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Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 15, Iss. 24 — Nov. 26, 2007
  • pp: 16102–16109
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Optimization of multiple filamentation of femtosecond laser pulses in air using a pinhole

Zuo-Qiang Hao, Jie Zhang, Ting-Ting Xi, Xiao-Hui Yuan, Zhi-Yuan Zheng, Xin Lu, Ming-Young Yu, Yu-Tong Li, Zhao-Hua Wang, Wei Zhao, and Zhi-Yi Wei  »View Author Affiliations


Optics Express, Vol. 15, Issue 24, pp. 16102-16109 (2007)
http://dx.doi.org/10.1364/OE.15.016102


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Abstract

The robustness and prolongation of multiple filamentation (MF) for femtosecond laser propagation in air are investigated experimentally and numerically. It is shown that the number, pattern, propagation distance, and spatial stability of MF can be controlled by a variable-aperture on-axis pinhole. The random MF pattern can be optimized to a deterministic pattern. In our numerical simulations, we configured double filaments to principlly simulate the experimental MF interactions. It is experimentally and numerically demonstrated that the pinhole can reduce the modulational instability of MF and is favorable for a more stable MF evolution.

© 2007 Optical Society of America

1. Introduction

The propagation of ultra-intense femtosecond (fs) laser pulses in air has been extensively investigated recently in view of many potential applications such as lightning control and remote sensing of the atmosphere [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]

10

10. S. Eisenmann, E. Louzon, Y. Katzir, T. Palchan, A. Zigler, Y. Sivan, and G. Fibich, “Control of the filamentation distance and pattern in long-range atmospheric propagation,” Opt. Express15, 2779–2784 (2007), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-15-6-2779. [CrossRef] [PubMed]

]. For a laser beam at a wavelength λ=800 nm, when the laser power exceeds the critical value Pcrit2/2πn0n2 of about 3.2 GW [11

11. E. Esarey, P. Sprangle, J. Krall, and A. Ting, “Self-focusing and guiding of short laser pulses in ionizing gases and plasmas,” IEEE J. Quantum Electron. 33, 1879–1914 (1997). [CrossRef]

], nonlinear Kerr self-focusing of the laser beam occurs and the increased intensity at the focus can cause multiphoton ionization (MPI) of molecules in air. The resulting electron generation contributes negatively to the index of refraction of air, namely nplasma=-ω 2 p(r)/2ω 2, where ωp=(4πe2ne/me)1/2 is the plasma frequency and ne is the electron density. This will defocus the laser beam [11

11. E. Esarey, P. Sprangle, J. Krall, and A. Ting, “Self-focusing and guiding of short laser pulses in ionizing gases and plasmas,” IEEE J. Quantum Electron. 33, 1879–1914 (1997). [CrossRef]

]. A dynamic balance between these two effects could then follow, leading to very-long filament propagation, exceeding many Rayleigh lengths of the laser beam. Usually, the light intensity inside the filaments is about 5×1013-1×1014 W/cm2 [12

12. B. La Fontaine, F. Vidal, Z. Jiang, C. Y. Chien, D. Comtois, A. Desparois, T. W. Johnston, J. -C. Kieffer, H. Pépin, and H. P. Mercure, “Filamentation of ultrashort pulse laser beams resulting from their propagation over long distances in air,” Phys. Plasmas 6, 1615–1621 (1999). [CrossRef]

] and the electron density is about 1016–1018 cm-3 [9

9. 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]

, 13

13. H. Yang, J. Zhang, Y. J. Li, J. Zhang, Y. T. Li, Z. L. Chen, H. Teng, Z. Y. Wei, and Z. M. Sheng, “Characteristics of self-guided laser plasma channels generated by femtosecond laser pulses in air,” Phys. Rev. E 66, 016406 (2002). [CrossRef]

], so that the filaments are conductive [4

4. H. Schillinger and R. Sauerbrey, “Electrical conductivity of long plasma channels in air generated by self-guided femtosecond laser pulses,” Appl. Phys. B 68, 753–756 (1999). [CrossRef]

