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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 19, Iss. 17 — Aug. 15, 2011
  • pp: 15919–15928
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Controlling the length of plasma waveguide up to 5 mm, produced by femtosecond laser pulses in atomic clustered gas

Walid Tawfik Mohamed, Guanglong Chen, Jaehoon Kim, Geng Xiao Tao, Jungkwen Ahn, and Dong Eon Kim  »View Author Affiliations


Optics Express, Vol. 19, Issue 17, pp. 15919-15928 (2011)
http://dx.doi.org/10.1364/OE.19.015919


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Abstract

We report the observation of longitudinally uniform plasma waveguide with a controlled length of up to nearly 5 mm, in argon clustered gas jet. This self-channeling plasma is obtained using a 35 mJ, 30 fs FWHM pulse as a pump laser pulse to create the plasma channel. A 1 mJ pulse of the same laser is used for probing the plasma channels using interferometric diagnostics. The radial distribution of the electron density confirms the formation of a plasma waveguide. Clustered argon enhances the absorption efficiency of femtosecond pulses which enables the use of pump pulses of only 35 mJ, approximately 10 times less energy than required for heating conventional gas targets. The plasma channel length is controlled by the laser focus point (F), the laser intensity (I), the pump-probe delay time (t) and the laser height from a nozzle (z). The variation of the electron density for these parameters is also studied. We found that the highest density of 1.2 x 1019 cm−3 was obtained at I = 5.2 x 1016 W/cm2, z = 2 mm and t = 7.6 ns. It was demonstrated that by using a clustered jet, both the plasma waveguide length and the plasma density could be controlled.

© 2011 OSA

1. Introduction

During the last two decades, the chirped pulse amplification (CPA) femtosecond (fs) terawatt (TW) lasers, has positioned itself as critical tools in science and its applications. The propagation over a long distance is a key issue for laser-driven acceleration [1

1. W. P. Leemans, P. Volfbeyn, K. Z. Guo, S. Chattopadhyay, C. B. Schroeder, B. A. Shadwick, P. B. Lee, J. S. Wurtele, and E. Esarey, “Laser-driven plasma-based accelerators: Wakefield excitation, channel guiding, and laser triggered particle injection,” Phys. Plasmas 5(5), 1615–1623 (1998). [CrossRef]

], advanced coherent sources of extreme ultraviolet radiation [2

2. X. F. Li, A. L’Huillier, M. Ferray, L. A. Lompré, and G. Mainfray, “Multiple-harmonic generation in rare gases at high laser intensity,” Phys. Rev. A 39(11), 5751–5761 (1989). [CrossRef] [PubMed]

], and inertial confinement fusion ICF [3

3. J. Denavit and D. W. Phillion, “Laser ionization and heating of gas targets for long-scale-length instability experiments,” Phys. Plasmas 1(6), 1971 (1994). [CrossRef]

]. The ability to create a plasma channel and control its length is also critical for these applications. Laser-induced cluster plasma is an interesting system spanning the regimes of laser-solid and laser-gas interaction [4

4. A. McPherson, B. D. Thompson, A. B. Borisov, K. Boyer, and C. K. Rhodes, “Multi-photon induced x-ray emission at 4-5 keV from Xe atoms with multiple core vacancies,” Nature 370(6491), 631–634 (1994). [CrossRef]

8

8. V. Malka, E. D. Wispelaere, F. Amiranoff, S. Baton, R. Bonadio, C. Coulaud, and R. Haroutunian, “channel Formation in Long Laser Pulse Interaction with a Helium Gas Jet,” Phys. Rev. Lett. 79(16), 2979–2982 (1997). [CrossRef]

].

The guided propagation of laser beam in gas and plasma depends on the interaction length, which is typically limited by laser diffraction to a few times the Rayleigh length ZR = π ωο 2 / λ, where ωο is the laser spot radius at focus and λ is the laser wavelength [8

8. V. Malka, E. D. Wispelaere, F. Amiranoff, S. Baton, R. Bonadio, C. Coulaud, and R. Haroutunian, “channel Formation in Long Laser Pulse Interaction with a Helium Gas Jet,” Phys. Rev. Lett. 79(16), 2979–2982 (1997). [CrossRef]

]. Many schemes for guided propagation have been demonstrated. It was reported that the diffractive spreading could be balanced by the refractive index profile of a medium and an intense pulse is then guided within a constant (small) radius over many Rayleigh ranges [9

9. H. M. Milchberg, K. Y. Kim, V. Kumarappan, B. D. Layer, and H. Sheng, “Clustered gases as a medium for efficient plasma waveguide generation,” Philos. Transact. A Math. Phys. Eng. Sci. 364(1840), 647–661 (2006). [CrossRef] [PubMed]

]. It was also known that the waveguide lifetime should be sufficiently long for practical applications. It points to this fact that steady state waveguides should survive for many laser shots. This means that waveguides produced synchronously with injected pulses should be reproducible at a high repetition rate for many shots, with a very high duty cycle. It is noteworthy that for a single guiding scheme to meet all these requirements is very challenging [9

9. H. M. Milchberg, K. Y. Kim, V. Kumarappan, B. D. Layer, and H. Sheng, “Clustered gases as a medium for efficient plasma waveguide generation,” Philos. Transact. A Math. Phys. Eng. Sci. 364(1840), 647–661 (2006). [CrossRef] [PubMed]

]. Relativistic and ponderomotive self-channeling is the natural way to do this [10

10. A. B. Borisov, A. V. Borovskiy, O. B. Shiryaev, V. V. Korobkin, A. M. Prokhorov, J. C. Solem, T. S. Luk, K. Boyer, and C. K. Rhodes, “Relativistic and charge-displacement self-channeling of intense ultrashort laser pulses in plasmas,” Phys. Rev. A 45(8), 5830–5845 (1992). [CrossRef] [PubMed]

]. The occurrence of self-channeling with the rapid formation of a stable, extended, and longitudinally homogeneous filament has achieved propagation lengths from nanometer range [11

11. J. F. Herbstman and A. J. Hunt, “High-aspect ratio nanochannel formation by single femtosecond laser pulses,” Opt. Express 18(16), 16840–16848 (2010). [CrossRef] [PubMed]

] up to hundred times the Rayleigh lengths [12

12. A. B. Borisov, X. Shi, V. B. Karpov, V. V. Korobkin, J. C. Solem, O. B. Shiryaev, A. McPherson, K. Boyer, and C. K. Rhodes, “Stable self-channeling of intense ultraviolet pulses in underdense plasma, producing channels exceeding 100 Rayleigh lengths,” J. Opt. Soc. Am. B 11(10), 1941–1947 (1994). [CrossRef]

]. However, in the later experiment, a high power (~460 GW) subpicosecond laser at 248 nm was used to reach an intensity of ~1018 W/cm2 to generate a self-focusing plasma channel in krypton gas using a differentially pumped target gas cell. Similar laser conditions were also used for the high-pressure gas jet targets, and relativistic self-guiding over no more than ~2 mm has been observed. That length was limited by pulse scattering and erosion owing to ionization-induced refraction and Raman instabilities [13

13. J. Fuchs, G. Malka, J. C. Adam, F. Amiranoff, S. D. Baton, N. Blanchot, A. Héron, G. Laval, J. L. Migel, P. Mora, H. Pépin, and C. Rousseaux, “Dynamics of Subpicosecond Relativistic Laser Pulse Self-Channeling in an Underdense Preformed Plasma,” Phys. Rev. Lett. 80(8), 1658–1661 (1998). [CrossRef]

]. However, the usage of such high laser intensities may be not preferable for X-ray lasers and harmonic generation experiments [5

5. W. G. John Tisch, “Phase-matched high-order harmonic generation in an ionized medium using a buffer gas of exploding atomic clusters,” Phys. Rev. A 62, 041802(R) (2000).

