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Optics Express

Optics Express

  • Editor: Michael Duncan
  • Vol. 14, Iss. 11 — May. 29, 2006
  • pp: 4915–4922
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Long lifetime plasma channel in air generated by multiple femtosecond laser pulses and an external electrical field

Jiabin Zhu, Zhonggang Ji, Yunpei Deng, Jiansheng Liu, Ruxin Li, and Zhizhan Xu  »View Author Affiliations


Optics Express, Vol. 14, Issue 11, pp. 4915-4922 (2006)
http://dx.doi.org/10.1364/OE.14.004915


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Abstract

The lifetime of a plasma channel produced by self-guiding intense femtosecond laser pulses in air is largely prolonged by adding a high voltage electrical field in the plasma and by introducing a series of femtosecond laser pulses. An optimal lifetime value is realized through adjusting the delay among these laser pulses. The lifetime of a plasma channel is greatly enhanced to 350 ns by using four sequential intense 100fs(FWHM) laser pulses with an external electrical field of about 350kV/m, which proves the feasibility of prolonging the lifetime of plasma by adding an external electrical field and employing multiple laser pulses.

© 2006 Optical Society of America

The generation of light filaments in air has attracted broad interest [1

1. A. Braun, G. Korn, X. Liu, D. Du, J. Squier, and G. Mourou, “Self-channeling of high-peak-power femtosecond laser pulses in air,” Opt. Lett. 20, 73–75 (1995). [CrossRef] [PubMed]

4

4. S. A. Hosseini, Q. Luo, B. Ferland, W. Liu, N. Akozbek, G. Roy, and S.L. Chin, “Effective length of filaments measurement using backscattered fluorescence from nitrogen molecules,” Appl. Phys. B 77, 697–702 (2003). [CrossRef]

] due to their applications for lightning protection [5

5. R. Ackermann, K. Stelmaszcyk, P. Rohwetter, G. Mejean, E. Salmon, J. Yu, J. Kasparian, G. Mechain, V. Bergmann, S. Schaper, B. Weise, T. Kumm, K. Rethmeier, W. Kalkner, L. Wöste, and J. P. Wolf, “Triggering and guiding of megavolt discharges by laser-induced filaments under rain conditions,” Appl.Phys. Lett. 85, 5781–5783 (2004). [CrossRef]

6

6. F. Vidal, D. Comtois, C.-Y. Chien, A. Desparois, B. La Fontaine, T. W. Johnston, J.-C. Kieffer, H. P. Mercure, and F. A. Rizk, “Modeling the triggering of streamers in air by ultrashort laser pulses,” IEEE Trans. Plasma Sci. 28, 418–433 (2000). [CrossRef]

] and atmospheric remote sensing [7

7. J. Kasparian, M. Rodriguez, G. Méjean, J. Yu, E. Salmon, H. Wille, R. Bourayou, S. Frey, Y.-B. André, A. Mysyrowicz, R. Sauerbrey, J.-P. Wolf, and L. Wöste, “White-Light Filaments for Atmospheric Analysis,” Science 301, 61–64 (2003). [CrossRef] [PubMed]

]. The filaments remain stable over tens of meters or more, which is much longer than the beam’s Rayleigh distance [1

1. A. Braun, G. Korn, X. Liu, D. Du, J. Squier, and G. Mourou, “Self-channeling of high-peak-power femtosecond laser pulses in air,” Opt. Lett. 20, 73–75 (1995). [CrossRef] [PubMed]

3

3. Miguel Rodriguez, Riad Bourayou, Guillaume Méjean, Jérôme Kasparian, Jin Yu, Estelle Salmon, Alexander Scholz, Bringfried Stecklum, Jochen Eislöffel, Uwe Laux, Artie P. Hatzes, Roland Sauerbrey, Ludger Wöste, and Jean-Pierre Wolf. “Kilometer-range nonlinear propagation of femtosecond laser pulses,” Phy. Rev. E 69, 036607 (2004). [CrossRef]

]. This self-guiding effect has been attributed to a dynamic balance between beam self-focusing (owing to the optical Kerr effect) and defocusing (owing to medium ionization). A high degree of ionization as well as a long lifetime of light filaments is preferred in practical application. Recent research on the lifetime of light filaments reported that the lifetime of a light filament could be enhanced by bringing in a second long-pulse laser after a femtosecond laser pulse mainly due to the optical detachment effect [8

