Abstract

Femtosecond laser filament arrays are generated in air by using three kinds of step phase plates with π phase lag, namely, the semicircular phase plate (SCPP), the quarter-circle phase plate (QCPP) and eight-octant phase plate (EOPP). Experimental results and simulations show that filament arrays consisting of two, four and eight filaments, respectively, are produced by three phase plates. The transverse patterns of the filament arrays are determined by the geometrical shapes of the phase plates. At the same time, the separation distances are found to vary with the focal lengths of the used lenses. We further propose that by using an axicon, filament array in the form of ring shape could be realized while the lengths of the filaments could be significantly elongated at the same time. Our study has suggested a realistic method to generate filament array by the step phase plate with π phase lag.

© 2013 OSA

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2012 (4)

H. Gao, X. Sun, B. Zeng, S. Xu, W. Chu, W. Liu, Y. Cheng, Z. Xu, and G. Mu, “Cylindrical symmetry breaking leads to multiple filamentation generation when focusing femtosecond lasers with axicons in methanol,” J. Opt.14(6), 065203 (2012).
[CrossRef]

M. Alshershby, Z. Q. Hao, and J. Q. Lin, “Guiding microwave radiation using laser-induced filaments: the hollow conducting waveguide concept,” J. Phys. D Appl. Phys.45(26), 265401 (2012).
[CrossRef]

X. D. Sun, H. Gao, B. Zeng, S. Q. Xu, W. W. Liu, Y. Cheng, Z. Z. Xu, and G. G. Mu, “Multiple filamentation generated by focusing femtosecond laser with axicon,” Opt. Lett.37(5), 857–859 (2012).
[CrossRef] [PubMed]

M. Petrarca, Y. Petit, S. Henin, R. Delagrange, P. Béjot, and J. Kasparian, “Higher-order Kerr improve quantitative modeling of laser filamentation,” Opt. Lett.37(20), 4347–4349 (2012).
[CrossRef] [PubMed]

2011 (6)

O. Kosareva, J.-F. Daigle, N. Panov, T. Wang, S. Hosseini, S. Yuan, G. Roy, V. Makarov, and S. Leang Chin, “Arrest of self-focusing collapse in femtosecond air filaments: higher order Kerr or plasma defocusing?” Opt. Lett.36(7), 1035–1037 (2011).
[CrossRef] [PubMed]

Z. X. Wang, C. J. Zhang, J. S. Liu, R. X. Li, and Z. Z. Xu, “Femtosecond filamentation in argon and higher-order nonlinearities,” Opt. Lett.36(12), 2336–2338 (2011).
[CrossRef] [PubMed]

P. Polynkin, M. Kolesik, E. M. Wright, and J. V. Moloney, “Experimental tests of the new paradigm for laser filamentation in gases,” Phys. Rev. Lett.106(15), 153902 (2011).
[CrossRef] [PubMed]

J. Liu, W. X. Li, H. F. Pan, and H. P. Zeng, “Two-dimensional plasma grating by non-collinear femtosecond filament interaction in air,” Appl. Phys. Lett.99(15), 151105 (2011).
[CrossRef]

Y. Fu, H. Gao, W. Chu, J. Ni, H. Xiong, H. Xu, J. Yao, B. Zeng, W. Liu, Y. Cheng, Z. Xu, and S. L. Chin, “Control of filament branching in air by astigmatically focused femtosecond laser pulses,” Appl. Phys. B103(2), 435–439 (2011).
[CrossRef]

P. Béjot, E. Hertz, J. Kasparian, B. Lavorel, J. P. Wolf, and O. Faucher, “Transition from plasma-driven to Kerr-driven laser filamentation,” Phys. Rev. Lett.106(24), 243902 (2011).
[CrossRef] [PubMed]

2010 (6)

P. Béjot, J. Kasparian, S. Henin, V. Loriot, T. Vieillard, E. Hertz, O. Faucher, B. Lavorel, and J. P. Wolf, “Higher-order Kerr terms allow ionization-free filamentation in gases,” Phys. Rev. Lett.104(10), 103903 (2010).
[CrossRef] [PubMed]

B. Shim, S. E. Schrauth, C. J. Hensley, L. T. Vuong, P. Hui, A. A. Ishaaya, and A. L. Gaeta, “Controlled interactions of femtosecond light filaments in air,” Phys. Rev. A81(6), 061803 (2010).
[CrossRef]

D. Majus, V. Jukna, G. Tamošauskas, G. Valiulis, and A. Dubietis, “Three-dimensional mapping of multiple filament arrays,” Phys. Rev. A81(4), 043811 (2010).
[CrossRef]

M. N. Shneider, A. M. Zheltikov, and R. B. Miles, “Long-lived laser-induced microwave plasma guides in the atmosphere: self-consistent plasma-dynamic analysis and numerical simulations,” J. Appl. Phys.108(3), 033113 (2010).
[CrossRef]

D. G. Papazoglou, S. Suntsov, D. Abdollahpour, and S. Tzortzakis, “Tunable intense Airy beams and tailored femtosecond laser filaments,” Phys. Rev. A81(6), 061807 (2010).
[CrossRef]

M. Kolesik, D. Mirell, J.-C. Diels, and J. V. Moloney, “On the higher-order Kerr effect in femtosecond filaments,” Opt. Lett.35(21), 3685–3687 (2010).
[CrossRef] [PubMed]

2009 (10)

B. Zhou, S. Akturk, B. Prade, Y. B. André, A. Houard, Y. Liu, M. Franco, C. D’Amico, E. Salmon, Z. Q. Hao, N. Lascoux, and A. Mysyrowicz, “Revival of femtosecond laser plasma filaments in air by a nanosecond laser,” Opt. Express17(14), 11450–11456 (2009).
[CrossRef] [PubMed]

E. D’Asaro, S. Heidari-Bateni, A. Pasquazi, G. Assanto, J. Gonzalo, J. Solis, and C. N. Afonso, “Interaction of self-trapped beams in high index glass,” Opt. Express17(19), 17150–17155 (2009).
[CrossRef] [PubMed]

Y. X. Fu, H. Xiong, H. Xu, J. P. Yao, B. Zeng, W. Chu, Y. Cheng, Z. Z. Xu, W. W. Liu, and S. L. Chin, “Generation of extended filaments of femtosecond pulses in air by use of a single-step phase plate,” Opt. Lett.34(23), 3752–3754 (2009).
[CrossRef] [PubMed]

X. Yang, J. Wu, Y. Peng, Y. Q. Tong, P. F. Lu, L. E. Ding, Z. Z. Xu, and H. P. Zeng, “Plasma waveguide array induced by filament interaction,” Opt. Lett.34(24), 3806–3808 (2009).
[CrossRef] [PubMed]

P. Polynkin, M. Kolesik, J. V. Moloney, G. A. Siviloglou, and D. N. Christodoulides, “Curved plasma channel generation using ultraintense Airy beams,” Science324(5924), 229–232 (2009).
[CrossRef] [PubMed]

D. Majus, V. Jukna, G. Valiulis, and A. Dubietis, “Generation of periodic filament arrays by self-focusing of highly elliptical ultrashort pulsed laser beams,” Phys. Rev. A79(3), 033843 (2009).
[CrossRef]

S. Akturk, B. Zhou, M. Franco, A. Couairon, and A. Mysyrowicz, “Generation of long plasma channels in air by focusing ultrashort laser pulses with an axicon,” Opt. Commun.282(1), 129–134 (2009).
[CrossRef]

G. Paunescu, G. Spindler, W. Riede, H. Schröder, and A. Giesen, “Multifilamentation of femtosecond laser pulses induced by small-scale air turbulence,” Appl. Phys. B96(1), 175–183 (2009).
[CrossRef]

G. Spindler and G. Paunescu, “Multifilamentation of femtosecond laser pulses propagating in turbulent air near the ground,” Appl. Phys. B96(1), 185–191 (2009).
[CrossRef]