].

In the present work we report the results of another approach using clustered gas jets, where we observed self-channeling over nearly 5 mm, with an intensity almost three orders of magnitude lower than required for relativistic self-focusing or ponderomotive filamentation [13

13. J. Fuchs, G. Malka, J. C. Adam, F. Amiranoff, S. D. Baton, N. Blanchot, A. Héron, G. Laval, J. L. Migel, P. Mora, H. Pépin, and C. Rousseaux, “Dynamics of Subpicosecond Relativistic Laser Pulse Self-Channeling in an Underdense Preformed Plasma,” Phys. Rev. Lett. 80(8), 1658–1661 (1998). [CrossRef]

]. It was noticed that such a plasma channel acts as a waveguide where the electron density increases with radius from the beam propagation axis [9

9. H. M. Milchberg, K. Y. Kim, V. Kumarappan, B. D. Layer, and H. Sheng, “Clustered gases as a medium for efficient plasma waveguide generation,” Philos. Transact. A Math. Phys. Eng. Sci. 364(1840), 647–661 (2006). [CrossRef] [PubMed]

].

Clusters are van der Waals-bonded assemblies of approximately 102–107 atoms, typically produced by rapid cooling during high-pressure gas flow through a gas jet nozzle into vacuum [14

14. O. F. Hagena, “Condensation in Free Jets: Comparison of Rare Gases and Metals,” Z. Phys. D 4(3), 291–299 (1987). [CrossRef]

]. Since clusters are intermediate to macroscopic condensed matter and microscopic systems such as atoms and molecules, the intense laser-cluster interaction creates small-scale plasmas (microplasmas). Detailed studies of these cluster microplasmas showed that it can eject hot electrons up to 3 keV [15

15. Y. L. Shao, T. Ditmire, J. W. G. Tisch, E. Springate, J. P. Marangos, and M. H. R. Hutchinson, “Multi-keV Electron Generation in the Interaction of Intense Laser Pulses with Xe Clusters,” Phys. Rev. Lett. 77(16), 3343–3346 (1996). [CrossRef] [PubMed]

]. Soon after the clusters are heated, the charge separation by the hot electrons causes the clusters to explode, and as a result, much of the energy deposited by the laser in a cluster is converted to ion kinetic energy [16

16. T. Ditmire, J. W. G. Tisch, E. Springate, M. B. Mason, N. Hay, R. A. Smith, J. P. Marangos, and M. H. R. Hutchinson, “Nuclear Fusion from Explosions of Femtosecond Laser-Heated Deuterium Clusters,” Nature 386, 54 (1997). [CrossRef]

]. Furthermore, it is indicated that clusters are rapidly heated by the laser to a nonequilibrium, superheated state, in large parts, due to the passage of the free electron density in the cluster through a Mie resonance with the laser field during the cluster expansion [17

17. T. Ditmire, T. Donnelly, A. M. Rubenchik, R. W. Falcone, and M. D. Perry, “Interaction of intense laser pulses with atomic clusters,” Phys. Rev. A 53(5), 3379–3402 (1996). [CrossRef] [PubMed]

]. Such studies suggested that plasmas formed by the intense irradiation on gases containing clusters will exhibit large laser absorption [18

18. T. Ditmire, R. A. Smith, J. W. G. Tisch, and M. H. R. Hutchinson, “High Intensity Laser Absorption by Gases of Atomic Clusters,” Phys. Rev. Lett. 78(16), 3121–3124 (1997). [CrossRef]

].

On the other hand, it was found that atomic cluster gases can promote laser pulse self-focusing at intensities lower than required for relativistic and ponderomotive self-focusing [19

19. H. M. Milchberg, S. J. McNaught, and E. Parra, “Plasma hydrodynamics of the intense laser-cluster interaction,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 64(5), 056402 (2001). [CrossRef] [PubMed]

]. This effect derives from the evolution of the transient cluster polarizability induced by the pulse according to the hydrodynamic model of individual cluster evolution [20

20. K. Y. Kim, I. Alexeev, E. Parra, and H. M. Milchberg, “Time-resolved explosion of intense-laser-heated clusters,” Phys. Rev. Lett. 90(2), 023401 (2003). [CrossRef] [PubMed]

]. In this model, it was considered that the complex cluster polarizability γ, where P = γ E is the cluster dipole moment and E is the external laser field, reveals the details of the cluster dynamics. The temporal behavior of the real part of the polarizability Re (γ) = γr for an individual cluster is determined by a competition in its optical response between the portion of its expanding plasma above critical density and the portion below: γr > 0 when the supercritical density material dominates the response, and γr < 0 when the subcritical density response dominates [20

20. K. Y. Kim, I. Alexeev, E. Parra, and H. M. Milchberg, “Time-resolved explosion of intense-laser-heated clusters,” Phys. Rev. Lett. 90(2), 023401 (2003). [CrossRef] [PubMed]

]. For clusters near the beam center, where the intensity is high, γr rises faster than at the edge of the beam. The self-focusing effect is understood by considering the radial and time variation of the average polarizability γ¯ over an ensemble of clusters in a gas. The result is a beam-axis-peaked radial profile of γ¯r, since real refractive index nr = 1 + 2πΝc γ¯r where Νc is the cluster number density, this profile gives rise to pulse self-focusing [21

21. I. Alexeev, T. M. Antonsen, K. Y. Kim, and H. M. Milchberg, “Self-focusing of intense laser pulses in a clustered gas,” Phys. Rev. Lett. 90(10), 103402 (2003). [CrossRef] [PubMed]

].The model for the complex polarizability and self-focusing have been experimentally confirmed [21

21. I. Alexeev, T. M. Antonsen, K. Y. Kim, and H. M. Milchberg, “Self-focusing of intense laser pulses in a clustered gas,” Phys. Rev. Lett. 90(10), 103402 (2003). [CrossRef] [PubMed]

]. So that the usage of atomic clusters provides two novel and important features; efficient absorption of femtosecond pulses [22