8. H. Yang, J. Zhang, W. Yu, Y. J. Li, and Z. Y. Wei, “Long plasma channels generated by femtosecond laser pulses,” Phys. Rev. E 65, 016406(2001). [CrossRef]

10

10. Hui Yang, Jie Zhang, Yingjun Li, Jun Zhang, Yutong Li, Zhenglin Chen, Hao Teng, Zhiyi Wei, and Zhengming Sheng, “Characteristics of self-guided laser plasma channels generated by femtosecond laser pulses in air,” Phys. Rev. E 66, 016406(2002). [CrossRef]

]. The electron density owing to the optical detachment effect maintains itself at about 1012 cm -3 ~1013 cm -3 [9

9. X. Lu, Xi Ting Ting, Li Ying-Jun, and Zhang Jie, “Lifetime of the plasma channel produced by ultra-short and ultra-high power laser pulse in the air,” Acta Physica Sinica 53, 3404–3408 (2004).

]. We hope to further increase the degree of ionization during the total lifetime of a plasma channel.

In our experiment, we applied a high voltage electrical field in the plasma channel induced by a femtosecond laser pulse in air. Results show that the lifetime of the plasma channel had been prolonged and also the degree of ionization increased. The lifetime of the plasma channel reaches about 60 ns with a field of about 350kV/m. We investigated the variation of the lifetime of the plasma channel with the increase in electric field. In addition, we brought in a second femtosecond laser pulse and found that the lifetime of the filament can reach 200 ns with a delay of 60 ns between the first and second pulse. Finally, the lifetime of plasma channel was enhanced to 350 ns by using four sequential laser pulses, which proves the feasibility of prolonging the lifetime of plasma by employing multiple laser pulses.

Fig. 1. Experimental setup; Electrodes a, b, and probe c are set close to the path of the plasma channel induced by femtosecond laser pulse.

We have measured the electrical signals when the fields are 0, 250, and 350kV/m respectively. Meanwhile, through a longitudinal diffraction detection method [14

14. Jiansheng Liu, Zuoliang Duan, Zhinan Zeng, Xinhua Xie, Yunpei Deng, Ruxin Li, and Zhizhan Xu, “Time-resolved investigation of low-density plasma channels produced by a kilohertz femtosecond laser in air,” Phys. Rev. E 72, 026412 (2005). [CrossRef]

], the initial electron density was estimated at about 1710 cm-3 and the diameter of the plasma channel was about 100µm. The visible length of the plasma channel was over 4 cm.

As shown in Fig. 2(a), the decay time of the electrical signal (defined as the duration lasting from the maximum value to 5% of the maximum value), increased by about 3 folds when the electrical field increased to 350 kV/m (dash-dotted line c). As we expected, the variation of the electrical signals in the channel showed that the lifetime of the plasma channel was prolonged when the electrical field increased. On the other hand, the solid line in Fig. 2(b), resulting from a theoretical model, which will be discussed later based on Eq. (1)(3), depicts the evolution of electron density in the absence of an electrical field. We calculated that within 20 ns the electron density would be expected to fall to1014 cm -3. Here, the initial electron density in our calculation was of the same order magnitude as the measurement in our experiment (1017 cm -3). Therefore, we expected that within the same 20 ns the electron density in the plasma would remain above1014cm-3. We regard this level as an indication of the lifetime of a plasma channel. In Fig. 2(a), compared to line a, line b and c indicate increased lifetimes of 40 and 60 ns respectively. Our experiment results show that an electrical field added in the plasma channel can affect the characteristics of the plasma and prolong the lifetime of the plasma channel.

Fig. 2. (a) Measured electrical signals (solid line a, dashed line b, and dash-dotted line c correspond to electrical fields of 0V/m, 250kV/m, 350kV/m respectively); (b) Theoretical calculation with initial condition that n e=×1017 cm -3.

In order to further extend the lifetime of the plasma channel, we added a second femtosecond laser pulse with the external electrical field still in place. The delay between the two laser pulses was adjusted and the corresponding lifetime of the plasma channel is measured as shown in Fig. 3 and Fig. 4. As we can see in Fig. 3, the lifetime is prolonged to about 150 ns when the delay between two pulses is 40 ns. With a delay of 60 ns, the lifetime increases to 200 ns. As shown in Fig. 4, further increase in delay (100 ns) no longer leads to further extension of the lifetime. This is because the distance between the two laser pulses is so long that the interaction between them is less pronounced than in situations with shorter delay time.