, 5

5. S. Tzortzakis, M. A. Franco, Y. -B. André, A. Chiron, B. Lamouroux, B. S. Prade, and A. Mysyrowicz, “Formation of a conducting channel in air by self-guided femtosecond laser pulses,” Phys. Rev. E 60, R3505–3507 (1999). [CrossRef]

]. Often, one finds that there is more than one filament in the beam, indicating laser- or plasma-induced inhomogeneity of the beam. The dynamics of the filamentation process is in fact rather complicated and the physics of multiple filamentation (MF) formation and evolution is still not well understood. Apart from the Kerr self-focusing and plasma defocusing, other nonlinear effects, such as self-phase modulation, four-wave mixing, stimulated Raman scattering, etc. can also play important roles.

Mlejnek et al. proposed a model of optical turbulent light guiding to explain the breakup and fusion of filaments [14

14. M. Mlejnek, M. Kolesik, J. V. Moloney, and E. M. Wright, “Optically turbulent femtosecond light guide in air,” Phys. Rev. Lett. 83, 2938–2941 (1999). [CrossRef]

]. This was confirmed experimentally by Bergé et al [15

15. L. Bergé, S. Skupin, F. Lederer, G. Méjean, J. Yu, J. Kasparian, E. Salmon, J. P. Wolf, M. Rodriguez, L. Wöste, R. Bourayou, and R. Sauerbrey, “Multiple filamentation of terawatt laser pulses in air,” Phys. Rev. Lett. 92, 225002 (2004) [CrossRef] [PubMed]

]. Tzortzakis et al. proposed that the main mechanism is the modulational instability (MI) of laser pulses [16

16. S. Tzortzakis, L. Bergé, A. Couairon, M. Franco, B. Prade, and A. Mysyrowicz, “Breakup and fusion of self-guided femtosecond light pulses in air,” Phys. Rev. Lett. 86, 5470–5473 (2001). [CrossRef] [PubMed]

]. Besides, the stability of MF is also affected by the ellipticity [17

17. A. Dubietis, G. Tamošauskas, G. Fibich, and B. Ilan, “Multiple filamentation induced by input-beam ellipticity,” Opt. Lett. 29, 1126–1128 (2004). [CrossRef] [PubMed]

] and vectorial effects [18

18. G. Fibich and B. Ilan, “Deterministic vectorial effects lead to multiple filamentation,” Opt. Lett. 26, 840–842 (2004). [CrossRef]

] of the initial laser beam. The apparently random MF can be harmful in applications where precise localization of the beam is required. Méchain et al. realized the organized MF using a trefoil or a fivefoil diaphragm [6

6. G. Méchain, A. Couairon, M. Franco, B. Prade, and A. Mysyrowicz, “Organizing multiple femtosecond filaments in air,” Phys. Rev. Lett. 93, 035003 (2004). [CrossRef] [PubMed]

]. Fibich et al. obtained a single filament with highly pointing stability by using a titled lens setup [19

19. G. Fibich, S. Eisenmann, B. Ilan, and A. Zigler, “Control of multiple filamentation in air,” Opt. Lett. 29, 1772–1774 (2004). [CrossRef] [PubMed]

]. In this paper, we propose an alternative approach to form more stable and longer filaments. We demonstrated that when the cross section of the plasma channel is restricted by a pinhole, remarkably robust and prolonged filaments are attained. The intensity and propagation distance of the filament are controllable by varying the aperture of the pinhole. Our simulations retrieve the phenomenon that the filaments can be prolonged and stabilized, which is in good agreement with experimental results.