22. K. Y. Kim, V. Kumarappan, and H. M. Milchberg, “Measurement of the average size and density of clusters in a gas jet,” Appl. Phys. Lett. 83(15), 3210 (2003). [CrossRef]

] and their self-guided propagation [21

21. I. Alexeev, T. M. Antonsen, K. Y. Kim, and H. M. Milchberg, “Self-focusing of intense laser pulses in a clustered gas,” Phys. Rev. Lett. 90(10), 103402 (2003). [CrossRef] [PubMed]

]. Recently, it was found that the requirement for adequate ionization and heating for channel formation in N2O gas clusters demands the high laser energy [23

23. K. Y. Kim, H. M. Milchberg, A. Ya. Faenov, A. I. Magunov, T. A. Pikuz, and I. Yu. Skobelev, “X-ray spectroscopy of 1 cm plasma channels produced by self-guided pulse propagation in elongated cluster jets,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 73(6), 066403 (2006). [CrossRef] [PubMed]

]. In these experiments, the self-guiding effect was made possible as the strongly heated large clusters (20 – 30 nm) exploded in the presence of the driving laser intensities of ~1017 W/cm2. Moreover, a long plasma channel of 1.5 cm was obtained for Ar clusters (~7 nm) using a 100 ps Nd:YAG laser pulse of high energy of 500 mJ (~1017 W/cm2) [24

24. B. D. Layer, A. G. York, S. Varma, Y. H. Chen, and H. M. Milchberg, “Periodic index-modulated plasma waveguide,” Opt. Express 17(6), 4263–4267 (2009). [CrossRef] [PubMed]

].

In our current experiment, we demonstrate the generation of a long plasma waveguide and control of its length using different experimental parameters with laser intensities (1015 - 1016 W/cm2) much lower than before [23

23. K. Y. Kim, H. M. Milchberg, A. Ya. Faenov, A. I. Magunov, T. A. Pikuz, and I. Yu. Skobelev, “X-ray spectroscopy of 1 cm plasma channels produced by self-guided pulse propagation in elongated cluster jets,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 73(6), 066403 (2006). [CrossRef] [PubMed]

,24

24. B. D. Layer, A. G. York, S. Varma, Y. H. Chen, and H. M. Milchberg, “Periodic index-modulated plasma waveguide,” Opt. Express 17(6), 4263–4267 (2009). [CrossRef] [PubMed]

]. This gives us a better understanding of the plasma channel effect of atomic clusters based on the measurements of the plasma density profile.

2. Experimental setup

3. Results and discussions

Figure 2(c) represents the radial electron density distribution observed from the interferogram in Fig. 2(a) using the Abel inversion. The electron density profile indicates that the plasma channel diameter is nearly 100 μm FWHM as observed by others [8

8. V. Malka, E. D. Wispelaere, F. Amiranoff, S. Baton, R. Bonadio, C. Coulaud, and R. Haroutunian, “channel Formation in Long Laser Pulse Interaction with a Helium Gas Jet,” Phys. Rev. Lett. 79(16), 2979–2982 (1997). [CrossRef]

,34

34. V. Kumarappan, K. Y. Kim, and H. M. Milchberg, “Guiding of intense laser pulses in plasma waveguides produced from efficient, femtosecond end-pumped heating of clustered gases,” Phys. Rev. Lett. 94(20), 205004 (2005). [CrossRef] [PubMed]

]. The variation of the electron density profile confirms the formation of the waveguide with a hollow electron density profile; a local minimum (7 x 1018 cm−3) on the axis and a maxima (1.3 x 1019 cm−3) at the walls as also observed by recent studies [35

35. M. Nakatsutsumi, J.-R. Marquès, P. Antici, N. Bourgeois, J. L. Feugeas, T. Lin, Ph. Nicolaï, L. Romagnani, R. Kodama, P. Audebert, and J. Fuchs, “High-power laser delocalization in plasmas leading to long-range beam merging,” Nat. Phys. 6(12), 1010–1016 (2010). [CrossRef]

]. It was shown that the heated clusters explode on a sub-ps time scale, eventually expanding and merging to form locally uniform plasma in ~10 –100 ps [19

19. H. M. Milchberg, S. J. McNaught, and E. Parra, “Plasma hydrodynamics of the intense laser-cluster interaction,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 64(5), 056402 (2001). [CrossRef] [PubMed]

,20

20. K. Y. Kim, I. Alexeev, E. Parra, and H. M. Milchberg, “Time-resolved explosion of intense-laser-heated clusters,” Phys. Rev. Lett. 90(2), 023401 (2003). [CrossRef] [PubMed]

,36

36. J. Fan, E. Parra, and H. M. Milchberg, “Resonant self-trapping and absorption of intense bessel beams,” Phys. Rev. Lett. 84(14), 3085–3088 (2000), http://prl.aps.org/abstract/PRL/v84/i14/p3085_1. [CrossRef] [PubMed]

]. This hot plasma expands radially, leading to the formation of a shock wave and the subsequent formation of waveguide structure over a nanosecond time scale as proved previously [32

32. T. Ditmire, R. A. Smith, and M. H. R. Hutchinson, “Plasma waveguide formation in predissociated clustering gases,” Opt. Lett. 23(5), 322–324 (1998), http://www.opticsinfobase.org/ol/abstract.cfm?uri=ol-23-5-322. [CrossRef] [PubMed]

]. H, we set our delay time between the pump and probe beams (t) to be in the nanosecond time range.

In the current experiment, controlling the length of the plasma waveguide was studied using four variables; the focus point (F), the delay time (t), the laser intensity (I) and the laser height (z). This was done by varying just one of them and fixing the others at the optimum values found. The position of the focus point F relative to the midpoint of the nozzle orifice can be varied under vacuum using a remotely controlled motorized stage. Figure 3(a)
Fig. 3 (a) The channel length change with the focus point (F) using laser intensity 5.2 x 1016 W/cm2 and delay time t = 7.6 ns between pump and probe and height z = 2 mm and Ar baking pressure 75 bars. (b) The channel length change with delay time (t) between the pump and probe pulses using different laser energies at z = 2 mm for clustered Ar jet.
shows the variation of the channel length with F, using I = 5.2 x 1016 W/cm2, t = 7.6 ns, z = 2 mm and Ar baking pressure of 75 bars. The figure reveals that the channel length reaches a maximum value of 4.7 mm at F = - 3.5 mm from the midpoint of the nozzle orifice. However, under our experimental conditions, the Ar gas stream flow was expected to take a conically shape [37

37. H. C. Man, J. Duan, and T. M. Yue, “Dynamic characteristics of gas jets from subsonic and supersonic slit nozzles for high pressure gas laser cutting,” Opt. Laser Technol. 30(8), 497–509 (1998). [CrossRef]