A multi-pulse scheme is employed here to reach a longer lifetime. In our experiment, we added three more laser pulses to the original laser pulse with a delay between two consecutive pulses at about 70 ns. This was done to obtain an optimal effect on the lifetime. These multiple laser pulses were generated by passing a main laser pulse through beam splitters and setting long-range fixed delays. The electrical field remained at about 350kV/m. The energy of the original pulse was 0.4 mJ and those of the later three laser pulses are all about 0.1 mJ±0.1 mJ due to long-range propagation. The measured electrical signal is shown in Fig. 5 with a total lifetime of about 350 ns. As we can see, the signal caused by subsequent pulses is not as intense as in the double-pulse experiments conducted. This is due to the relatively low energy of later pulses. According to our double-pulse experimental results, we can expect that with relatively high energy of each later pulse at about 0.4 mJ, the lifetime of the plasma channel can be increased longer than what we acquired in Fig. 5. Therefore, we can conclude that a multi-pulse scheme with an electrical field added is efficacious for the extension of the lifetime of the plasma channel.

Fig. 3. Electrical signals in double-pulse scheme. The energies of two pulses with the delay of 20 ns are 0.5 mJ and 0.4 mJ respectively. The energies of two pulses with the delay of 40 ns are also 0.5 mJ and 0.4 mJ respectively.
Fig. 4. Electrical signals in double-pulse scheme. The energies of two pulses with the delay of 60 ns are 0.5 mJ respectively. The energies of two pulses with the delay of 100 ns are 0.3 mJ respectively.
Fig. 5. Electrical signal in four-pulse scheme. The energy of the first pulse is 0.4 mJ, and the energies of later pulses are all about 0.1 mJ. The delay between two contiguous pulses is 70 ns.

The main mechanisms involved in the decay process of the plasma channel in a high electrical field include the photo-ionization, impact ionization, dissociative attachments of electrons to oxygen molecules, charged particle recombination, detachments of electrons by ion-ion collision, and electron diffusion. Among these effects, the attachment of electrons to oxygen molecules is detrimental to the lifetime of the plasma channel. The effect of detachments of electrons caused by ion-ion collision is relatively weak compared with the others and thus is omitted in our analysis. And the electron diffusion is a slow process, on the time scale of tens of µs [11

11. X .M . Zhao, Jean-Claude Diels, Cai Yi Wang, and Juan M. Elizondo, “Femtosecond Ultraviolet Laser Pulse Induced Lightning Discharges in Gases,” IEEE J. Quantum Electron. 31.599–612(1995). [CrossRef]

]. And electron generation and plasma formation are on the time scale of ns to µs. At this time scale, effects from electron diffusion can be neglected. Therefore, we can estimate the lifetime of the plasma channel following the equation of continuity as follows [10

10. Hui Yang, Jie Zhang, Yingjun Li, Jun Zhang, Yutong Li, Zhenglin Chen, Hao Teng, Zhiyi Wei, and Zhengming Sheng, “Characteristics of self-guided laser plasma channels generated by femtosecond laser pulses in air,” Phys. Rev. E 66, 016406(2002). [CrossRef]

, 11

11. X .M . Zhao, Jean-Claude Diels, Cai Yi Wang, and Juan M. Elizondo, “Femtosecond Ultraviolet Laser Pulse Induced Lightning Discharges in Gases,” IEEE J. Quantum Electron. 31.599–612(1995). [CrossRef]

]

net=αneηneβepnenp
(1)
npt=αneβepnenpβnpnnnp
(2)
nnt=ηneβnpnnnp
(3)

where ne, np, nn are electron density, positive ion density, and negative ion density in air respectively. α is the impact ionization coefficient. η is the attachment rate. Initial conditions for theoretical analysis is that ne=2×1017 cm -3, np=2×1017 cm -3, nn=0. Through our simulation, α and η in different electric fields did not exert a noticeable effect on the lifetime of a plasma channel. Therefore, we expect that βep and βnp may play a role in extending the lifetime when an external electrical field is added.

Without considering the effect of external electric field, a general expression of electron-ion recombination coefficient βep as a function of electron temperature Te is [11

11. X .M . Zhao, Jean-Claude Diels, Cai Yi Wang, and Juan M. Elizondo, “Femtosecond Ultraviolet Laser Pulse Induced Lightning Discharges in Gases,” IEEE J. Quantum Electron. 31.599–612(1995). [CrossRef]

, 12

12. M.A. BiondiG. Bekefi, “Recombination,” in Principles of Laser Plasmas, ed. pp.125–157 (New York, Wiley, 1976)

]:

β1(m3s)=2.035×1012Te0.39,(eN2+)
β2(m3s)=1.138×1011Te0.70,(eO2+)
βep=0.79β1+0.21β2
(4)

We take βnp=βep in our calculation since the ion-ion recombination coefficient βnp is of the same order of magnitude as the electron-ion recombination coefficient βep.