2. Experimental setup and results

The laser used is a Ti:sapphire laser system, Xtreme Light II (XL-II), with an output energy of up to 640 mJ in 30 fs duration. The central wavelength is 800 nm and the repetition rate is 10 Hz. In the experiments, a laser pulse of energy 15 mJ is focused by an f=200 cm convex lens. The experimental setup is shown in Fig. 1. The laser beam is focused in air and forms a long plasma channel that can be observed directly by naked eyes. A charged-coupled device (CCD) camera (512×512 pixels) with a pixel size of 24 µm records the beam cross-section at 520 cm and 690 cm distance from the lens. Another CCD camera records the beam along the laser axis. Filters with a wavelength range of 350 nm <λ<500 nm are used at both CCD cameras to reduce the scattering noise from the pump laser. A typical profile of the plasma channel is shown in Fig. 2. Because of the Kerr self-focusing, the laser beam focuses before the geometrical focus which is indicated by the arrow in the figure. A pinhole as long as 4 mm in a copper plate (see the inset of Fig. 1) is centered on the beam axis at Z0=190 cm. The purpose of using the relative long pinhole is to effectively eliminate the small filaments with large angle to the main ones. The axial and transverse profiles of the plasma filaments are measured directly by the two CCD cameras.

Fig. 1. Schematic diagram of the experimental setup. Z0=190 cm is the position of the pinhole. The insert shows the copper pinhole.
Fig. 2. A typical profile of the plasma channel with laser energy of 35 mJ. The position of the arrow is the geometrical focus.
Fig. 3. The filaments propagation distance from the lens versus the diameter of the pinhole.

In the experiments, 15 mJ of laser pulse energy, corresponding to a peak power of about 500 GW, is used. This power is significantly higher than the critical power for self-focusing. A long plasma channel begins to form at about 170 cm after the convex lens. The fluorescence emitted from excited nitrogen molecules in the channel can be observed directly by naked eyes [20

20. A. Talebpour, S. Petit, and S. L. Chin, “Re-focusing during the propagation of a focused femtosecond Ti:Sapphire laser pulse in air,” Opt. Commun. 171, 285–290 (1999). [CrossRef]

, 21

21. Z. Q. Hao, J. Zhang, J. Yu, Z. Zhang, J. Y. Zhong, C. Z. Zang, Z. Jin, Z. H. Wang, and Z. Y. Wei, “Fluorescence measurement and acoustic diagnostics of plasma channels in air,” Acta Phys. Sin. 55, 299–303 (2006).

]. Therefore, the filamentation process can be visualized by the observation of the fluorescence, and we can image it by the CCD cameras. To control the diameter of the channel, a pinhole with variable apertures is placed at the center of the laser beam axis. In our experiments condition, the pinhole position Z0=190 cm is the optimized choice to study the filaments. We find that if the distance between the lens and the pinhole is smaller, there is no chance for filaments to develop into mature ones. The filaments will decay fast due to the lack of laser energy. However, if the distance is too large, some dynamic interactions have already harmfully influenced the MF. As a result, the MF cannot be effectively controlled by the pinhole setup. Therefore, we chose Z0=190 cm of the pinhole position, which results in a remarkable phenomenon that the intensity of the fluorescence from the filaments becomes brighter and the propagation distance of the filaments longer when a pinhole between 0.8 and 1.8 mm in diameter is inserted. Figure 3 shows the dependence of the propagation distance Z of the MF on the diameter D of the pinhole. When the diameter of the pinhole is D=0.3 and 0.4 mm, the filament is almost terminated and its length is only several centimeters beyond the pinhole, as Liu et al. observed [22

22. W. Liu, F. Théberge, E. Arévalo, J. -F. Gravel, A. Becker, and S. L. Chin, “Experiment and simulations on the energy reservoir effect in femtosecond light filaments,” Opt. Lett. 30, 2602–2604 (2005). [CrossRef] [PubMed]

]. The longest filament occurs for D=1.2 mm, corresponding to a channel distance of beyond 340 cm. When D≥2.0 mm, the pinhole has no observable effect on the filaments since almost the entire laser beam can get through. In the absence of the pinhole, the measured propagation distance of filaments is about 310 cm. That is, the plasma channel can be prolonged by inserting a pinhole of appropriate aperture along the optical axis.