] near to the nozzle surface up to the height z = 2 mm with the same half opening angle of the nozzle of 24.2°. In this case, the tangential distance is given by 2 x tan (24.2) ≈0.9 mm from the nozzle orifice edge, i.e. 0.9 + 2.5 = 3.4 mm which is close to our experimental measured value of 3.5 mm from the midpoint of the nozzle orifice as illustrated in Fig. 1(c). We noticed that, putting F a little earlier before the nozzle orifice edge helps to increase the interaction length and allows more Ar clusters to be ionized which in turn increases the channel length. On the other hand, if F is too far from or near to the midpoint of the nozzle orifice, less Ar clusters will be ionized which leads to a rapid decrease in the plasma channel length as revealed in Fig. 3(a). Figure 3(b) shows a performed scanning of the pump and probe delay time (t) for different laser intensities. Laser intensities of 4.6 x 1015 W/cm2, 1.3 x 1016 W/cm2, 3.72 x 1016 W/cm2 and 5.2 x 1016 W/cm2 were used. It was observed that, for each of these intensities, the channel length increased gradually from t = 4 up to 7.6 ns and then decreased with time. The channel length varies between 3 and 4.7 mm for 5.2 x 1016 W/cm2 while for 4.6 x 1015 W/cm2 it varies between 1 and 2 mm.

Thus, maximum channel lengths were reached at 7.6 ns. If the delay time is earlier than 7.6 ns then the channel length will be shorter. For longer delay times, we expected that the plasma density will decrease and thus the channel length reduces as well. It is noteworthy that the time needed for the maximum length of the plasma channel is insensitive to the laser intensity.

Figure 4(a)
Fig. 4 (a) The plasma channel length change with laser height (z) at different laser intensities for t = 7.6 ns using clustered Ar jet with backing pressure of 75 bars. (b) The radial distribution of electron density for different pump-probe delay times at optimum conditions for plasma channel length of 4.7 mm.
shows the change of the plasma channel length with laser height (z) for different intensities at a delay of t = 7.6 ns and an Ar baking pressure of 75 bars. Laser intensities of 4.6 x 1015 W/cm2, 1.3 x 1016 W/cm2, 3.72 x 1016 W/cm2, 5.2 x 1016 W/cm2 were used. The figure reveals that for each of these intensities, the channel length increases with increasing the height gradually from z = 0.5 μm up to 2 mm then it decreases. Also, the channel length increases gradually with the laser intensity that it varies between 2.7 and 4.7 mm for the highest intensity while between 1 and 2 mm for the lowest ones. Hence, the change of the channel length depends on the Ar gas jet dynamics under our conditions. The gas jet dynamics from supersonic slit nozzle has been studied previously by others [37

37. H. C. Man, J. Duan, and T. M. Yue, “Dynamic characteristics of gas jets from subsonic and supersonic slit nozzles for high pressure gas laser cutting,” Opt. Laser Technol. 30(8), 497–509 (1998). [CrossRef]

,38

38. J. F. Han, C. W. Yanga, J. W. Miao, J. F. Lu, M. Liu, X. B. Luo, and M. G. Shi, “The spatial distribution of argon clusters in gas jet,” Eur. Phys. J. D 56(3), 347–352 (2010). [CrossRef]

]. These studies found that for a nozzle width of < 1 mm, the gas jet may expand out conically in the area near to the nozzle surface. At higher distances from the nozzle, they claimed that the gas jet is tapered and the gas density decreases with z2 [37

37. H. C. Man, J. Duan, and T. M. Yue, “Dynamic characteristics of gas jets from subsonic and supersonic slit nozzles for high pressure gas laser cutting,” Opt. Laser Technol. 30(8), 497–509 (1998). [CrossRef]

]. Furthermore, when the gas expands out of the nozzle, a certain distance is required for the clusters to grow, beyond which the cluster size keeps the same value for a long distance before eventually decreasing [37

37. H. C. Man, J. Duan, and T. M. Yue, “Dynamic characteristics of gas jets from subsonic and supersonic slit nozzles for high pressure gas laser cutting,” Opt. Laser Technol. 30(8), 497–509 (1998). [CrossRef]

]. By applying these dynamics on the experimental findings, as demonstrated in Fig. 4(a), we can assume that the Ar jet may expand conically with an angle of about 24.2° near to the surface of the nozzle and then it starts to taper at z > 2 mm. Above the z = 2 mm, the gas density decreases and consequently the laser absorption decreases which leads to lower ionization and shorter channeling length.

Figure 4(b) shows the time-resolved electron density profiles for clustered Ar jet with a backing pressure of 75 bars, using the maximum laser intensity of 5.2 x 1016 W/cm2 with z = 2 mm and F = - 3.5 mm. A central minimum in the electron density profile starts to develop around 6.93 ns. This reveals the plasma expansion and the flattening of the central density as the time goes. These results illustrate the ability to control the guide electron density from 2 x1019 cm−3 to low levels of ~1018 cm−3. Similar profile and behavior have been observed by others in different experiments [39

39. C. G. Durfee 3rd and H. M. Milchberg, “Light pipe for high intensity laser pulses,” Phys. Rev. Lett. 71(15), 2409–2412 (1993), http://prl.aps.org/abstract/PRL/v71/i15/p2409_1. [CrossRef] [PubMed]

].

The pump laser energy used in our experiment is only 35 mJ, approximately 10 times less energy than required for heating conventional gas targets for plasma waveguide generation [40

40. T. R. Clark and H. M. Milchberg, “Time- and Space-Resolved Density Evolution of the Plasma Waveguide,” Phys. Rev. Lett. 78(12), 2373–2376 (1997), http://prl.aps.org/abstract/PRL/v78/i12/p2373_1. [CrossRef]

]. We noted that the radial wings of the electron density profiles extended considerably further out than for channels generated in non-clustered gases [40

40. T. R. Clark and H. M. Milchberg, “Time- and Space-Resolved Density Evolution of the Plasma Waveguide,” Phys. Rev. Lett. 78(12), 2373–2376 (1997), http://prl.aps.org/abstract/PRL/v78/i12/p2373_1. [CrossRef]

]. The channel develops into a waveguide over a short distance (100 μm) along the pump laser propagation direction. The clusters radially surrounding the hot plasma of the laser interaction region are preheated by the leading edge of the pump pulse (exceeding 1014 W/cm2) [40

40. T. R. Clark and H. M. Milchberg, “Time- and Space-Resolved Density Evolution of the Plasma Waveguide,” Phys. Rev. Lett. 78(12), 2373–2376 (1997), http://prl.aps.org/abstract/PRL/v78/i12/p2373_1. [CrossRef]

], which ionizes and disassembles clusters in advance of the shock wave arrival. Hence, the cluster method provides a route to control the waveguide density since cluster size and density can be adjusted to give desired levels of merged plasma density. These experiments serve to indicate the viability of the technique to generate and control longer Ar channels as a waveguide. If an additional fs laser pulse is added, synchronized with the pump pulse, the current plasma waveguide is well suit to the study of the guided propagation and the generation of high-order harmonic generation (HHG) [41

41. Y. Ehrlich, A. Zigler, C. Cohen, J. Krall, and P. Sprangle, “Guiding of High Intensity Laser Pulses in Straight and Curved Plasma Channel Experiments, ” Phys. Rev. Lett. 77, 4186 (1996). http://prl.aps.org/abstract/PRL/v77/i20/p4186_1.