The theoretical simulation of the lifetime of the plasma channel is shown in Fig. 6. As line a, b and c shown, the lifetime of the plasma channel is prolonged from 20 ns to 60 ns as the dissociative recombination coefficient βep and βnp decrease.

Potential energy curves play a role in dissociative recombination. In a favorable potential curve crossing case, a sharper falloff in this coefficient than Te -0.39 and Te -0.70 will occur with increasing incident electron energy [12

12. M.A. BiondiG. Bekefi, “Recombination,” in Principles of Laser Plasmas, ed. pp.125–157 (New York, Wiley, 1976)

]. When the external electrical field is added along the plasma channel, the incident energy of electrons will be increased. Meanwhile, Te can be assumed to thermalize at the same ambient air temperature as the gas molecules [11

11. X .M . Zhao, Jean-Claude Diels, Cai Yi Wang, and Juan M. Elizondo, “Femtosecond Ultraviolet Laser Pulse Induced Lightning Discharges in Gases,” IEEE J. Quantum Electron. 31.599–612(1995). [CrossRef]

]. Because potential energy curves will change due to the external electrical field, we expect that a favorable potential curve crossing may exist in this case. And this can lead to a quicker falloff in βep and βnp, and corresponding extension in the lifetime as electron energy increases, as we can see from the comparison of line a, b and c shown in Fig. 6.

Fig. 6. Theoretical simulation with α=7.4×104 s -1 and η=2.5×107 s -1 [11]; Solid line a, dashed line b and dash-dotted line c correspond to different dissociative recombination rates 2.2×10-13 m 3/s, 0.8×10-13 m 3/s and 0.3×10-13 m 3/s respectively.

Similarly, in double-pulse and multi-pulse case, the dissociative recombination rate can decline more intensively than the case without an external electrical field and this will thus lead to an extension of the lifetime of the plasma channel. Moreover, the addition of the second and later pulses will again cause a large number of electrons due to photo-ionization [13

13. Quanli Dong, Fei Yan, Jie Zhang, Zhan Jin, Hui Yang, Zuoqiang Hao, Zhenglin Chen, Yutong Li, Zhiyi Wei, and Zhengming Sheng, “The measurement and analysis of the prolonged lifetime of the plasma channel formed by short pulse laser in air,” Acta Physica Sinica 54, 3247–3250 (2005).

]. With these extra electrons, the lifetime of the plasma channel will further extend.

As a conclusion, characteristics of the lifetime of the plasma channel are investigated by adding an external electrical field and also extra laser pulses. The lifetime increases by 3 folds when the external electrical field is about 350kV/m in our experiment. We expect that a favorable crossing case may exist when an external electrical field is in place, and this can lead to a corresponding growth in the lifetime of the plasma channel. In addition, the lifetime of plasma channel is greatly enhanced to 350 ns by using four sequential intense 100fs (FWHM) laser pulses with the external electrical field (350kV/m). Therefore, we conclude that a multi-pulse scheme with an external electrical field added is feasible for greatly prolonging the lifetime of a plasma channel.

This research is supported by a Major Basic Research project of the Shanghai Commission of Science and Technology, the Chinese Academy of Sciences, the Chinese Ministry of Science and Technology, and the Natural Science Foundation of China.

References and links

1.

A. Braun, G. Korn, X. Liu, D. Du, J. Squier, and G. Mourou, “Self-channeling of high-peak-power femtosecond laser pulses in air,” Opt. Lett. 20, 73–75 (1995). [CrossRef] [PubMed]

2.

E. T. J. Nibbering, P. F. Curley, G. Grillon, B. S. Prade, M. A. Franco, F. Salin, and A. Mysyrowicz, “Conical emission from self-guided femtosecond pulses in air,” Opt. Lett. 21, 62–64 (1996). [CrossRef] [PubMed]

3.