H. Cai, J. Wu, P. F. Lu, X. S. Bai, L. E. Ding, and H. P. Zeng, “Attraction and repulsion of parallel femtosecond filaments in air,” Phys. Rev. A80(5), 051802 (2009).
[CrossRef]

2008 (9)

Y.-Y. Ma, X. Lu, T.-T. Xi, Q.-H. Gong, and J. Zhang, “Filamentation of interacting femtosecond laser pulses in air,” Appl. Phys. B93(2-3), 463–468 (2008).
[CrossRef]

C. P. Hauri, J. Gautier, A. Trisorio, E. Papalazarou, and P. Zeitoun, “Two-dimensional organization of a large number of stationary optical filaments by adaptive wave front control,” Appl. Phys. B90(3-4), 391–394 (2008).
[CrossRef]

P. Rohwetter, M. Queißer, K. Stelmaszczyk, M. Fechner, and L. Wöste, “Laser multiple filamentation control in air using a smooth phase mask,” Phys. Rev. A77(1), 013812 (2008).
[CrossRef]

L. Guyon, K. M. Hajek, F. Courvoisier, V. Boutou, R. Nuter, A. Vincotte, S. Champeaux, L. Bergé, and J.-P. Wolf, “Control of lasing filament arrays in nonlinear liquid media,” Appl. Phys. B90(3-4), 383–390 (2008).
[CrossRef]

M. Châteauneuf, S. Payeur, J. Dubois, and J.-C. Kieffer, “Microwave guiding in air by a cylindrical filament array waveguide,” Appl. Phys. Lett.92(9), 091104 (2008).
[CrossRef]

A. Pasquazi, S. Stivala, G. Assanto, J. Gonzalo, and J. Solis, “Transverse nonlinear optics in heavy-metal-oxide glass,” Phys. Rev. A77(4), 043808 (2008).
[CrossRef]

P. Polesana, M. Franco, A. Couairon, D. Faccio, and P. Di Trapani, “Filamentation in Kerr media from pulsed Bessel beams,” Phys. Rev. A77(4), 043814 (2008).
[CrossRef]

J. Kasparian and J.-P. Wolf, “Physics and applications of atmospheric nonlinear optics and filamentation,” Opt. Express16(1), 466–493 (2008).
[CrossRef] [PubMed]

P. Polynkin, M. Kolesik, A. Roberts, D. Faccio, P. Di Trapani, and J. Moloney, “Generation of extended plasma channels in air using femtosecond Bessel beams,” Opt. Express16(20), 15733–15740 (2008).
[CrossRef] [PubMed]

2007 (5)

A. Pasquazi, S. Stivala, G. Assanto, J. Gonzalo, J. Solis, and C. N. Afonso, “Near-infrared spatial solitons in heavy metal oxide glasses,” Opt. Lett.32(15), 2103–2105 (2007).
[CrossRef] [PubMed]

Z.-Q. Hao, J. Zhang, T. T. Xi, X. H. Yuan, Z. Y. Zheng, X. Lu, M. Y. Yu, Y. T. Li, Z. H. Wang, W. Zhao, and Z. Y. Wei, “Optimization of multiple filamentation of femtosecond laser pulses in air using a pinhole,” Opt. Express15(24), 16102–16109 (2007).
[CrossRef] [PubMed]

S. L. Chin, F. Théberge, and W. Liu, “Filamentation nonlinear optics,” Appl. Phys. B86(3), 477–483 (2007).
[CrossRef]

A. Couairon and A. Mysyrowicz, “Femtosecond filamentation in transparent media,” Phys. Rep.441(2-4), 47–189 (2007).
[CrossRef]

L. Bergé, S. Skupin, R. Nuter, J. Kasparian, and J.-P. Wolf, “Ultrashort filaments of light in weakly ionized, optically transparent media,” Rep. Prog. Phys.70(10), 1633–1713 (2007).
[CrossRef]

2006 (3)

T. T. Xi, X. Lu, and J. Zhang, “Interaction of light filaments generated by femtosecond laser pulses in air,” Phys. Rev. Lett.96(2), 025003 (2006).
[CrossRef] [PubMed]

O. G. Kosareva, N. A. Panov, N. Akozbek, V. P. Kandidov, Q. Luo, S. A. Hosseini, W. Liu, J.-F. Gravel, G. Roy, and S. L. Chin, “Controlling a bunch of multiple filaments by means of a beam diameter,” Appl. Phys. B82(1), 111–122 (2006).
[CrossRef]

T. Pfeifer, L. Gallmann, M. J. Abel, D. M. Neumark, and S. R. Leone, “Circular phase mask for control and stabilization of single optical filaments,” Opt. Lett.31(15), 2326–2328 (2006).
[CrossRef] [PubMed]

2005 (6)

T. D. Grow and A. L. Gaeta, “Dependence of multiple filamentation on beam ellipticity,” Opt. Express13(12), 4594–4599 (2005).
[CrossRef] [PubMed]

O. G. Kosareva, A. V. Grigor’evskii, and V. P. Kandidov, “Formation of extended plasma channels in a condensed medium upon axicon focusing of a femtosecond laser pulse,” Quantum Electron.35(11), 1013–1014 (2005).
[CrossRef]

O. Sakai, T. Sakaguchi, and K. Tachibana, “Verification of a plasma photonic crystal for microwaves of millimeter wavelength range using two-dimensional array of columnar microplasmas,” Appl. Phys. Lett.87(24), 241505 (2005).
[CrossRef]

J. Liu, H. Schroeder, S. L. Chin, R. Li, and Z. Xu, “Ultrafast control of multiple filamentation by ultrafast laser pulses,” Appl. Phys. Lett.87(16), 161105 (2005).
[CrossRef]

V. P. Kandidov, N. Aközbek, M. Scalora, O. G. Kosareva, A. V. Nyakk, Q. Luo, S. A. Hosseini, and S. L. Chin, “Towards a control of multiple filamentation by spatial regularization of a high-power femtosecond laser pulse,” Appl. Phys. B80(2), 267–275 (2005).
[CrossRef]

S. L. Chin, S. A. Hosseini, W. Liu, Q. Luo, F. Théberge, N. Aközbek, A. Becker, V. P. Kandidov, O. G. Kosareva, and H. Schroeder, “The propagation of powerful femtosecond laser pulses in optical media: physics, applications, and new challenges,” Can. J. Phys.83(9), 863–905 (2005).
[CrossRef]

2004 (5)

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. B80(1), 35–38 (2004).
[CrossRef]

G. Méchain, A. Couairon, M. Franco, B. Prade, and A. Mysyrowicz, “Organizing multiple femtosecond filaments in air,” Phys. Rev. Lett.93(3), 035003 (2004).
[CrossRef] [PubMed]

A. Dubietis, G. Tamosauskas, G. Fibich, and B. Ilan, “Multiple filamentation induced by input-beam ellipticity,” Opt. Lett.29(10), 1126–1128 (2004).
[CrossRef] [PubMed]

G. Fibich, S. Eisenmann, B. Ilan, and A. Zigler, “Control of multiple filamentation in air,” Opt. Lett.29(15), 1772–1774 (2004).
[CrossRef] [PubMed]

H. Schroeder, J. Liu, and S. L. Chin, “From random to controlled small-scale filamentation in water,” Opt. Express12(20), 4768–4774 (2004).
[CrossRef] [PubMed]

2003 (1)

W. Liu, S. L. Chin, O. Kosareva, I. S. Golubtsov, and V. P. Kandidov, “Multiple refocusing of a femtosecond laser in a dispersive liquid (methanol),” Opt. Commun.225(1-3), 193–209 (2003).
[CrossRef]

2002 (2)

Z. X. Wu, H. B. Jiang, L. Luo, H. C. Guo, H. Yang, and Q. H. Gong, “Multiple foci and a long filament observed with focused femtosecond laser pulse propagation in fused silica,” Opt. Lett.27(6), 448–450 (2002).
[CrossRef] [PubMed]