] from multiplied charged ions, which is currently in progress.

4. Conclusion

Following through intense experimental research, we have demonstrated the formation of a plasma waveguide using a clustered Ar gas jet with a laser intensity (5.2 x 1016) about 100 times lower than required in non-clustered gas target. Femtosecond laser pulses have been successfully used to generate and control the formation of long plasma channel waveguide up to nearly 5 mm in a clustered argon gas jet. The observed waveguide can have both low central density and small diameter. We confirmed experimentally that the use of clustered jets realizes the possibility of achieving on-axis plasma density control. Moreover, the length of the waveguide can be controlled by plasma channel parameters (the focus point, the pumb-probe delay time, the laser intensity and the laser height from the nozzle). Our results are of great importance where high-intensity optical guiding is needed. This waveguide could be used for the high-order harmonic generation (HHG). By controlling the plasma channel parameters, the phase-matching could be enhanced which results an increase of the HHG efficiency. This will represent a progress in producing new high efficiency XUV source. The controlled long plasma channel represented here may also enable studies of laser wakefield acceleration beyond the dephasing limit for electron density ne 1018 cm−3 [42

42. C. W. Leemans, “Siders, E. Esarey, N. E. Andreev, G. Shvets, and W. B. Mori, “Plasma Guiding and Wakefield Generation for S econd-Generation Experiments,” IEEE Trans. Plasma Sci. 24 (2), 331–342 (1996), http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=509997. [CrossRef]

].

Acknowledgment

This research has been supported in part by Global Research Laboratory Program [Grant No 2009-00439] and by Leading Foreign Research Institute Recruitment Program [Grant No 2010-00471] through the National Research Foundation of Korea(NRF) funded by the Ministry of Education, Science and Technology (MEST).

References and links

1.

W. P. Leemans, P. Volfbeyn, K. Z. Guo, S. Chattopadhyay, C. B. Schroeder, B. A. Shadwick, P. B. Lee, J. S. Wurtele, and E. Esarey, “Laser-driven plasma-based accelerators: Wakefield excitation, channel guiding, and laser triggered particle injection,” Phys. Plasmas 5(5), 1615–1623 (1998). [CrossRef]

2.

X. F. Li, A. L’Huillier, M. Ferray, L. A. Lompré, and G. Mainfray, “Multiple-harmonic generation in rare gases at high laser intensity,” Phys. Rev. A 39(11), 5751–5761 (1989). [CrossRef] [PubMed]

3.

J. Denavit and D. W. Phillion, “Laser ionization and heating of gas targets for long-scale-length instability experiments,” Phys. Plasmas 1(6), 1971 (1994). [CrossRef]

4.

A. McPherson, B. D. Thompson, A. B. Borisov, K. Boyer, and C. K. Rhodes, “Multi-photon induced x-ray emission at 4-5 keV from Xe atoms with multiple core vacancies,” Nature 370(6491), 631–634 (1994). [CrossRef]

5.

W. G. John Tisch, “Phase-matched high-order harmonic generation in an ionized medium using a buffer gas of exploding atomic clusters,” Phys. Rev. A 62, 041802(R) (2000).

6.

S. B. Hansen, K. B. Fournier, A. Y. Faenov, A. I. Magunov, T. A. Pikuz, I. Y. Skobelev, Y. Fukuda, Y. Akahane, M. Aoyama, N. Inoue, H. Ueda, and K. Yamakawa, “Measurement of 2l-nl’ x-ray transitions from approximately 1 μm Kr clusters irradiated by high-intensity femtosecond laser pulses,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 71(1 Pt 2), 016408 (2005). [CrossRef] [PubMed]

7.

Y. Fukuda, K. Yamakawa, Y. Akahane, M. Aoyama, N. Inoue, H. Ueda, and Y. Kishimoto, “Optimized Energetic Particle Emissions from Xe Cluster in Intense Laser Fields,” Phys. Rev. A 67(6), 061201 (2003). [CrossRef]

8.

V. Malka, E. D. Wispelaere, F. Amiranoff, S. Baton, R. Bonadio, C. Coulaud, and R. Haroutunian, “channel Formation in Long Laser Pulse Interaction with a Helium Gas Jet,” Phys. Rev. Lett. 79(16), 2979–2982 (1997). [CrossRef]

9.

H. M. Milchberg, K. Y. Kim, V. Kumarappan, B. D. Layer, and H. Sheng, “Clustered gases as a medium for efficient plasma waveguide generation,” Philos. Transact. A Math. Phys. Eng. Sci. 364(1840), 647–661 (2006). [CrossRef] [PubMed]

10.

A. B. Borisov, A. V. Borovskiy, O. B. Shiryaev, V. V. Korobkin, A. M. Prokhorov, J. C. Solem, T. S. Luk, K. Boyer, and C. K. Rhodes, “Relativistic and charge-displacement self-channeling of intense ultrashort laser pulses in plasmas,” Phys. Rev. A 45(8), 5830–5845 (1992). [CrossRef] [PubMed]

11.

J. F. Herbstman and A. J. Hunt, “High-aspect ratio nanochannel formation by single femtosecond laser pulses,” Opt. Express 18(16), 16840–16848 (2010). [CrossRef] [PubMed]

12.

A. B. Borisov, X. Shi, V. B. Karpov, V. V. Korobkin, J. C. Solem, O. B. Shiryaev, A. McPherson, K. Boyer, and C. K. Rhodes, “Stable self-channeling of intense ultraviolet pulses in underdense plasma, producing channels exceeding 100 Rayleigh lengths,” J. Opt. Soc. Am. B 11(10), 1941–1947 (1994). [CrossRef]

13.

J. Fuchs, G. Malka, J. C. Adam, F. Amiranoff, S. D. Baton, N. Blanchot, A. Héron, G. Laval, J. L. Migel, P. Mora, H. Pépin, and C. Rousseaux, “Dynamics of Subpicosecond Relativistic Laser Pulse Self-Channeling in an Underdense Preformed Plasma,” Phys. Rev. Lett. 80(8), 1658–1661 (1998). [CrossRef]

14.

O. F. Hagena, “Condensation in Free Jets: Comparison of Rare Gases and Metals,” Z. Phys. D 4(3), 291–299 (1987). [CrossRef]

15.