The important role of the pinhole lies in not only the prolongation of MF, but also the stability of the MF. The traverse profiles of the MF at Z=520 and 690 cm are recorded by the second CCD camera. Figure 4 shows the spatial variation of the filaments as a function of the aperture of the pinhole.

Fig. 4. Typical traverse filamentation patterns at Z=520 cm (a) and Z=690 cm (b) versus the diameter of the pinhole.

Figure 4(a) shows the MF patterns for different diameters of the pinhole. The first image is for a free propagation without any pinhole. We see that the beam is dispersed into a relatively large area showing several bright spots. The positions of these spots are unfixed from shot to shot. As we limit the plasma channel by pinholes of diameters from 2.0 to 0.8 mm, the laser beam cross section becomes smaller, and the number, position, and intensity of the filaments change. When the diameter is 1.6 mm, the filaments are robust and distinct from each other. With further decrease of the diameter, the number of filaments becomes less. When the pinhole diameter is 0.8 mm, there are only two filaments, one large and one small. All the pinhole controlled MF patterns are reproducible. Finally, for D<0.6 mm we observe only a dispersed light spot. We can conclude that the MF patterns for D=1.6-0.8 mm are highly stable and reproducible. The number and locations of the MF rarely change from shot to shot.

At Z=690 cm, as shown in Fig. 4(b), the dependence of the MF profiles on the pinhole aperture is similar to the case of 520 cm distance. Comparing the MF patterns at two distances, we see that the differences are only in the number, intensity, and spatial extent of the filaments. From the MF patterns at the two positions, we can also infer the longitudinal evolution of the MF. For example, at 690 cm there are only two intense filaments for D=1.6, 1.4 and 1.2 mm, and a single stable filament for D=0.8 mm. These numbers are less than that observed at 520 cm, indicating that some filaments have terminated or combined.

It is noted that the free propagation MF generated in our experiments is not stable compared with our recent experiments used a longer focal length (f=400 cm) lens [23

23. Z. Q. Hao, J. Zhang, X. Lu, T. T. Xi, Y. T. Li, X. H. Yuan, Z. Y. Zheng, Z. H. Wang, W. J. Ling, and Z. Y. Wei, “Spatial evolution of multiple filaments in air induced by femtosecond laser pulses,” Opt. Express, 14, 773–778 (2006), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-14-2-773. [CrossRef] [PubMed]

]. Our theoretical investigation verified that the difference should be dependent on the focus of the lens. The stability of the MF has a close relationship on the incident angle of two plasma filaments [24

24. T. T. Xi, X. Lu, and J. Zhang, “Interaction of light filaments generated by femtosecond laser pulses in air,” Phys. Rev. Lett. 96, 025003 (2006). [CrossRef] [PubMed]

]. Therefore, the MF generated by a lens with shorter focal length will boost stronger instability.

3. Numerical simulation and discussion

Fig. 5. The energy fluence distribution (fluenceiso=1.65) of the configured double filaments along the propagation direction when the insert diaphragm diameter is ∞ (without pinhole) (a); 0.4 mm (b); 0.6 mm (c); 0.8 mm (d); 1.0 mm (e); 1.2 mm (f); 1.4 mm (g); 1.6 mm (h); 1.8 mm (i); 2.0 mm (j) at the initial distance (corresponding to z0=190 cm in the experiment); 0.6 mm at the distance of 5 cm (k) and 10 cm (l) from the initial distance.

We note that in our simulations the double filaments evolved into a single filament after we added the pinhole with a diameter of 0.4–1.8 mm, as shown in Fig. 5. We achieved the cleaner MF patterns using the pinhole setup not only in experiment but also in simulation. We can conclude that the appropriate elimination of the disordered small filaments surrounding the main filaments results in the formation of cleaner, more stable and more robust MF patterns.