S. L. Chin, A. Talebpour, J. Yang, S. Petit, V. P. Kandidov, O. G. Kosareva, and M. P. Tamarov, “Filamentation of femtosecond laser pulses in turbulent air,” Appl. Phys. B74(1), 67–76 (2002).
[CrossRef]

2001 (1)

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(24), 5470–5473 (2001).
[CrossRef] [PubMed]

2000 (1)

J. Kasparian, R. Sauerbrey, and S. L. Chin, “The critical laser intensity of self-guided light filaments in air,” Appl. Phys. B71(6), 877–879 (2000).
[CrossRef]

1999 (2)

M. Mlejnek, M. Kolesik, J. V. Moloney, and E. M. Wright, “Optically turbulent femtosecond light guide in air,” Phys. Rev. Lett.83(15), 2938–2941 (1999).
[CrossRef]

A. Talebpour, J. Yang, and S. L. Chin, “Semi-empirical model for the rate of tunnel ionization of N2 and O2 molecule in an intense Ti: sapphire laser pulse,” Opt. Commun.163(1-3), 29–32 (1999).
[CrossRef]

1997 (2)

S. P. Kuo and J. Faith, “Interaction of an electromagnetic wave with a rapidly created spatially periodic plasma,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics56(2), 2143–2150 (1997).
[CrossRef]

E. T. J. Nibbering, G. Grillon, M. A. Franco, B. S. Prade, and A. Mysyrowicz, “Determination of the inertial contribution to the nonlinear refractive index of air, N2, and O2 by use of unfocused high-intensity femtosecond laser pulses,” J. Opt. Soc. Am. B14(3), 650–660 (1997).
[CrossRef]

1987 (1)

J. Durnin, J. J. Miceli, and J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett.58(15), 1499–1501 (1987).
[CrossRef] [PubMed]

1966 (1)

V. I. Bespalov and V. I. Talanov, “Filamentary structure of light beams in non-linear liquids,” JETP Lett.3, 307–310 (1966).

1954 (1)

Abdollahpour, D.

D. G. Papazoglou, S. Suntsov, D. Abdollahpour, and S. Tzortzakis, “Tunable intense Airy beams and tailored femtosecond laser filaments,” Phys. Rev. A81(6), 061807 (2010).
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Abel, M. J.

Afonso, C. N.

Akozbek, N.

O. G. Kosareva, N. A. Panov, N. Akozbek, V. P. Kandidov, Q. Luo, S. A. Hosseini, W. Liu, J.-F. Gravel, G. Roy, and S. L. Chin, “Controlling a bunch of multiple filaments by means of a beam diameter,” Appl. Phys. B82(1), 111–122 (2006).
[CrossRef]

Aközbek, N.

V. P. Kandidov, N. Aközbek, M. Scalora, O. G. Kosareva, A. V. Nyakk, Q. Luo, S. A. Hosseini, and S. L. Chin, “Towards a control of multiple filamentation by spatial regularization of a high-power femtosecond laser pulse,” Appl. Phys. B80(2), 267–275 (2005).
[CrossRef]

S. L. Chin, S. A. Hosseini, W. Liu, Q. Luo, F. Théberge, N. Aközbek, A. Becker, V. P. Kandidov, O. G. Kosareva, and H. Schroeder, “The propagation of powerful femtosecond laser pulses in optical media: physics, applications, and new challenges,” Can. J. Phys.83(9), 863–905 (2005).
[CrossRef]

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. B80(1), 35–38 (2004).
[CrossRef]

Akturk, S.

B. Zhou, S. Akturk, B. Prade, Y. B. André, A. Houard, Y. Liu, M. Franco, C. D’Amico, E. Salmon, Z. Q. Hao, N. Lascoux, and A. Mysyrowicz, “Revival of femtosecond laser plasma filaments in air by a nanosecond laser,” Opt. Express17(14), 11450–11456 (2009).
[CrossRef] [PubMed]

S. Akturk, B. Zhou, M. Franco, A. Couairon, and A. Mysyrowicz, “Generation of long plasma channels in air by focusing ultrashort laser pulses with an axicon,” Opt. Commun.282(1), 129–134 (2009).
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Alshershby, M.

M. Alshershby, Z. Q. Hao, and J. Q. Lin, “Guiding microwave radiation using laser-induced filaments: the hollow conducting waveguide concept,” J. Phys. D Appl. Phys.45(26), 265401 (2012).
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André, Y. B.

Assanto, G.

Bai, X. S.

H. Cai, J. Wu, P. F. Lu, X. S. Bai, L. E. Ding, and H. P. Zeng, “Attraction and repulsion of parallel femtosecond filaments in air,” Phys. Rev. A80(5), 051802 (2009).
[CrossRef]

Becker, A.

S. L. Chin, S. A. Hosseini, W. Liu, Q. Luo, F. Théberge, N. Aközbek, A. Becker, V. P. Kandidov, O. G. Kosareva, and H. Schroeder, “The propagation of powerful femtosecond laser pulses in optical media: physics, applications, and new challenges,” Can. J. Phys.83(9), 863–905 (2005).
[CrossRef]

Béjot, P.

M. Petrarca, Y. Petit, S. Henin, R. Delagrange, P. Béjot, and J. Kasparian, “Higher-order Kerr improve quantitative modeling of laser filamentation,” Opt. Lett.37(20), 4347–4349 (2012).
[CrossRef] [PubMed]

P. Béjot, E. Hertz, J. Kasparian, B. Lavorel, J. P. Wolf, and O. Faucher, “Transition from plasma-driven to Kerr-driven laser filamentation,” Phys. Rev. Lett.106(24), 243902 (2011).
[CrossRef] [PubMed]

P. Béjot, J. Kasparian, S. Henin, V. Loriot, T. Vieillard, E. Hertz, O. Faucher, B. Lavorel, and J. P. Wolf, “Higher-order Kerr terms allow ionization-free filamentation in gases,” Phys. Rev. Lett.104(10), 103903 (2010).
[CrossRef] [PubMed]

Bergé, L.

L. Guyon, K. M. Hajek, F. Courvoisier, V. Boutou, R. Nuter, A. Vincotte, S. Champeaux, L. Bergé, and J.-P. Wolf, “Control of lasing filament arrays in nonlinear liquid media,” Appl. Phys. B90(3-4), 383–390 (2008).
[CrossRef]

L. Bergé, S. Skupin, R. Nuter, J. Kasparian, and J.-P. Wolf, “Ultrashort filaments of light in weakly ionized, optically transparent media,” Rep. Prog. Phys.70(10), 1633–1713 (2007).
[CrossRef]

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(24), 5470–5473 (2001).
[CrossRef] [PubMed]

Bespalov, V. I.

V. I. Bespalov and V. I. Talanov, “Filamentary structure of light beams in non-linear liquids,” JETP Lett.3, 307–310 (1966).

Boutou, V.

L. Guyon, K. M. Hajek, F. Courvoisier, V. Boutou, R. Nuter, A. Vincotte, S. Champeaux, L. Bergé, and J.-P. Wolf, “Control of lasing filament arrays in nonlinear liquid media,” Appl. Phys. B90(3-4), 383–390 (2008).
[CrossRef]

Cai, H.

H. Cai, J. Wu, P. F. Lu, X. S. Bai, L. E. Ding, and H. P. Zeng, “Attraction and repulsion of parallel femtosecond filaments in air,” Phys. Rev. A80(5), 051802 (2009).
[CrossRef]

Champeaux, S.

L. Guyon, K. M. Hajek, F. Courvoisier, V. Boutou, R. Nuter, A. Vincotte, S. Champeaux, L. Bergé, and J.-P. Wolf, “Control of lasing filament arrays in nonlinear liquid media,” Appl. Phys. B90(3-4), 383–390 (2008).
[CrossRef]

Châteauneuf, M.

M. Châteauneuf, S. Payeur, J. Dubois, and J.-C. Kieffer, “Microwave guiding in air by a cylindrical filament array waveguide,” Appl. Phys. Lett.92(9), 091104 (2008).
[CrossRef]

Cheng, Y.