Y. L. Shao, T. Ditmire, J. W. G. Tisch, E. Springate, J. P. Marangos, and M. H. R. Hutchinson, “Multi-keV Electron Generation in the Interaction of Intense Laser Pulses with Xe Clusters,” Phys. Rev. Lett. 77(16), 3343–3346 (1996). [CrossRef] [PubMed]

16.

T. Ditmire, J. W. G. Tisch, E. Springate, M. B. Mason, N. Hay, R. A. Smith, J. P. Marangos, and M. H. R. Hutchinson, “Nuclear Fusion from Explosions of Femtosecond Laser-Heated Deuterium Clusters,” Nature 386, 54 (1997). [CrossRef]

17.

T. Ditmire, T. Donnelly, A. M. Rubenchik, R. W. Falcone, and M. D. Perry, “Interaction of intense laser pulses with atomic clusters,” Phys. Rev. A 53(5), 3379–3402 (1996). [CrossRef] [PubMed]

18.

T. Ditmire, R. A. Smith, J. W. G. Tisch, and M. H. R. Hutchinson, “High Intensity Laser Absorption by Gases of Atomic Clusters,” Phys. Rev. Lett. 78(16), 3121–3124 (1997). [CrossRef]

19.

H. M. Milchberg, S. J. McNaught, and E. Parra, “Plasma hydrodynamics of the intense laser-cluster interaction,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 64(5), 056402 (2001). [CrossRef] [PubMed]

20.

K. Y. Kim, I. Alexeev, E. Parra, and H. M. Milchberg, “Time-resolved explosion of intense-laser-heated clusters,” Phys. Rev. Lett. 90(2), 023401 (2003). [CrossRef] [PubMed]

21.

I. Alexeev, T. M. Antonsen, K. Y. Kim, and H. M. Milchberg, “Self-focusing of intense laser pulses in a clustered gas,” Phys. Rev. Lett. 90(10), 103402 (2003). [CrossRef] [PubMed]

22.

K. Y. Kim, V. Kumarappan, and H. M. Milchberg, “Measurement of the average size and density of clusters in a gas jet,” Appl. Phys. Lett. 83(15), 3210 (2003). [CrossRef]

23.

K. Y. Kim, H. M. Milchberg, A. Ya. Faenov, A. I. Magunov, T. A. Pikuz, and I. Yu. Skobelev, “X-ray spectroscopy of 1 cm plasma channels produced by self-guided pulse propagation in elongated cluster jets,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 73(6), 066403 (2006). [CrossRef] [PubMed]

24.

B. D. Layer, A. G. York, S. Varma, Y. H. Chen, and H. M. Milchberg, “Periodic index-modulated plasma waveguide,” Opt. Express 17(6), 4263–4267 (2009). [CrossRef] [PubMed]

25.

B. C. Walker, C. Toth, D. N. Fittinghoff, T. Guo, D.-E. Kim, C. Rose-Petruck, J. A. Squier, K. Yamakawa, K. R. Wilson, and C. Barty, “A 50 EW/cm;2 Ti:sapphire laser system for studying relativistic light-matter interactions,” Opt. Express 5(10), 196–202 (1999). [CrossRef] [PubMed]

26.

G. Chen, B. Kim, B. Ahn, and D.-E. Kim, “Pressure dependence of argon cluster size for different nozzle geometries,” J. Appl. Phys. 106(5), 053507 (2009). [CrossRef]

27.

I. H. Hutchinson, “Principles of Plasma Diagnostics,” Cambridge University Press, New York, (1987).

28.

A. E. Seigman, “Lasers” University Science Books, Mill Valley, California, section 17 (1986).

29.

G. Chen, B. Kim, B. Ahn, and D.-E. Kim, “Experimental investigation on argon cluster sizes for conical nozzles with different opening angles,” J. Appl. Phys. 108, 1 (2010), http://link.aip.org/link/?JAPIAU/108/064329/1.

30.

O. F. Hagena and W. Obert, “Cluster Formation in Expanding Supersonic Jets: Effect of Pressure, Temperature, Nozzle Size, and Test Gas,” J. Chem. Phys. 56(5), 1793 (1972). [CrossRef]

31.

O. F. Hagena, “Cluster ion sources,” Rev. Sci. Instrum. 63(4), 2374 (1992), http://link.aip.org/link/doi/10.1063/1.1142933. [CrossRef]

32.

T. Ditmire, R. A. Smith, and M. H. R. Hutchinson, “Plasma waveguide formation in predissociated clustering gases,” Opt. Lett. 23(5), 322–324 (1998), http://www.opticsinfobase.org/ol/abstract.cfm?uri=ol-23-5-322. [CrossRef] [PubMed]

33.

S. Augst, D. D. Meyerhofer, D. Strickland, and S. L. Chin, “Laser ionization of noble gases by Coulomb-barrier suppression,” J. Opt. Soc. Am. B 8(4), 858 (1991), http://www.opticsinfobase.org/abstract.cfm?&id=5984. [CrossRef]

34.

V. Kumarappan, K. Y. Kim, and H. M. Milchberg, “Guiding of intense laser pulses in plasma waveguides produced from efficient, femtosecond end-pumped heating of clustered gases,” Phys. Rev. Lett. 94(20), 205004 (2005). [CrossRef] [PubMed]

35.

M. Nakatsutsumi, J.-R. Marquès, P. Antici, N. Bourgeois, J. L. Feugeas, T. Lin, Ph. Nicolaï, L. Romagnani, R. Kodama, P. Audebert, and J. Fuchs, “High-power laser delocalization in plasmas leading to long-range beam merging,” Nat. Phys. 6(12), 1010–1016 (2010). [CrossRef]

36.

J. Fan, E. Parra, and H. M. Milchberg, “Resonant self-trapping and absorption of intense bessel beams,” Phys. Rev. Lett. 84(14), 3085–3088 (2000), http://prl.aps.org/abstract/PRL/v84/i14/p3085_1. [CrossRef] [PubMed]

37.

H. C. Man, J. Duan, and T. M. Yue, “Dynamic characteristics of gas jets from subsonic and supersonic slit nozzles for high pressure gas laser cutting,” Opt. Laser Technol. 30(8), 497–509 (1998). [CrossRef]

38.

J. F. Han, C. W. Yanga, J. W. Miao, J. F. Lu, M. Liu, X. B. Luo, and M. G. Shi, “The spatial distribution of argon clusters in gas jet,” Eur. Phys. J. D 56(3), 347–352 (2010). [CrossRef]

39.

C. G. Durfee 3rd and H. M. Milchberg, “Light pipe for high intensity laser pulses,” Phys. Rev. Lett. 71(15), 2409–2412 (1993), http://prl.aps.org/abstract/PRL/v71/i15/p2409_1. [CrossRef] [PubMed]

40.

T. R. Clark and H. M. Milchberg, “Time- and Space-Resolved Density Evolution of the Plasma Waveguide,” Phys. Rev. Lett. 78(12), 2373–2376 (1997), http://prl.aps.org/abstract/PRL/v78/i12/p2373_1. [CrossRef]

41.

