_i=-\pi /2$ (solid curve) and $\mathrm{\Delta }{\varphi }_i=0$ (dashed curve) with (j) a 3-mm-long plasma and (k) a 30-mm-long filament. Corresponding simulation results are shown in (l) for a 3-mm-long plasma and (m) for a 30-mm-long filament.

Figure 3

Spatial distributions of the THz electric field for (a) a 3-mm-long plasma and (b) a 30-mm-long filament. The $r\text{−}z$ plane is defined in Fig. 1. Angular distributions of the intensity of the THz emitted from (c) the 3-mm-long plasma and (d) the 30-mm-long filament, respectively.

Figure 4

The location of an iris is (a) 0, (b) 5, and (c) 15 mm right to the beginning of the filament. (d)–(f) THz waveforms change with $\mathrm{\Delta }{\varphi }_i$ measured with an iris at the location of (a)–(c), respectively.

Figure 5

THz amplitudes change with the filament length. The triangles show the experimental data obtained with $\mathrm{\Delta }{\varphi }_i=0$, and the dashed line is the corresponding simulation result. The circles show the experimental data with $\mathrm{\Delta }{\varphi }_i=-\pi /2$, and the solid line is the corresponding simulation result.