Owing to rapid development in laser technology, femtosecond lasers can form plasma filaments of up to 100 m in length. This type of plasma channel has good continuity and relatively low resistivity, which is conducive to guiding long-distance discharge. Therefore, it has broad application prospects in the fields of high-voltage discharge and electric field measurement. Accurate measurement of the relevant parameters of femtosecond lasers is the premise of applying femtosecond lasers in various fields. Existing optical photography methods can accurately measure optical parameters such as the size, number, and service life of the laser filament, but there are few accurate measurement methods for the electrical characteristics of femtosecond laser filaments. The electrical characteristics of laser filaments mainly include the current characteristics and equivalent resistance in an external electric field. Scholars have studied the plasma characteristics of femtosecond laser filaments. This type of research can reflect the current-carrying capacity of the laser filament and qualitatively reflect the equivalent resistance of the laser filament; however, it cannot quantify the equivalent resistance of the laser filament. To measure the femtosecond laser filament equivalent resistance, the measurement principle, measurement accuracy, equivalent circuit, and measurement signal processing of the experimental measurement device must be considered. In this study, a method combining experiments and simulations is used. The experimental data are input into the simulation model, an expression for the femtosecond laser filament equivalent resistance is obtained, and the influence of the laser parameters on the femtosecond laser filament equivalent resistance is analyzed. We hope that this research method can characterize the electrical characteristics of femtosecond laser filaments under specific laser energies and focusing distances to provide parameter support for the application of femtosecond lasers in high-voltage fields.

In this study, the laser filament is injected into a plate-plate gap with a central opening, and a uniform electric field is applied between the plates. The sampling resistance and direct current (DC) voltage source are connected in series between the two plate electrodes to form a discharge circuit. The high-voltage probe is connected through the oscilloscope at both ends of the sampling resistance to obtain the voltage waveform of the sampling resistance. According to the circuit principle, the board-to-board discharge branch in the discharge circuit is equivalent to a discharge branch comprising resistance, inductance, and capacitance. The sampling resistance waveform measured in the experiment is input into the simulation model to obtain the parameter values of each equivalent element in the plate-plate gap discharge branch and the equivalent resistance of the laser filament in a uniform electric field.

Through the joint analysis of experimental data and simulation, the equivalent circuit of the experimental circuit and the parameters of each element in the equivalent circuit are obtained. The waveform simulated in the equivalent circuit better simulates the wavefront characteristics of the sampled resistance voltage waveform in the experiment and has good follow-up to the subsequent waveform. The oscillation period and amplitude of the simulated waveforms are similar to those of the measured waveforms. According to the experimental data and simulation circuit, the characteristics of the laser filament equivalent resistance are as follows: the applied electric field and laser energy have a significant impact on the laser filament equivalent resistance. Under an applied electric field of 0.2-1.2 kV/cm and within 2-30 mJ laser energy, the laser filament equivalent resistance decreases approximately linearly with the increase in the applied electric field or laser energy, as shown in Fig. 2 and Fig. 3. The equivalent resistance of the filament formed by femtosecond laser-assisted focusing in the experimental circuit first decreases and then increases with an increase in the propagation distance of the filament. When the 2.7 mJ femtosecond laser filament passing through a 5 m focal length lens passes through a 2.5 cm discharge gap, the equivalent resistance corresponding to the propagation distance of the filament in the range of 473.6-501.6 cm is 457.5-9122.5 kΩ, as shown in Fig. 11.

In this study, a method for measuring the equivalent resistance of femtosecond laser filament is improved, which could give the measurement results more accurate physical significance, and the electrical characteristics of femtosecond laser filaments are studied in combination with a simulation circuit. The current characteristics of the femtosecond laser filament in a uniform electric field and the variation effect of the equivalent resistance of the filament channel in the circuit are obtained when the distance between the focusing lens and plate gap changes. This measurement method considers the influence of stray capacitance, laser filament inductance, and charging capacitance of the measuring device on the measurement results, and it can more accurately measure the equivalent resistance of the laser filament when the laser energy and focusing distance are determined to provide parameter support for the application of femtosecond lasers in the field of high voltage.