Y. Ehrlich, A. Zigler, C. Cohen, J. Krall, and P. Sprangle, “Guiding of High Intensity Laser Pulses in Straight and Curved Plasma Channel Experiments, ” Phys. Rev. Lett. 77, 4186 (1996). http://prl.aps.org/abstract/PRL/v77/i20/p4186_1.

42.

C. W. Leemans, “Siders, E. Esarey, N. E. Andreev, G. Shvets, and W. B. Mori, “Plasma Guiding and Wakefield Generation for S econd-Generation Experiments,” IEEE Trans. Plasma Sci. 24 (2), 331–342 (1996), http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=509997. [CrossRef]

OCIS Codes
(320.0320) Ultrafast optics : Ultrafast optics
(320.2250) Ultrafast optics : Femtosecond phenomena
(320.7100) Ultrafast optics : Ultrafast measurements

ToC Category:
Ultrafast Optics

History
Original Manuscript: June 7, 2011
Revised Manuscript: July 22, 2011
Manuscript Accepted: July 22, 2011
Published: August 4, 2011

Citation
Walid Tawfik Mohamed, Guanglong Chen, Jaehoon Kim, Geng Xiao Tao, Jungkwen Ahn, and Dong Eon Kim, "Controlling the length of plasma waveguide up to 5 mm, produced by femtosecond laser pulses in atomic clustered gas," Opt. Express 19, 15919-15928 (2011)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-17-15919


