Experimental measurement of the wake field in a plasma filament created by a single-color ultrafast laser pulse

A laser plasma wake field in a single-color femtosecond laser filament determines the acceleration of ionized electrons, which affects the intensity and bandwidth of the emitted terahertz wave and is important for understanding the fundamental nonlinear process of THz generation. Since the THz wave generated by a laser wake field is extremely small and easily hidden by other THz generation mechanisms, no method exists to measure this wake field directly. In this paper, a simple and stable method for determining the amplitude of the laser plasma wake field is presented. Based on the cancellation of a positive laser plasma wake field and an external negative electric field, the “zero point” of the intensity of the generated THz wave at some frequency can be used to determine the exact amplitude of the corresponding laser plasma wake field. This finding opens an avenue toward the clarification of ultrafast electronic dynamic processes in laser-induced plasmas.

Figure 1

(a) Simulation result of the amplitude of the current spectrum originating from the laser plasma wake field [$j_z^w\left(\omega \right)$, blue (upper) solid line], the external electric field [$j_z^e\left(\omega \right)$, red (lower) solid line], and the sum of the two [$j_z^{w+e}\left(\omega \right)$, black dot dash line] for an external electric field of −2 kV/cm. (b) The amplitude of the total current spectrum for different values of the external electric field.

Figure 2

Theoretical relations among the THz frequency, the external electric field, and the amplitude of the laser plasma wake field. (a) Simulation result of THz radiation at different frequencies as a function of the external electric field. The black (dot dash), blue (solid), green (dash), and orange (double-dot dash) lines represent THz frequencies of 0.5, 1.5, 2.0, and 2.5 THz, respectively. (b) The calculated amplitude of the laser plasma wake field $E_L$ as a function of the generated THz frequency.

Figure 3

Schematic diagram of the experimental setup showing the generation and detection of THz radiation. The orientation of the EO crystal and optical detection polarization are chosen to measure the appropriate THz field polarization. Inset (a) shows the construction of two circular copper electrodes and the direction of electron movement in the laser plasma under the synthesized electric field.

Figure 4

Experimental measured relations among the THz frequency, external electric field and amplitude of the laser plasma wake field. (a) Measured THz radiation with different frequencies under different external electric fields and their quadratic fit curves. The black (circle), blue (triangle), green (star), and orange (square) points represent a THz frequency of 0.1, 0.5, 1.0, and 1.5 THz, respectively. The inset shows several examples of the measured time-domain electric fields. (b) Comparison of the amplitude of the laser plasma wake field $E_L$ corresponding to different THz frequencies (black triangles) with the calculated results (gray circles).

Figure 5

The dependence of the zero point position of the 1.5-THz component on the angle of the external electric field. (a) The solid line from upper to lower are simulated intensity evolution of the THz amplitude as a function of the external electric field with an angle of 15 °, 35 °, 45 °, and 55 °, respectively. (b) The dot line from upper to lower are measured intensity evolution of the THz amplitude as a function of the external electric field with an angle of 4 °, 16.7 °, and 35 °, respectively.