X. D. Sun, H. Gao, B. Zeng, S. Q. Xu, W. W. Liu, Y. Cheng, Z. Z. Xu, and G. G. Mu, “Multiple filamentation generated by focusing femtosecond laser with axicon,” Opt. Lett.37(5), 857–859 (2012).
[CrossRef] [PubMed]

H. Gao, X. Sun, B. Zeng, S. Xu, W. Chu, W. Liu, Y. Cheng, Z. Xu, and G. Mu, “Cylindrical symmetry breaking leads to multiple filamentation generation when focusing femtosecond lasers with axicons in methanol,” J. Opt.14(6), 065203 (2012).
[CrossRef]

Y. Fu, H. Gao, W. Chu, J. Ni, H. Xiong, H. Xu, J. Yao, B. Zeng, W. Liu, Y. Cheng, Z. Xu, and S. L. Chin, “Control of filament branching in air by astigmatically focused femtosecond laser pulses,” Appl. Phys. B103(2), 435–439 (2011).
[CrossRef]

Y. X. Fu, H. Xiong, H. Xu, J. P. Yao, B. Zeng, W. Chu, Y. Cheng, Z. Z. Xu, W. W. Liu, and S. L. Chin, “Generation of extended filaments of femtosecond pulses in air by use of a single-step phase plate,” Opt. Lett.34(23), 3752–3754 (2009).
[CrossRef] [PubMed]

Chin, S. L.

Y. Fu, H. Gao, W. Chu, J. Ni, H. Xiong, H. Xu, J. Yao, B. Zeng, W. Liu, Y. Cheng, Z. Xu, and S. L. Chin, “Control of filament branching in air by astigmatically focused femtosecond laser pulses,” Appl. Phys. B103(2), 435–439 (2011).
[CrossRef]

Y. X. Fu, H. Xiong, H. Xu, J. P. Yao, B. Zeng, W. Chu, Y. Cheng, Z. Z. Xu, W. W. Liu, and S. L. Chin, “Generation of extended filaments of femtosecond pulses in air by use of a single-step phase plate,” Opt. Lett.34(23), 3752–3754 (2009).
[CrossRef] [PubMed]

S. L. Chin, F. Théberge, and W. Liu, “Filamentation nonlinear optics,” Appl. Phys. B86(3), 477–483 (2007).
[CrossRef]

O. G. Kosareva, N. A. Panov, N. Akozbek, V. P. Kandidov, Q. Luo, S. A. Hosseini, W. Liu, J.-F. Gravel, G. Roy, and S. L. Chin, “Controlling a bunch of multiple filaments by means of a beam diameter,” Appl. Phys. B82(1), 111–122 (2006).
[CrossRef]

V. P. Kandidov, N. Aközbek, M. Scalora, O. G. Kosareva, A. V. Nyakk, Q. Luo, S. A. Hosseini, and S. L. Chin, “Towards a control of multiple filamentation by spatial regularization of a high-power femtosecond laser pulse,” Appl. Phys. B80(2), 267–275 (2005).
[CrossRef]

J. Liu, H. Schroeder, S. L. Chin, R. Li, and Z. Xu, “Ultrafast control of multiple filamentation by ultrafast laser pulses,” Appl. Phys. Lett.87(16), 161105 (2005).
[CrossRef]

S. L. Chin, S. A. Hosseini, W. Liu, Q. Luo, F. Théberge, N. Aközbek, A. Becker, V. P. Kandidov, O. G. Kosareva, and H. Schroeder, “The propagation of powerful femtosecond laser pulses in optical media: physics, applications, and new challenges,” Can. J. Phys.83(9), 863–905 (2005).
[CrossRef]

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. B80(1), 35–38 (2004).
[CrossRef]

H. Schroeder, J. Liu, and S. L. Chin, “From random to controlled small-scale filamentation in water,” Opt. Express12(20), 4768–4774 (2004).
[CrossRef] [PubMed]

W. Liu, S. L. Chin, O. Kosareva, I. S. Golubtsov, and V. P. Kandidov, “Multiple refocusing of a femtosecond laser in a dispersive liquid (methanol),” Opt. Commun.225(1-3), 193–209 (2003).
[CrossRef]

S. L. Chin, A. Talebpour, J. Yang, S. Petit, V. P. Kandidov, O. G. Kosareva, and M. P. Tamarov, “Filamentation of femtosecond laser pulses in turbulent air,” Appl. Phys. B74(1), 67–76 (2002).
[CrossRef]

J. Kasparian, R. Sauerbrey, and S. L. Chin, “The critical laser intensity of self-guided light filaments in air,” Appl. Phys. B71(6), 877–879 (2000).
[CrossRef]

A. Talebpour, J. Yang, and S. L. Chin, “Semi-empirical model for the rate of tunnel ionization of N2 and O2 molecule in an intense Ti: sapphire laser pulse,” Opt. Commun.163(1-3), 29–32 (1999).
[CrossRef]

Christodoulides, D. N.

P. Polynkin, M. Kolesik, J. V. Moloney, G. A. Siviloglou, and D. N. Christodoulides, “Curved plasma channel generation using ultraintense Airy beams,” Science324(5924), 229–232 (2009).
[CrossRef] [PubMed]

Chu, W.

H. Gao, X. Sun, B. Zeng, S. Xu, W. Chu, W. Liu, Y. Cheng, Z. Xu, and G. Mu, “Cylindrical symmetry breaking leads to multiple filamentation generation when focusing femtosecond lasers with axicons in methanol,” J. Opt.14(6), 065203 (2012).
[CrossRef]

Y. Fu, H. Gao, W. Chu, J. Ni, H. Xiong, H. Xu, J. Yao, B. Zeng, W. Liu, Y. Cheng, Z. Xu, and S. L. Chin, “Control of filament branching in air by astigmatically focused femtosecond laser pulses,” Appl. Phys. B103(2), 435–439 (2011).
[CrossRef]

Y. X. Fu, H. Xiong, H. Xu, J. P. Yao, B. Zeng, W. Chu, Y. Cheng, Z. Z. Xu, W. W. Liu, and S. L. Chin, “Generation of extended filaments of femtosecond pulses in air by use of a single-step phase plate,” Opt. Lett.34(23), 3752–3754 (2009).
[CrossRef] [PubMed]

Couairon, A.

S. Akturk, B. Zhou, M. Franco, A. Couairon, and A. Mysyrowicz, “Generation of long plasma channels in air by focusing ultrashort laser pulses with an axicon,” Opt. Commun.282(1), 129–134 (2009).
[CrossRef]

P. Polesana, M. Franco, A. Couairon, D. Faccio, and P. Di Trapani, “Filamentation in Kerr media from pulsed Bessel beams,” Phys. Rev. A77(4), 043814 (2008).
[CrossRef]

A. Couairon and A. Mysyrowicz, “Femtosecond filamentation in transparent media,” Phys. Rep.441(2-4), 47–189 (2007).
[CrossRef]

G. Méchain, A. Couairon, M. Franco, B. Prade, and A. Mysyrowicz, “Organizing multiple femtosecond filaments in air,” Phys. Rev. Lett.93(3), 035003 (2004).
[CrossRef] [PubMed]

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(24), 5470–5473 (2001).
[CrossRef] [PubMed]

Courvoisier, F.

L. Guyon, K. M. Hajek, F. Courvoisier, V. Boutou, R. Nuter, A. Vincotte, S. Champeaux, L. Bergé, and J.-P. Wolf, “Control of lasing filament arrays in nonlinear liquid media,” Appl. Phys. B90(3-4), 383–390 (2008).
[CrossRef]

D’Amico, C.

D’Asaro, E.

Daigle, J.-F.

Delagrange, R.

Di Trapani, P.