The pinhole aperture plays an important role in controlling the filaments. On the one hand, it reduces the turbulence in the periphery of the plasma channel and leads to relatively stable MF. On the other hand, it should allow enough energy through to feed the remaining filaments. In our experiments, the optimum diameter of the pinhole is 1.2 mm, and a deterministic MF pattern is obtained. In our simulations, the optimal pinhole diameter is 1.0 mm. The differences between them are mainly due to the different initial laser parameters and some simplifications in our numerical simulations.

4. Conclusions

In conclusion, the effect of an on-axis pinhole on the MF of an fs laser beam has been studied. For appropriate pinhole diameters, the MF can be stable, and propagates for a longer distance. By eliminating the disordered energy reservoir in the periphery of the plasma channel, the pinhole setup leads to a longer and more regular MF pattern. We configured double filaments in theory to simulate the phenomenon in our experiments. The numerical simulations retrieve the essential features of the experimental results. Further experimental and numerical optimization of filamentation enables one to achieve optimized or otherwise desired MF patterns, which are important for many research and practical applications.

Acknowledgments

This work was supported by the National Nature Science Foundation of China under Grant Nos. 10634020, 10390161, 60621063, and 60478047, and National Basic Research Program of China (973 Program) (Grant No. 2007CB815101).

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.

L. Wöste, C. Wedekind, H. Wille, P. Rairoux, B. Stein, S. Nikolov, C. Werner, S. Niedermeier, F. Ronneberger, H. Schillinger, and R. Sauerbrey, “Femtosecond atmospheric lamp,” Las. Optoelektron. 29, 51–53 (1997).

3.

S. L. Chin, F. Théberge, and W. Liu, “Filamentation nonlinear optics,” Appl. Phys. B 86, 477–483 (2007). [CrossRef]

4.

H. Schillinger and R. Sauerbrey, “Electrical conductivity of long plasma channels in air generated by self-guided femtosecond laser pulses,” Appl. Phys. B 68, 753–756 (1999). [CrossRef]

5.

S. Tzortzakis, M. A. Franco, Y. -B. André, A. Chiron, B. Lamouroux, B. S. Prade, and A. Mysyrowicz, “Formation of a conducting channel in air by self-guided femtosecond laser pulses,” Phys. Rev. E 60, R3505–3507 (1999). [CrossRef]

6.

G. Méchain, A. Couairon, M. Franco, B. Prade, and A. Mysyrowicz, “Organizing multiple femtosecond filaments in air,” Phys. Rev. Lett. 93, 035003 (2004). [CrossRef] [PubMed]

7.

J. Kasparian, R. Sauerbrey, D. Mondelain, S. Niedermeier, J. Yu, J. -P. Wolf, Y. -B. André, M. Franco, B. Prade, S. Tzortzakis, A. Mysyrowicz, M. Rodriguez, H. Wille, and L. Wöste, “Infrared extension of the supercontinuum generated by femtosecond terawatt laser pulses propagating in the atmosphere,” Opt. Lett. 25, 1397–1399 (2000). [CrossRef]

8.

Z. Q. Hao, J. Zhang, Z. Zhang, X. H. Yuan, Z. Y. Zheng, X. Lu, Z. Jin, Z. H. Wang, J. Y. Zhong, and Y. Q. Liu, “Characteristics of multiple filaments generated by femotosecond laser pulses in air: Prefocused versus free propagation,” Phys. Rev. E 74, 066402 (2006). [CrossRef]

9.

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]

10.

S. Eisenmann, E. Louzon, Y. Katzir, T. Palchan, A. Zigler, Y. Sivan, and G. Fibich, “Control of the filamentation distance and pattern in long-range atmospheric propagation,” Opt. Express15, 2779–2784 (2007), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-15-6-2779. [CrossRef] [PubMed]

11.

E. Esarey, P. Sprangle, J. Krall, and A. Ting, “Self-focusing and guiding of short laser pulses in ionizing gases and plasmas,” IEEE J. Quantum Electron. 33, 1879–1914 (1997). [CrossRef]

12.