Miguel Rodriguez, Riad Bourayou, Guillaume Méjean, Jérôme Kasparian, Jin Yu, Estelle Salmon, Alexander Scholz, Bringfried Stecklum, Jochen Eislöffel, Uwe Laux, Artie P. Hatzes, Roland Sauerbrey, Ludger Wöste, and Jean-Pierre Wolf. “Kilometer-range nonlinear propagation of femtosecond laser pulses,” Phy. Rev. E 69, 036607 (2004). [CrossRef]

4.

S. A. Hosseini, Q. Luo, B. Ferland, W. Liu, N. Akozbek, G. Roy, and S.L. Chin, “Effective length of filaments measurement using backscattered fluorescence from nitrogen molecules,” Appl. Phys. B 77, 697–702 (2003). [CrossRef]

5.

R. Ackermann, K. Stelmaszcyk, P. Rohwetter, G. Mejean, E. Salmon, J. Yu, J. Kasparian, G. Mechain, V. Bergmann, S. Schaper, B. Weise, T. Kumm, K. Rethmeier, W. Kalkner, L. Wöste, and J. P. Wolf, “Triggering and guiding of megavolt discharges by laser-induced filaments under rain conditions,” Appl.Phys. Lett. 85, 5781–5783 (2004). [CrossRef]

6.

F. Vidal, D. Comtois, C.-Y. Chien, A. Desparois, B. La Fontaine, T. W. Johnston, J.-C. Kieffer, H. P. Mercure, and F. A. Rizk, “Modeling the triggering of streamers in air by ultrashort laser pulses,” IEEE Trans. Plasma Sci. 28, 418–433 (2000). [CrossRef]

7.

J. Kasparian, M. Rodriguez, G. Méjean, J. Yu, E. Salmon, H. Wille, R. Bourayou, S. Frey, Y.-B. André, A. Mysyrowicz, R. Sauerbrey, J.-P. Wolf, and L. Wöste, “White-Light Filaments for Atmospheric Analysis,” Science 301, 61–64 (2003). [CrossRef] [PubMed]

8.

H. Yang, J. Zhang, W. Yu, Y. J. Li, and Z. Y. Wei, “Long plasma channels generated by femtosecond laser pulses,” Phys. Rev. E 65, 016406(2001). [CrossRef]

9.

X. Lu, Xi Ting Ting, Li Ying-Jun, and Zhang Jie, “Lifetime of the plasma channel produced by ultra-short and ultra-high power laser pulse in the air,” Acta Physica Sinica 53, 3404–3408 (2004).

10.

Hui Yang, Jie Zhang, Yingjun Li, Jun Zhang, Yutong Li, Zhenglin Chen, Hao Teng, Zhiyi Wei, and Zhengming Sheng, “Characteristics of self-guided laser plasma channels generated by femtosecond laser pulses in air,” Phys. Rev. E 66, 016406(2002). [CrossRef]

11.

X .M . Zhao, Jean-Claude Diels, Cai Yi Wang, and Juan M. Elizondo, “Femtosecond Ultraviolet Laser Pulse Induced Lightning Discharges in Gases,” IEEE J. Quantum Electron. 31.599–612(1995). [CrossRef]

12.

M.A. BiondiG. Bekefi, “Recombination,” in Principles of Laser Plasmas, ed. pp.125–157 (New York, Wiley, 1976)

13.

Quanli Dong, Fei Yan, Jie Zhang, Zhan Jin, Hui Yang, Zuoqiang Hao, Zhenglin Chen, Yutong Li, Zhiyi Wei, and Zhengming Sheng, “The measurement and analysis of the prolonged lifetime of the plasma channel formed by short pulse laser in air,” Acta Physica Sinica 54, 3247–3250 (2005).

14.

Jiansheng Liu, Zuoliang Duan, Zhinan Zeng, Xinhua Xie, Yunpei Deng, Ruxin Li, and Zhizhan Xu, “Time-resolved investigation of low-density plasma channels produced by a kilohertz femtosecond laser in air,” Phys. Rev. E 72, 026412 (2005). [CrossRef]

OCIS Codes
(320.7120) Ultrafast optics : Ultrafast phenomena
(350.5400) Other areas of optics : Plasmas

ToC Category:
Ultrafast Optics

History
Original Manuscript: February 17, 2006
Revised Manuscript: May 9, 2006
Manuscript Accepted: May 10, 2006
Published: May 29, 2006

Citation
Jiabin Zhu, Zhonggang Ji, Yunpei Deng, Jiansheng Liu, Ruxin Li, and Zhizhan Xu, "Long lifetime plasma channel in air generated by multiple femtosecond laser pulses and an external electrical field," Opt. Express 14, 4915-4922 (2006)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-14-11-4915


