† Corresponding author. E-mail:
Project supported by the National Natural Science Foundation of China (Grant Nos. 11574387, 11404335, 11474002, and 11535001), the National Basic Research Program of China (Grant Nos. 2013CBA01501 and 2013CB922401), the Strategic Priority Research Program of the Chinese Academy of Sciences (Grants Nos. XDB16010200 and XDB07030300), and the Science Challenge Project, China (Grant No. TZ2016005).
The multiple filamentation of terawatt femtosecond (fs) laser pulses is experimentally studied in a natural environment. A more than 30-m long plasma filament with a millimeter diameter is formed by the collimated fs laser pulse freely propagating in an open atmosphere. This study provides the first quantitative experimental data about the electron density of a long range light filament in the atmosphere. The electron density of such a filament is quantitatively detected by using an electric method, showing that it is at the 1011-cm−3 level.
During the propagation of intense fs laser pulse in air, the filamentation could take place when the self-focusing effect is saturated by the optical field ionization-induced plasma, diffraction, higher-order nonlinear effect, and other linear or nonlinear factors.[1–5] As a result of filamentation in air, a long conductive channel can be produced. Based on this phenomenon, many potential applications were proposed, such as guiding of lightning discharge,[6–9] transportation of electromagnetic energy,[10,11] laser assisted precipitation,[12,13] etc. The physical properties of light filaments over a long distance (hundred meters level and longer) are meaningful for applications based on the conductivity of a filament. However, most experiments studied the meter-scale filaments under laboratory conditions by using initial geometric focusing of fs laser pulse. Several research groups observed multiple filamentation of collimated intense femtosecond laser pulse in a range from tens of meters to kilometers.[14–20] The experimental observations showed that the diameter of such a long filament is at the millimeter level,[16–18] and the electron density was numerically estimated at 1011 cm−3 ∼ 1012 cm−3.[16] Some researches confirmed the existence of free electrons in a filament by detecting the electromagnetic radiation from the filament.[19] However, there have been no reported quantitative experimental data about electron density of such long filaments in air to our knowledge.
In this paper, we study the long distance filamentation of a femtosecond laser pulse freely propagating in atmosphere in a natural environment. Diagnosis of the filament is performed over a 30-meter propagation distance. The electron density inside the filament, detected by an electric method is at a 1011 cm−3 level.
The experiment was carried out in a meteorological observatory in the Tianshan Mountains of the Xinjiang Uygur Autonomous Region, China. The local altitude is about 2000 meters. The light source was a 2-TW Ti: sapphire laser system at a 40-fs pulse duration and 10-Hz repetition rate. The initial width of the laser beam was about 10 mm, and the beam pattern was recorded by photo paper as shown in Fig.
The pulse energy used for detecting the electron density inside filaments was 55 mJ. The laser pulse was reflected from the laser room to the courtyard wall of the observatory by several mirrors. The optical path of the laser pulse from the compressor to the last mirror was about 10 meters. The total propagation distance of the laser pulse was about 53 meters. When the laser pulse was compressed to the best condition of about 40-fs pulse duration, the strong thin multi-filaments were formed at about a 3-m propagation distance. These thin filaments could damage any optical elements. Therefore, in order to protect the mirrors, we applied some negative chirps to the laser pulse to extend the start position of filamentation to an over 20-m distance. The intensity distributions of laser beam at different propagation distances were recorded by light-sensitive photo paper and it was vertically placed along the horizontal propagate direction. The electron density of the filament was detected by an electric method,[21–28] the setup is presented in Fig.
Figure
It should be noted that the orientations of filaments randomly drift from shot to shot due to the wind and air turbulence.[29–31] With the increase of the propagation distance, the drift area of multi-filaments becomes larger and larger. Figures
When the diameter of the filament is about 1 mm, it can easily pass through the 2-mm hole on the front electrode without being blocked if there is no drift of its position. The plane electrode is larger than the whole beam pattern, and the distance between filaments is always longer than 2 mm, in which condition, only one of the filaments is allowed to pass through the front electrode. The filament may be partially blocked by this hole, in this case the electric signal could be weakened, and therefore the electric signal is also changed shot by shot. Figure
The resistance of the plasma channel between the two electrodes can be calculated from the electric signal by Ohm’s law. Furthermore, we can estimate the electron density of the plasma channel from the formula for electrical conductivity of plasma:[26]
In this work, the light filament with more than 30 m in length has been produced by freely propagating femtosecond laser pulses. The multi-filament structure and the drift of filament are recorded by photo paper. The electron density of such a long filament has been quantitatively measured by using the electric method, showing that it is at a 1011-cm−3 level. This electron density of freely propagating filament is much lower than that of the filament produced by pre-focused laser pulse (1015 cm−3 ∼ 1016 cm−3), but the advantage of freely propagating filaments is that their length can be extended to the kilometer level,[15,17,19] which is necessary for massive applications such as lighting control[6] and remote transport of electromagnetic energy.[10] The electron density and lifetime of a long range filament can be increased by a fs laser pulse sequence.[28] However, a lot of research work still needs to be performed to make the long-range filament applicable.
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