B. La Fontaine, F. Vidal, Z. Jiang, C. Y. Chien, D. Comtois, A. Desparois, T. W. Johnston, J. -C. Kieffer, H. Pépin, and H. P. Mercure, “Filamentation of ultrashort pulse laser beams resulting from their propagation over long distances in air,” Phys. Plasmas 6, 1615–1621 (1999). [CrossRef]

13.

H. Yang, J. Zhang, Y. J. Li, J. Zhang, Y. T. Li, Z. L. Chen, H. Teng, Z. Y. Wei, and Z. M. Sheng, “Characteristics of self-guided laser plasma channels generated by femtosecond laser pulses in air,” Phys. Rev. E 66, 016406 (2002). [CrossRef]

14.

M. Mlejnek, M. Kolesik, J. V. Moloney, and E. M. Wright, “Optically turbulent femtosecond light guide in air,” Phys. Rev. Lett. 83, 2938–2941 (1999). [CrossRef]

15.

L. Bergé, S. Skupin, F. Lederer, G. Méjean, J. Yu, J. Kasparian, E. Salmon, J. P. Wolf, M. Rodriguez, L. Wöste, R. Bourayou, and R. Sauerbrey, “Multiple filamentation of terawatt laser pulses in air,” Phys. Rev. Lett. 92, 225002 (2004) [CrossRef] [PubMed]

16.

S. Tzortzakis, L. Bergé, A. Couairon, M. Franco, B. Prade, and A. Mysyrowicz, “Breakup and fusion of self-guided femtosecond light pulses in air,” Phys. Rev. Lett. 86, 5470–5473 (2001). [CrossRef] [PubMed]

17.

A. Dubietis, G. Tamošauskas, G. Fibich, and B. Ilan, “Multiple filamentation induced by input-beam ellipticity,” Opt. Lett. 29, 1126–1128 (2004). [CrossRef] [PubMed]

18.

G. Fibich and B. Ilan, “Deterministic vectorial effects lead to multiple filamentation,” Opt. Lett. 26, 840–842 (2004). [CrossRef]

19.

G. Fibich, S. Eisenmann, B. Ilan, and A. Zigler, “Control of multiple filamentation in air,” Opt. Lett. 29, 1772–1774 (2004). [CrossRef] [PubMed]

20.

A. Talebpour, S. Petit, and S. L. Chin, “Re-focusing during the propagation of a focused femtosecond Ti:Sapphire laser pulse in air,” Opt. Commun. 171, 285–290 (1999). [CrossRef]

21.

Z. Q. Hao, J. Zhang, J. Yu, Z. Zhang, J. Y. Zhong, C. Z. Zang, Z. Jin, Z. H. Wang, and Z. Y. Wei, “Fluorescence measurement and acoustic diagnostics of plasma channels in air,” Acta Phys. Sin. 55, 299–303 (2006).

22.

W. Liu, F. Théberge, E. Arévalo, J. -F. Gravel, A. Becker, and S. L. Chin, “Experiment and simulations on the energy reservoir effect in femtosecond light filaments,” Opt. Lett. 30, 2602–2604 (2005). [CrossRef] [PubMed]

23.

Z. Q. Hao, J. Zhang, X. Lu, T. T. Xi, Y. T. Li, X. H. Yuan, Z. Y. Zheng, Z. H. Wang, W. J. Ling, and Z. Y. Wei, “Spatial evolution of multiple filaments in air induced by femtosecond laser pulses,” Opt. Express, 14, 773–778 (2006), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-14-2-773. [CrossRef] [PubMed]

24.

T. T. Xi, X. Lu, and J. Zhang, “Interaction of light filaments generated by femtosecond laser pulses in air,” Phys. Rev. Lett. 96, 025003 (2006). [CrossRef] [PubMed]

25.

S. A. Hosseini, Q. Luo, B. Ferland, W. Liu, S. L. Chin, O. G. Kosareva, N. A. Panov, N. Aközbek, and V. P. Kandidov, “Competition of multiple filaments during the propagation of intense femtosecond laser pulses,” Phys. Rev. A 70, 033802 (2004). [CrossRef]

26.