P. Polesana, M. Franco, A. Couairon, D. Faccio, and P. Di Trapani, “Filamentation in Kerr media from pulsed Bessel beams,” Phys. Rev. A77(4), 043814 (2008).
[CrossRef]

P. Polynkin, M. Kolesik, A. Roberts, D. Faccio, P. Di Trapani, and J. Moloney, “Generation of extended plasma channels in air using femtosecond Bessel beams,” Opt. Express16(20), 15733–15740 (2008).
[CrossRef] [PubMed]

Diels, J.-C.

Ding, L. E.

X. Yang, J. Wu, Y. Peng, Y. Q. Tong, P. F. Lu, L. E. Ding, Z. Z. Xu, and H. P. Zeng, “Plasma waveguide array induced by filament interaction,” Opt. Lett.34(24), 3806–3808 (2009).
[CrossRef] [PubMed]

H. Cai, J. Wu, P. F. Lu, X. S. Bai, L. E. Ding, and H. P. Zeng, “Attraction and repulsion of parallel femtosecond filaments in air,” Phys. Rev. A80(5), 051802 (2009).
[CrossRef]

Dubietis, A.

D. Majus, V. Jukna, G. Tamošauskas, G. Valiulis, and A. Dubietis, “Three-dimensional mapping of multiple filament arrays,” Phys. Rev. A81(4), 043811 (2010).
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D. Majus, V. Jukna, G. Valiulis, and A. Dubietis, “Generation of periodic filament arrays by self-focusing of highly elliptical ultrashort pulsed laser beams,” Phys. Rev. A79(3), 033843 (2009).
[CrossRef]

A. Dubietis, G. Tamosauskas, G. Fibich, and B. Ilan, “Multiple filamentation induced by input-beam ellipticity,” Opt. Lett.29(10), 1126–1128 (2004).
[CrossRef] [PubMed]

Dubois, J.

M. Châteauneuf, S. Payeur, J. Dubois, and J.-C. Kieffer, “Microwave guiding in air by a cylindrical filament array waveguide,” Appl. Phys. Lett.92(9), 091104 (2008).
[CrossRef]

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J. Durnin, J. J. Miceli, and J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett.58(15), 1499–1501 (1987).
[CrossRef] [PubMed]

Eberly, J. H.

J. Durnin, J. J. Miceli, and J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett.58(15), 1499–1501 (1987).
[CrossRef] [PubMed]

Eisenmann, S.

Faccio, D.

P. Polynkin, M. Kolesik, A. Roberts, D. Faccio, P. Di Trapani, and J. Moloney, “Generation of extended plasma channels in air using femtosecond Bessel beams,” Opt. Express16(20), 15733–15740 (2008).
[CrossRef] [PubMed]

P. Polesana, M. Franco, A. Couairon, D. Faccio, and P. Di Trapani, “Filamentation in Kerr media from pulsed Bessel beams,” Phys. Rev. A77(4), 043814 (2008).
[CrossRef]

Faith, J.

S. P. Kuo and J. Faith, “Interaction of an electromagnetic wave with a rapidly created spatially periodic plasma,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics56(2), 2143–2150 (1997).
[CrossRef]

Faucher, O.

P. Béjot, E. Hertz, J. Kasparian, B. Lavorel, J. P. Wolf, and O. Faucher, “Transition from plasma-driven to Kerr-driven laser filamentation,” Phys. Rev. Lett.106(24), 243902 (2011).
[CrossRef] [PubMed]

P. Béjot, J. Kasparian, S. Henin, V. Loriot, T. Vieillard, E. Hertz, O. Faucher, B. Lavorel, and J. P. Wolf, “Higher-order Kerr terms allow ionization-free filamentation in gases,” Phys. Rev. Lett.104(10), 103903 (2010).
[CrossRef] [PubMed]

Fechner, M.

P. Rohwetter, M. Queißer, K. Stelmaszczyk, M. Fechner, and L. Wöste, “Laser multiple filamentation control in air using a smooth phase mask,” Phys. Rev. A77(1), 013812 (2008).
[CrossRef]

Fibich, G.

Franco, M.

B. Zhou, S. Akturk, B. Prade, Y. B. André, A. Houard, Y. Liu, M. Franco, C. D’Amico, E. Salmon, Z. Q. Hao, N. Lascoux, and A. Mysyrowicz, “Revival of femtosecond laser plasma filaments in air by a nanosecond laser,” Opt. Express17(14), 11450–11456 (2009).
[CrossRef] [PubMed]

S. Akturk, B. Zhou, M. Franco, A. Couairon, and A. Mysyrowicz, “Generation of long plasma channels in air by focusing ultrashort laser pulses with an axicon,” Opt. Commun.282(1), 129–134 (2009).
[CrossRef]

P. Polesana, M. Franco, A. Couairon, D. Faccio, and P. Di Trapani, “Filamentation in Kerr media from pulsed Bessel beams,” Phys. Rev. A77(4), 043814 (2008).
[CrossRef]

G. Méchain, A. Couairon, M. Franco, B. Prade, and A. Mysyrowicz, “Organizing multiple femtosecond filaments in air,” Phys. Rev. Lett.93(3), 035003 (2004).
[CrossRef] [PubMed]

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B. Shim, S. E. Schrauth, C. J. Hensley, L. T. Vuong, P. Hui, A. A. Ishaaya, and A. L. Gaeta, “Controlled interactions of femtosecond light filaments in air,” Phys. Rev. A81(6), 061803 (2010).
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O. G. Kosareva, N. A. Panov, N. Akozbek, V. P. Kandidov, Q. Luo, S. A. Hosseini, W. Liu, J.-F. Gravel, G. Roy, and S. L. Chin, “Controlling a bunch of multiple filaments by means of a beam diameter,” Appl. Phys. B82(1), 111–122 (2006).
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V. P. Kandidov, N. Aközbek, M. Scalora, O. G. Kosareva, A. V. Nyakk, Q. Luo, S. A. Hosseini, and S. L. Chin, “Towards a control of multiple filamentation by spatial regularization of a high-power femtosecond laser pulse,” Appl. Phys. B80(2), 267–275 (2005).
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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. B80(1), 35–38 (2004).
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W. Liu, S. L. Chin, O. Kosareva, I. S. Golubtsov, and V. P. Kandidov, “Multiple refocusing of a femtosecond laser in a dispersive liquid (methanol),” Opt. Commun.225(1-3), 193–209 (2003).
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O. G. Kosareva, N. A. Panov, N. Akozbek, V. P. Kandidov, Q. Luo, S. A. Hosseini, W. Liu, J.-F. Gravel, G. Roy, and S. L. Chin, “Controlling a bunch of multiple filaments by means of a beam diameter,” Appl. Phys. B82(1), 111–122 (2006).
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S. L. Chin, S. A. Hosseini, W. Liu, Q. Luo, F. Théberge, N. Aközbek, A. Becker, V. P. Kandidov, O. G. Kosareva, and H. Schroeder, “The propagation of powerful femtosecond laser pulses in optical media: physics, applications, and new challenges,” Can. J. Phys.83(9), 863–905 (2005).
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O. G. Kosareva, A. V. Grigor’evskii, and V. P. Kandidov, “Formation of extended plasma channels in a condensed medium upon axicon focusing of a femtosecond laser pulse,” Quantum Electron.35(11), 1013–1014 (2005).
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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. B80(1), 35–38 (2004).
[CrossRef]

S. L. Chin, A. Talebpour, J. Yang, S. Petit, V. P. Kandidov, O. G. Kosareva, and M. P. Tamarov, “Filamentation of femtosecond laser pulses in turbulent air,” Appl. Phys. B74(1), 67–76 (2002).
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H. Gao, X. Sun, B. Zeng, S. Xu, W. Chu, W. Liu, Y. Cheng, Z. Xu, and G. Mu, “Cylindrical symmetry breaking leads to multiple filamentation generation when focusing femtosecond lasers with axicons in methanol,” J. Opt.14(6), 065203 (2012).
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Y. Fu, H. Gao, W. Chu, J. Ni, H. Xiong, H. Xu, J. Yao, B. Zeng, W. Liu, Y. Cheng, Z. Xu, and S. L. Chin, “Control of filament branching in air by astigmatically focused femtosecond laser pulses,” Appl. Phys. B103(2), 435–439 (2011).
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[CrossRef]

S. L. Chin, S. A. Hosseini, W. Liu, Q. Luo, F. Théberge, N. Aközbek, A. Becker, V. P. Kandidov, O. G. Kosareva, and H. Schroeder, “The propagation of powerful femtosecond laser pulses in optical media: physics, applications, and new challenges,” Can. J. Phys.83(9), 863–905 (2005).
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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. B80(1), 35–38 (2004).
[CrossRef]

W. Liu, S. L. Chin, O. Kosareva, I. S. Golubtsov, and V. P. Kandidov, “Multiple refocusing of a femtosecond laser in a dispersive liquid (methanol),” Opt. Commun.225(1-3), 193–209 (2003).
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Liu, Y.