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References

  1. A. Braun, G. Korn, X. Liu, D. Du, J. Squier, and G. Mourou, "Self-channeling of high-peak-power femtosecond laser pulses in air," Opt. Lett. 20, 73-75 (1995). [CrossRef] [PubMed]
  2. E. T. J. Nibbering, P. F. Curley, G. Grillon, B. S. Prade, M. A. Franco, F. Salin, and A. Mysyrowicz, "Conical emission from self-guided femtosecond pulses in air," Opt. Lett. 21, 62-64 (1996). [CrossRef] [PubMed]
  3. M. Rodriguez, R. Bourayou, G. Méjean, J. Kasparian, J. Yu, E. Salmon, A. Scholz, B. Stecklum, J. Eislöffel, U. Laux, A. P. Hatzes, R. Sauerbrey, L. Wöste, and J.-P. Wolf, "Kilometer-range nonlinear propagation of femtosecond laser pulses," Phy. Rev. E 69, 036607 (2004). [CrossRef]
  4. S. A. Hosseini, Q. Luo, B. Ferland, W. Liu, N. Akozbek, G. Roy, and S. L. Chin, "Effective length of filaments measurement using backscattered fluorescence from nitrogen molecules," Appl. Phys. B 77, 697-702 (2003). [CrossRef]
  5. R. Ackermann, K. Stelmaszcyk, P. Rohwetter, G. Mejean, E. Salmon, J. Yu, J. Kasparian, G. Mechain, V. Bergmann, S. Schaper, B. Weise, T. Kumm, K. Rethmeier, W. Kalkner, L. Wöste, and J. P. Wolf, "Triggering and guiding of megavolt discharges by laser-induced filaments under rain conditions," Appl. Phys. Lett. 85, 5781-5783 (2004). [CrossRef]
  6. F. Vidal, D. Comtois, C.-Y. Chien, A. Desparois, B. La Fontaine, T. W. Johnston, J.-C. Kieffer, H. P. Mercure, and F. A. Rizk, "Modeling the triggering of streamers in air by ultrashort laser pulses," IEEE Trans. Plasma Sci. 28, 418-433 (2000). [CrossRef]
  7. J. Kasparian, M. Rodriguez, G. Méjean, J. Yu, E. Salmon, H. Wille, R. Bourayou, S. Frey, Y.-B. André, A. Mysyrowicz, R. Sauerbrey, J.-P. Wolf, and L. Wöste, "White-light filaments for atmospheric analysis," Science 301, 61-64 (2003). [CrossRef] [PubMed]
  8. H. Yang, J. Zhang, W. Yu, Y. J. Li, and Z. Y. Wei, "Long plasma channels generated by femtosecond laser pulses," Phys. Rev. E 65, 016406(2001). [CrossRef]
  9. X. Lu, X. T. Ting, L. Ying-Jun, and Z. Jie, "Lifetime of the plasma channel produced by ultra-short and ultra-high power laser pulse in the air," Acta Physica Sin. 53, 3404-3408 (2004).
  10. H. Yang, J. Zhang, Y. Li, J. Zhang, Y. Li, Z. Chen, H. Teng, Z. Wei, and Z. Sheng, "Characteristics of self-guided laser plasma channels generated by femtosecond laser pulses in air," Phys. Rev. E 66, 016406(2002). [CrossRef]
  11. X.M. Zhao, J.-Claude Diels, C. Y. Wang, and J. M. Elizondo, "Femtosecond ultraviolet laser pulse induced lightning discharges in gases," IEEE J. Quantum Electron. 31. 599-612(1995). [CrossRef]
  12. M. A. Biondi, "Recombination," in Principles of Laser Plasmas, G. Bekefi, ed. pp.125-157 (New York, Wiley, 1976).
  13. Q. Dong, F. Yan, J. Zhang, Z. Jin, H. Yang, Z. Hao, Z. Chen, Y. Li, Z. Wei, and Z. Sheng, "The measurement and analysis of the prolonged lifetime of the plasma channel formed by short pulse laser in air," Acta Physica Sin. 54, 3247-3250 (2005).
  14. J. Liu, Z. Duan, Z. Zeng, X. Xie, Y. Deng, R. Li, and Z. Xu, "Time-resolved investigation of low-density plasma channels produced by a kilohertz femtosecond laser in air," Phys. Rev. E 72, 026412 (2005). [CrossRef]

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