Q. Luo, S. A. Hosseini, W. Liu, J. -F. Gravel, O. G. Kosareva, N. A. Panov, N. Aközbek, V. P. Kandidov, G. Roy, and S. L. Chin, “Effect of beam diameter on the propagation of intense femtosecond laser pulses,” Appl. Phys. B 80, 35–38 (2004). [CrossRef]

27.

V. P. Kandidov, O. G. Kosareva, M. P. Tamatov, A. Brodeur, and S. L. Chin, “Nucleation and random movement of filaments in the propagation of high-power laser radiation in a turbulent atmosphere,” Quantum Electron. 29, 911–915 (1999). [CrossRef]

OCIS Codes
(190.5530) Nonlinear optics : Pulse propagation and temporal solitons
(320.7110) Ultrafast optics : Ultrafast nonlinear optics

ToC Category:
Nonlinear Optics

History
Original Manuscript: September 14, 2007
Revised Manuscript: October 10, 2007
Manuscript Accepted: October 10, 2007
Published: November 20, 2007

Citation
Zuo-Qiang Hao, Jie Zhang, Ting-Ting Xi, Xiao-Hui Yuan, Zhi-Yuan Zheng, Xin Lu, Ming-Young Yu, Yu-Tong Li, Zhao-Hua Wang, Wei Zhao, and Zhi-Yi Wei, "Optimization of multiple filamentation of femtosecond laser pulses in air using a pinhole," Opt. Express 15, 16102-16109 (2007)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-15-24-16102


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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. L. Wöste, C. Wedekind, H. Wille, P. Rairoux, B. Stein, S. Nikolov, C. Werner, S. Niedermeier, F. Ronneberger, H. Schillinger, and R. Sauerbrey, "Femtosecond atmospheric lamp," Laser Optoelektron. 29, 51-53 (1997).
  3. S. L. Chin, F. Théberge, and W. Liu, "Filamentation nonlinear optics," Appl. Phys. B 86, 477-483 (2007). [CrossRef]
  4. H. Schillinger and R. Sauerbrey, "Electrical conductivity of long plasma channels in air generated by self-guided femtosecond laser pulses," Appl. Phys. B 68, 753-756 (1999). [CrossRef]
  5. S. Tzortzakis, M. A. Franco, Y. -B. André, A. Chiron, B. Lamouroux, B. S. Prade, and A. Mysyrowicz, "Formation of a conducting channel in air by self-guided femtosecond laser pulses," Phys. Rev. E 60, R3505-3507 (1999). [CrossRef]
  6. G. Méchain, A. Couairon, M. Franco, B. Prade, and A. Mysyrowicz, "Organizing multiple femtosecond filaments in air," Phys. Rev. Lett. 93, 035003 (2004). [CrossRef] [PubMed]
  7. J. Kasparian, R. Sauerbrey, D. Mondelain, S. Niedermeier, J. Yu, J. -P. Wolf, Y. -B. André, M. Franco, B. Prade, S. Tzortzakis, A. Mysyrowicz, M. Rodriguez, H. Wille, and L. Wöste, "Infrared extension of the supercontinuum generated by femtosecond terawatt laser pulses propagating in the atmosphere," Opt. Lett. 25, 1397-1399 (2000). [CrossRef]
  8. Z. Q. Hao, J. Zhang, Z. Zhang, X. H. Yuan, Z. Y. Zheng, X. Lu, Z. Jin, Z. H. Wang, J. Y. Zhong, and Y. Q. Liu, "Characteristics of multiple filaments generated by femotosecond laser pulses in air: Prefocused versus free propagation," Phys. Rev. E 74, 066402 (2006). [CrossRef]
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  10. S. Eisenmann, E. Louzon, Y. Katzir, T. Palchan, A. Zigler, Y. Sivan, and G. Fibich, "Control of the filamentation distance and pattern in long-range atmospheric propagation," Opt. Express 15, 2779-2784 (2007). [CrossRef] [PubMed]
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