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P. Béjot, J. Kasparian, S. Henin, V. Loriot, T. Vieillard, E. Hertz, O. Faucher, B. Lavorel, and J. P. Wolf, “Higher-order Kerr terms allow ionization-free filamentation in gases,” Phys. Rev. Lett.104(10), 103903 (2010).
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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. B80(1), 35–38 (2004).
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Moloney, J.

Moloney, J. V.

P. Polynkin, M. Kolesik, E. M. Wright, and J. V. Moloney, “Experimental tests of the new paradigm for laser filamentation in gases,” Phys. Rev. Lett.106(15), 153902 (2011).
[CrossRef] [PubMed]

M. Kolesik, D. Mirell, J.-C. Diels, and J. V. Moloney, “On the higher-order Kerr effect in femtosecond filaments,” Opt. Lett.35(21), 3685–3687 (2010).
[CrossRef] [PubMed]

P. Polynkin, M. Kolesik, J. V. Moloney, G. A. Siviloglou, and D. N. Christodoulides, “Curved plasma channel generation using ultraintense Airy beams,” Science324(5924), 229–232 (2009).
[CrossRef] [PubMed]

M. Mlejnek, M. Kolesik, J. V. Moloney, and E. M. Wright, “Optically turbulent femtosecond light guide in air,” Phys. Rev. Lett.83(15), 2938–2941 (1999).
[CrossRef]

Mu, G.

H. Gao, X. Sun, B. Zeng, S. Xu, W. Chu, W. Liu, Y. Cheng, Z. Xu, and G. Mu, “Cylindrical symmetry breaking leads to multiple filamentation generation when focusing femtosecond lasers with axicons in methanol,” J. Opt.14(6), 065203 (2012).
[CrossRef]

Mu, G. G.

Mysyrowicz, A.

S. Akturk, B. Zhou, M. Franco, A. Couairon, and A. Mysyrowicz, “Generation of long plasma channels in air by focusing ultrashort laser pulses with an axicon,” Opt. Commun.282(1), 129–134 (2009).
[CrossRef]

B. Zhou, S. Akturk, B. Prade, Y. B. André, A. Houard, Y. Liu, M. Franco, C. D’Amico, E. Salmon, Z. Q. Hao, N. Lascoux, and A. Mysyrowicz, “Revival of femtosecond laser plasma filaments in air by a nanosecond laser,” Opt. Express17(14), 11450–11456 (2009).
[CrossRef] [PubMed]

A. Couairon and A. Mysyrowicz, “Femtosecond filamentation in transparent media,” Phys. Rep.441(2-4), 47–189 (2007).
[CrossRef]

G. Méchain, A. Couairon, M. Franco, B. Prade, and A. Mysyrowicz, “Organizing multiple femtosecond filaments in air,” Phys. Rev. Lett.93(3), 035003 (2004).
[CrossRef] [PubMed]

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(24), 5470–5473 (2001).
[CrossRef] [PubMed]

E. T. J. Nibbering, G. Grillon, M. A. Franco, B. S. Prade, and A. Mysyrowicz, “Determination of the inertial contribution to the nonlinear refractive index of air, N2, and O2 by use of unfocused high-intensity femtosecond laser pulses,” J. Opt. Soc. Am. B14(3), 650–660 (1997).
[CrossRef]

Neumark, D. M.

Ni, J.

Y. Fu, H. Gao, W. Chu, J. Ni, H. Xiong, H. Xu, J. Yao, B. Zeng, W. Liu, Y. Cheng, Z. Xu, and S. L. Chin, “Control of filament branching in air by astigmatically focused femtosecond laser pulses,” Appl. Phys. B103(2), 435–439 (2011).
[CrossRef]

Nibbering, E. T. J.

Nuter, R.

L. Guyon, K. M. Hajek, F. Courvoisier, V. Boutou, R. Nuter, A. Vincotte, S. Champeaux, L. Bergé, and J.-P. Wolf, “Control of lasing filament arrays in nonlinear liquid media,” Appl. Phys. B90(3-4), 383–390 (2008).
[CrossRef]

L. Bergé, S. Skupin, R. Nuter, J. Kasparian, and J.-P. Wolf, “Ultrashort filaments of light in weakly ionized, optically transparent media,” Rep. Prog. Phys.70(10), 1633–1713 (2007).
[CrossRef]

Nyakk, A. V.

V. P. Kandidov, N. Aközbek, M. Scalora, O. G. Kosareva, A. V. Nyakk, Q. Luo, S. A. Hosseini, and S. L. Chin, “Towards a control of multiple filamentation by spatial regularization of a high-power femtosecond laser pulse,” Appl. Phys. B80(2), 267–275 (2005).
[CrossRef]

Pan, H. F.

J. Liu, W. X. Li, H. F. Pan, and H. P. Zeng, “Two-dimensional plasma grating by non-collinear femtosecond filament interaction in air,” Appl. Phys. Lett.99(15), 151105 (2011).
[CrossRef]

Panov, N.

Panov, N. A.

O. G. Kosareva, N. A. Panov, N. Akozbek, V. P. Kandidov, Q. Luo, S. A. Hosseini, W. Liu, J.-F. Gravel, G. Roy, and S. L. Chin, “Controlling a bunch of multiple filaments by means of a beam diameter,” Appl. Phys. B82(1), 111–122 (2006).
[CrossRef]

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. B80(1), 35–38 (2004).
[CrossRef]

Papalazarou, E.

C. P. Hauri, J. Gautier, A. Trisorio, E. Papalazarou, and P. Zeitoun, “Two-dimensional organization of a large number of stationary optical filaments by adaptive wave front control,” Appl. Phys. B90(3-4), 391–394 (2008).
[CrossRef]

Papazoglou, D. G.

D. G. Papazoglou, S. Suntsov, D. Abdollahpour, and S. Tzortzakis, “Tunable intense Airy beams and tailored femtosecond laser filaments,” Phys. Rev. A81(6), 061807 (2010).
[CrossRef]

Pasquazi, A.

Paunescu, G.

G. Spindler and G. Paunescu, “Multifilamentation of femtosecond laser pulses propagating in turbulent air near the ground,” Appl. Phys. B96(1), 185–191 (2009).
[CrossRef]

G. Paunescu, G. Spindler, W. Riede, H. Schröder, and A. Giesen, “Multifilamentation of femtosecond laser pulses induced by small-scale air turbulence,” Appl. Phys. B96(1), 175–183 (2009).
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M. Châteauneuf, S. Payeur, J. Dubois, and J.-C. Kieffer, “Microwave guiding in air by a cylindrical filament array waveguide,” Appl. Phys. Lett.92(9), 091104 (2008).
[CrossRef]

Peng, Y.

Petit, S.

S. L. Chin, A. Talebpour, J. Yang, S. Petit, V. P. Kandidov, O. G. Kosareva, and M. P. Tamarov, “Filamentation of femtosecond laser pulses in turbulent air,” Appl. Phys. B74(1), 67–76 (2002).
[CrossRef]

Petit, Y.

Petrarca, M.