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References

  1. W. P. Leemans, P. Volfbeyn, K. Z. Guo, S. Chattopadhyay, C. B. Schroeder, B. A. Shadwick, P. B. Lee, J. S. Wurtele, and E. Esarey, “Laser-driven plasma-based accelerators: Wakefield excitation, channel guiding, and laser triggered particle injection,” Phys. Plasmas 5(5), 1615–1623 (1998). [CrossRef]
  2. X. F. Li, A. L’Huillier, M. Ferray, L. A. Lompré, and G. Mainfray, “Multiple-harmonic generation in rare gases at high laser intensity,” Phys. Rev. A 39(11), 5751–5761 (1989). [CrossRef] [PubMed]
  3. J. Denavit and D. W. Phillion, “Laser ionization and heating of gas targets for long-scale-length instability experiments,” Phys. Plasmas 1(6), 1971 (1994). [CrossRef]
  4. A. McPherson, B. D. Thompson, A. B. Borisov, K. Boyer, and C. K. Rhodes, “Multi-photon induced x-ray emission at 4-5 keV from Xe atoms with multiple core vacancies,” Nature 370(6491), 631–634 (1994). [CrossRef]
  5. W. G. John Tisch, “Phase-matched high-order harmonic generation in an ionized medium using a buffer gas of exploding atomic clusters,” Phys. Rev. A 62, 041802(R) (2000).
  6. S. B. Hansen, K. B. Fournier, A. Y. Faenov, A. I. Magunov, T. A. Pikuz, I. Y. Skobelev, Y. Fukuda, Y. Akahane, M. Aoyama, N. Inoue, H. Ueda, and K. Yamakawa, “Measurement of 2l-nl’ x-ray transitions from approximately 1 μm Kr clusters irradiated by high-intensity femtosecond laser pulses,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 71(1 Pt 2), 016408 (2005). [CrossRef] [PubMed]
  7. Y. Fukuda, K. Yamakawa, Y. Akahane, M. Aoyama, N. Inoue, H. Ueda, and Y. Kishimoto, “Optimized Energetic Particle Emissions from Xe Cluster in Intense Laser Fields,” Phys. Rev. A 67(6), 061201 (2003). [CrossRef]
  8. V. Malka, E. D. Wispelaere, F. Amiranoff, S. Baton, R. Bonadio, C. Coulaud, and R. Haroutunian, “channel Formation in Long Laser Pulse Interaction with a Helium Gas Jet,” Phys. Rev. Lett. 79(16), 2979–2982 (1997). [CrossRef]
  9. H. M. Milchberg, K. Y. Kim, V. Kumarappan, B. D. Layer, and H. Sheng, “Clustered gases as a medium for efficient plasma waveguide generation,” Philos. Transact. A Math. Phys. Eng. Sci. 364(1840), 647–661 (2006). [CrossRef] [PubMed]
  10. A. B. Borisov, A. V. Borovskiy, O. B. Shiryaev, V. V. Korobkin, A. M. Prokhorov, J. C. Solem, T. S. Luk, K. Boyer, and C. K. Rhodes, “Relativistic and charge-displacement self-channeling of intense ultrashort laser pulses in plasmas,” Phys. Rev. A 45(8), 5830–5845 (1992). [CrossRef] [PubMed]
  11. J. F. Herbstman and A. J. Hunt, “High-aspect ratio nanochannel formation by single femtosecond laser pulses,” Opt. Express 18(16), 16840–16848 (2010). [CrossRef] [PubMed]
  12. A. B. Borisov, X. Shi, V. B. Karpov, V. V. Korobkin, J. C. Solem, O. B. Shiryaev, A. McPherson, K. Boyer, and C. K. Rhodes, “Stable self-channeling of intense ultraviolet pulses in underdense plasma, producing channels exceeding 100 Rayleigh lengths,” J. Opt. Soc. Am. B 11(10), 1941–1947 (1994). [CrossRef]
  13. J. Fuchs, G. Malka, J. C. Adam, F. Amiranoff, S. D. Baton, N. Blanchot, A. Héron, G. Laval, J. L. Migel, P. Mora, H. Pépin, and C. Rousseaux, “Dynamics of Subpicosecond Relativistic Laser Pulse Self-Channeling in an Underdense Preformed Plasma,” Phys. Rev. Lett. 80(8), 1658–1661 (1998). [CrossRef]
  14. O. F. Hagena, “Condensation in Free Jets: Comparison of Rare Gases and Metals,” Z. Phys. D 4(3), 291–299 (1987). [CrossRef]
  15. Y. L. Shao, T. Ditmire, J. W. G. Tisch, E. Springate, J. P. Marangos, and M. H. R. Hutchinson, “Multi-keV Electron Generation in the Interaction of Intense Laser Pulses with Xe Clusters,” Phys. Rev. Lett. 77(16), 3343–3346 (1996). [CrossRef] [PubMed]
  16. T. Ditmire, J. W. G. Tisch, E. Springate, M. B. Mason, N. Hay, R. A. Smith, J. P. Marangos, and M. H. R. Hutchinson, “Nuclear Fusion from Explosions of Femtosecond Laser-Heated Deuterium Clusters,” Nature 386, 54 (1997). [CrossRef]
  17. T. Ditmire, T. Donnelly, A. M. Rubenchik, R. W. Falcone, and M. D. Perry, “Interaction of intense laser pulses with atomic clusters,” Phys. Rev. A 53(5), 3379–3402 (1996). [CrossRef] [PubMed]
  18. T. Ditmire, R. A. Smith, J. W. G. Tisch, and M. H. R. Hutchinson, “High Intensity Laser Absorption by Gases of Atomic Clusters,” Phys. Rev. Lett. 78(16), 3121–3124 (1997). [CrossRef]
  19. H. M. Milchberg, S. J. McNaught, and E. Parra, “Plasma hydrodynamics of the intense laser-cluster interaction,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 64(5), 056402 (2001). [CrossRef] [PubMed]
  20. K. Y. Kim, I. Alexeev, E. Parra, and H. M. Milchberg, “Time-resolved explosion of intense-laser-heated clusters,” Phys. Rev. Lett. 90(2), 023401 (2003). [CrossRef] [PubMed]
  21. I. Alexeev, T. M. Antonsen, K. Y. Kim, and H. M. Milchberg, “Self-focusing of intense laser pulses in a clustered gas,” Phys. Rev. Lett. 90(10), 103402 (2003). [CrossRef] [PubMed]
  22. K. Y. Kim, V. Kumarappan, and H. M. Milchberg, “Measurement of the average size and density of clusters in a gas jet,” Appl. Phys. Lett. 83(15), 3210 (2003). [CrossRef]
  23. K. Y. Kim, H. M. Milchberg, A. Ya. Faenov, A. I. Magunov, T. A. Pikuz, and I. Yu. Skobelev, “X-ray spectroscopy of 1 cm plasma channels produced by self-guided pulse propagation in elongated cluster jets,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 73(6), 066403 (2006). [CrossRef] [PubMed]
  24. B. D. Layer, A. G. York, S. Varma, Y. H. Chen, and H. M. Milchberg, “Periodic index-modulated plasma waveguide,” Opt. Express 17(6), 4263–4267 (2009). [CrossRef] [PubMed]
  25. B. C. Walker, C. Toth, D. N. Fittinghoff, T. Guo, D.-E. Kim, C. Rose-Petruck, J. A. Squier, K. Yamakawa, K. R. Wilson, and C. Barty, “A 50 EW/cm;2 Ti:sapphire laser system for studying relativistic light-matter interactions,” Opt. Express 5(10), 196–202 (1999). [CrossRef] [PubMed]
  26. G. Chen, B. Kim, B. Ahn, and D.-E. Kim, “Pressure dependence of argon cluster size for different nozzle geometries,” J. Appl. Phys. 106(5), 053507 (2009). [CrossRef]
  27. I. H. Hutchinson, “Principles of Plasma Diagnostics,” Cambridge University Press, New York, (1987).
  28. A. E. Seigman, “Lasers” University Science Books, Mill Valley, California, section 17 (1986).
  29. G. Chen, B. Kim, B. Ahn, and D.-E. Kim, “Experimental investigation on argon cluster sizes for conical nozzles with different opening angles,” J. Appl. Phys. 108, 1 (2010), http://link.aip.org/link/?JAPIAU/108/064329/1 .
  30. O. F. Hagena and W. Obert, “Cluster Formation in Expanding Supersonic Jets: Effect of Pressure, Temperature, Nozzle Size, and Test Gas,” J. Chem. Phys. 56(5), 1793 (1972). [CrossRef]
  31. O. F. Hagena, “Cluster ion sources,” Rev. Sci. Instrum. 63(4), 2374 (1992), http://link.aip.org/link/doi/10.1063/1.1142933 . [CrossRef]
  32. T. Ditmire, R. A. Smith, and M. H. R. Hutchinson, “Plasma waveguide formation in predissociated clustering gases,” Opt. Lett. 23(5), 322–324 (1998), http://www.opticsinfobase.org/ol/abstract.cfm?uri=ol-23-5-322 . [CrossRef] [PubMed]
  33. S. Augst, D. D. Meyerhofer, D. Strickland, and S. L. Chin, “Laser ionization of noble gases by Coulomb-barrier suppression,” J. Opt. Soc. Am. B 8(4), 858 (1991), http://www.opticsinfobase.org/abstract.cfm?&id=5984 . [CrossRef]
  34. V. Kumarappan, K. Y. Kim, and H. M. Milchberg, “Guiding of intense laser pulses in plasma waveguides produced from efficient, femtosecond end-pumped heating of clustered gases,” Phys. Rev. Lett. 94(20), 205004 (2005). [CrossRef] [PubMed]
  35. M. Nakatsutsumi, J.-R. Marquès, P. Antici, N. Bourgeois, J. L. Feugeas, T. Lin, Ph. Nicolaï, L. Romagnani, R. Kodama, P. Audebert, and J. Fuchs, “High-power laser delocalization in plasmas leading to long-range beam merging,” Nat. Phys. 6(12), 1010–1016 (2010). [CrossRef]
  36. J. Fan, E. Parra, and H. M. Milchberg, “Resonant self-trapping and absorption of intense bessel beams,” Phys. Rev. Lett. 84(14), 3085–3088 (2000), http://prl.aps.org/abstract/PRL/v84/i14/p3085_1 . [CrossRef] [PubMed]
  37. H. C. Man, J. Duan, and T. M. Yue, “Dynamic characteristics of gas jets from subsonic and supersonic slit nozzles for high pressure gas laser cutting,” Opt. Laser Technol. 30(8), 497–509 (1998). [CrossRef]
  38. J. F. Han, C. W. Yanga, J. W. Miao, J. F. Lu, M. Liu, X. B. Luo, and M. G. Shi, “The spatial distribution of argon clusters in gas jet,” Eur. Phys. J. D 56(3), 347–352 (2010). [CrossRef]
  39. C. G. Durfee and H. M. Milchberg, “Light pipe for high intensity laser pulses,” Phys. Rev. Lett. 71(15), 2409–2412 (1993), http://prl.aps.org/abstract/PRL/v71/i15/p2409_1 . [CrossRef] [PubMed]
  40. T. R. Clark and H. M. Milchberg, “Time- and Space-Resolved Density Evolution of the Plasma Waveguide,” Phys. Rev. Lett. 78(12), 2373–2376 (1997), http://prl.aps.org/abstract/PRL/v78/i12/p2373_1 . [CrossRef]
  41. Y. Ehrlich, A. Zigler, C. Cohen, J. Krall, and P. Sprangle, “Guiding of High Intensity Laser Pulses in Straight and Curved Plasma Channel Experiments, ” Phys. Rev. Lett. 77, 4186 (1996). http://prl.aps.org/abstract/PRL/v77/i20/p4186_ 1.
  42. C. W. Leemans, “Siders, E. Esarey, N. E. Andreev, G. Shvets, and W. B. Mori, “Plasma Guiding and Wakefield Generation for S econd-Generation Experiments,” IEEE Trans. Plasma Sci. 24 (2), 331–342 (1996), http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=509997 . [CrossRef]

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