Pfeifer, T.

Polesana, P.

P. Polesana, M. Franco, A. Couairon, D. Faccio, and P. Di Trapani, “Filamentation in Kerr media from pulsed Bessel beams,” Phys. Rev. A77(4), 043814 (2008).
[CrossRef]

Polynkin, P.

P. Polynkin, M. Kolesik, E. M. Wright, and J. V. Moloney, “Experimental tests of the new paradigm for laser filamentation in gases,” Phys. Rev. Lett.106(15), 153902 (2011).
[CrossRef] [PubMed]

P. Polynkin, M. Kolesik, J. V. Moloney, G. A. Siviloglou, and D. N. Christodoulides, “Curved plasma channel generation using ultraintense Airy beams,” Science324(5924), 229–232 (2009).
[CrossRef] [PubMed]

P. Polynkin, M. Kolesik, A. Roberts, D. Faccio, P. Di Trapani, and J. Moloney, “Generation of extended plasma channels in air using femtosecond Bessel beams,” Opt. Express16(20), 15733–15740 (2008).
[CrossRef] [PubMed]

Prade, B.

B. Zhou, S. Akturk, B. Prade, Y. B. André, A. Houard, Y. Liu, M. Franco, C. D’Amico, E. Salmon, Z. Q. Hao, N. Lascoux, and A. Mysyrowicz, “Revival of femtosecond laser plasma filaments in air by a nanosecond laser,” Opt. Express17(14), 11450–11456 (2009).
[CrossRef] [PubMed]

G. Méchain, A. Couairon, M. Franco, B. Prade, and A. Mysyrowicz, “Organizing multiple femtosecond filaments in air,” Phys. Rev. Lett.93(3), 035003 (2004).
[CrossRef] [PubMed]

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(24), 5470–5473 (2001).
[CrossRef] [PubMed]

Prade, B. S.

Queißer, M.

P. Rohwetter, M. Queißer, K. Stelmaszczyk, M. Fechner, and L. Wöste, “Laser multiple filamentation control in air using a smooth phase mask,” Phys. Rev. A77(1), 013812 (2008).
[CrossRef]

Riede, W.

G. Paunescu, G. Spindler, W. Riede, H. Schröder, and A. Giesen, “Multifilamentation of femtosecond laser pulses induced by small-scale air turbulence,” Appl. Phys. B96(1), 175–183 (2009).
[CrossRef]

Roberts, A.

Rohwetter, P.

P. Rohwetter, M. Queißer, K. Stelmaszczyk, M. Fechner, and L. Wöste, “Laser multiple filamentation control in air using a smooth phase mask,” Phys. Rev. A77(1), 013812 (2008).
[CrossRef]

Roy, G.

O. Kosareva, J.-F. Daigle, N. Panov, T. Wang, S. Hosseini, S. Yuan, G. Roy, V. Makarov, and S. Leang Chin, “Arrest of self-focusing collapse in femtosecond air filaments: higher order Kerr or plasma defocusing?” Opt. Lett.36(7), 1035–1037 (2011).
[CrossRef] [PubMed]

O. G. Kosareva, N. A. Panov, N. Akozbek, V. P. Kandidov, Q. Luo, S. A. Hosseini, W. Liu, J.-F. Gravel, G. Roy, and S. L. Chin, “Controlling a bunch of multiple filaments by means of a beam diameter,” Appl. Phys. B82(1), 111–122 (2006).
[CrossRef]

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. B80(1), 35–38 (2004).
[CrossRef]

Sakaguchi, T.

O. Sakai, T. Sakaguchi, and K. Tachibana, “Verification of a plasma photonic crystal for microwaves of millimeter wavelength range using two-dimensional array of columnar microplasmas,” Appl. Phys. Lett.87(24), 241505 (2005).
[CrossRef]

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O. Sakai, T. Sakaguchi, and K. Tachibana, “Verification of a plasma photonic crystal for microwaves of millimeter wavelength range using two-dimensional array of columnar microplasmas,” Appl. Phys. Lett.87(24), 241505 (2005).
[CrossRef]

Salmon, E.

Sauerbrey, R.

J. Kasparian, R. Sauerbrey, and S. L. Chin, “The critical laser intensity of self-guided light filaments in air,” Appl. Phys. B71(6), 877–879 (2000).
[CrossRef]

Scalora, M.

V. P. Kandidov, N. Aközbek, M. Scalora, O. G. Kosareva, A. V. Nyakk, Q. Luo, S. A. Hosseini, and S. L. Chin, “Towards a control of multiple filamentation by spatial regularization of a high-power femtosecond laser pulse,” Appl. Phys. B80(2), 267–275 (2005).
[CrossRef]

Schrauth, S. E.

B. Shim, S. E. Schrauth, C. J. Hensley, L. T. Vuong, P. Hui, A. A. Ishaaya, and A. L. Gaeta, “Controlled interactions of femtosecond light filaments in air,” Phys. Rev. A81(6), 061803 (2010).
[CrossRef]

Schröder, H.

G. Paunescu, G. Spindler, W. Riede, H. Schröder, and A. Giesen, “Multifilamentation of femtosecond laser pulses induced by small-scale air turbulence,” Appl. Phys. B96(1), 175–183 (2009).
[CrossRef]

Schroeder, H.

S. L. Chin, S. A. Hosseini, W. Liu, Q. Luo, F. Théberge, N. Aközbek, A. Becker, V. P. Kandidov, O. G. Kosareva, and H. Schroeder, “The propagation of powerful femtosecond laser pulses in optical media: physics, applications, and new challenges,” Can. J. Phys.83(9), 863–905 (2005).
[CrossRef]

J. Liu, H. Schroeder, S. L. Chin, R. Li, and Z. Xu, “Ultrafast control of multiple filamentation by ultrafast laser pulses,” Appl. Phys. Lett.87(16), 161105 (2005).
[CrossRef]

H. Schroeder, J. Liu, and S. L. Chin, “From random to controlled small-scale filamentation in water,” Opt. Express12(20), 4768–4774 (2004).
[CrossRef] [PubMed]

Shim, B.

B. Shim, S. E. Schrauth, C. J. Hensley, L. T. Vuong, P. Hui, A. A. Ishaaya, and A. L. Gaeta, “Controlled interactions of femtosecond light filaments in air,” Phys. Rev. A81(6), 061803 (2010).
[CrossRef]

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M. N. Shneider, A. M. Zheltikov, and R. B. Miles, “Long-lived laser-induced microwave plasma guides in the atmosphere: self-consistent plasma-dynamic analysis and numerical simulations,” J. Appl. Phys.108(3), 033113 (2010).
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P. Polynkin, M. Kolesik, J. V. Moloney, G. A. Siviloglou, and D. N. Christodoulides, “Curved plasma channel generation using ultraintense Airy beams,” Science324(5924), 229–232 (2009).
[CrossRef] [PubMed]

Skupin, S.

L. Bergé, S. Skupin, R. Nuter, J. Kasparian, and J.-P. Wolf, “Ultrashort filaments of light in weakly ionized, optically transparent media,” Rep. Prog. Phys.70(10), 1633–1713 (2007).
[CrossRef]

Solis, J.

Spindler, G.

G. Spindler and G. Paunescu, “Multifilamentation of femtosecond laser pulses propagating in turbulent air near the ground,” Appl. Phys. B96(1), 185–191 (2009).
[CrossRef]

G. Paunescu, G. Spindler, W. Riede, H. Schröder, and A. Giesen, “Multifilamentation of femtosecond laser pulses induced by small-scale air turbulence,” Appl. Phys. B96(1), 175–183 (2009).
[CrossRef]

Stelmaszczyk, K.

P. Rohwetter, M. Queißer, K. Stelmaszczyk, M. Fechner, and L. Wöste, “Laser multiple filamentation control in air using a smooth phase mask,” Phys. Rev. A77(1), 013812 (2008).
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A. Pasquazi, S. Stivala, G. Assanto, J. Gonzalo, and J. Solis, “Transverse nonlinear optics in heavy-metal-oxide glass,” Phys. Rev. A77(4), 043808 (2008).
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A. Pasquazi, S. Stivala, G. Assanto, J. Gonzalo, J. Solis, and C. N. Afonso, “Near-infrared spatial solitons in heavy metal oxide glasses,” Opt. Lett.32(15), 2103–2105 (2007).
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H. Gao, X. Sun, B. Zeng, S. Xu, W. Chu, W. Liu, Y. Cheng, Z. Xu, and G. Mu, “Cylindrical symmetry breaking leads to multiple filamentation generation when focusing femtosecond lasers with axicons in methanol,” J. Opt.14(6), 065203 (2012).
[CrossRef]

Sun, X. D.

Suntsov, S.

D. G. Papazoglou, S. Suntsov, D. Abdollahpour, and S. Tzortzakis, “Tunable intense Airy beams and tailored femtosecond laser filaments,” Phys. Rev. A81(6), 061807 (2010).
[CrossRef]

Tachibana, K.

O. Sakai, T. Sakaguchi, and K. Tachibana, “Verification of a plasma photonic crystal for microwaves of millimeter wavelength range using two-dimensional array of columnar microplasmas,” Appl. Phys. Lett.87(24), 241505 (2005).
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V. I. Bespalov and V. I. Talanov, “Filamentary structure of light beams in non-linear liquids,” JETP Lett.3, 307–310 (1966).

Talebpour, A.

S. L. Chin, A. Talebpour, J. Yang, S. Petit, V. P. Kandidov, O. G. Kosareva, and M. P. Tamarov, “Filamentation of femtosecond laser pulses in turbulent air,” Appl. Phys. B74(1), 67–76 (2002).
[CrossRef]

A. Talebpour, J. Yang, and S. L. Chin, “Semi-empirical model for the rate of tunnel ionization of N2 and O2 molecule in an intense Ti: sapphire laser pulse,” Opt. Commun.163(1-3), 29–32 (1999).
[CrossRef]

Tamarov, M. P.

S. L. Chin, A. Talebpour, J. Yang, S. Petit, V. P. Kandidov, O. G. Kosareva, and M. P. Tamarov, “Filamentation of femtosecond laser pulses in turbulent air,” Appl. Phys. B74(1), 67–76 (2002).
[CrossRef]

Tamosauskas, G.

Tamošauskas, G.

D. Majus, V. Jukna, G. Tamošauskas, G. Valiulis, and A. Dubietis, “Three-dimensional mapping of multiple filament arrays,” Phys. Rev. A81(4), 043811 (2010).
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S. L. Chin, F. Théberge, and W. Liu, “Filamentation nonlinear optics,” Appl. Phys. B86(3), 477–483 (2007).
[CrossRef]

S. L. Chin, S. A. Hosseini, W. Liu, Q. Luo, F. Théberge, N. Aközbek, A. Becker, V. P. Kandidov, O. G. Kosareva, and H. Schroeder, “The propagation of powerful femtosecond laser pulses in optical media: physics, applications, and new challenges,” Can. J. Phys.83(9), 863–905 (2005).
[CrossRef]

Tong, Y. Q.

Trisorio, A.

C. P. Hauri, J. Gautier, A. Trisorio, E. Papalazarou, and P. Zeitoun, “Two-dimensional organization of a large number of stationary optical filaments by adaptive wave front control,” Appl. Phys. B90(3-4), 391–394 (2008).
[CrossRef]

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D. G. Papazoglou, S. Suntsov, D. Abdollahpour, and S. Tzortzakis, “Tunable intense Airy beams and tailored femtosecond laser filaments,” Phys. Rev. A81(6), 061807 (2010).
[CrossRef]

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(24), 5470–5473 (2001).
[CrossRef] [PubMed]

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D. Majus, V. Jukna, G. Tamošauskas, G. Valiulis, and A. Dubietis, “Three-dimensional mapping of multiple filament arrays,” Phys. Rev. A81(4), 043811 (2010).
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D. Majus, V. Jukna, G. Valiulis, and A. Dubietis, “Generation of periodic filament arrays by self-focusing of highly elliptical ultrashort pulsed laser beams,” Phys. Rev. A79(3), 033843 (2009).
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P. Béjot, J. Kasparian, S. Henin, V. Loriot, T. Vieillard, E. Hertz, O. Faucher, B. Lavorel, and J. P. Wolf, “Higher-order Kerr terms allow ionization-free filamentation in gases,” Phys. Rev. Lett.104(10), 103903 (2010).
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L. Guyon, K. M. Hajek, F. Courvoisier, V. Boutou, R. Nuter, A. Vincotte, S. Champeaux, L. Bergé, and J.-P. Wolf, “Control of lasing filament arrays in nonlinear liquid media,” Appl. Phys. B90(3-4), 383–390 (2008).
[CrossRef]

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B. Shim, S. E. Schrauth, C. J. Hensley, L. T. Vuong, P. Hui, A. A. Ishaaya, and A. L. Gaeta, “Controlled interactions of femtosecond light filaments in air,” Phys. Rev. A81(6), 061803 (2010).
[CrossRef]

Wang, T.

Wang, Z. H.

Wang, Z. X.

Wei, Z. Y.

Wolf, J. P.

P. Béjot, E. Hertz, J. Kasparian, B. Lavorel, J. P. Wolf, and O. Faucher, “Transition from plasma-driven to Kerr-driven laser filamentation,” Phys. Rev. Lett.106(24), 243902 (2011).
[CrossRef] [PubMed]

P. Béjot, J. Kasparian, S. Henin, V. Loriot, T. Vieillard, E. Hertz, O. Faucher, B. Lavorel, and J. P. Wolf, “Higher-order Kerr terms allow ionization-free filamentation in gases,” Phys. Rev. Lett.104(10), 103903 (2010).
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J. Kasparian and J.-P. Wolf, “Physics and applications of atmospheric nonlinear optics and filamentation,” Opt. Express16(1), 466–493 (2008).
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L. Guyon, K. M. Hajek, F. Courvoisier, V. Boutou, R. Nuter, A. Vincotte, S. Champeaux, L. Bergé, and J.-P. Wolf, “Control of lasing filament arrays in nonlinear liquid media,” Appl. Phys. B90(3-4), 383–390 (2008).
[CrossRef]

L. Bergé, S. Skupin, R. Nuter, J. Kasparian, and J.-P. Wolf, “Ultrashort filaments of light in weakly ionized, optically transparent media,” Rep. Prog. Phys.70(10), 1633–1713 (2007).
[CrossRef]

Wöste, L.

P. Rohwetter, M. Queißer, K. Stelmaszczyk, M. Fechner, and L. Wöste, “Laser multiple filamentation control in air using a smooth phase mask,” Phys. Rev. A77(1), 013812 (2008).
[CrossRef]

Wright, E. M.

P. Polynkin, M. Kolesik, E. M. Wright, and J. V. Moloney, “Experimental tests of the new paradigm for laser filamentation in gases,” Phys. Rev. Lett.106(15), 153902 (2011).
[CrossRef] [PubMed]

M. Mlejnek, M. Kolesik, J. V. Moloney, and E. M. Wright, “Optically turbulent femtosecond light guide in air,” Phys. Rev. Lett.83(15), 2938–2941 (1999).
[CrossRef]

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H. Cai, J. Wu, P. F. Lu, X. S. Bai, L. E. Ding, and H. P. Zeng, “Attraction and repulsion of parallel femtosecond filaments in air,” Phys. Rev. A80(5), 051802 (2009).
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X. Yang, J. Wu, Y. Peng, Y. Q. Tong, P. F. Lu, L. E. Ding, Z. Z. Xu, and H. P. Zeng, “Plasma waveguide array induced by filament interaction,” Opt. Lett.34(24), 3806–3808 (2009).
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Wu, Z. X.

Xi, T. T.

Xi, T.-T.

Y.-Y. Ma, X. Lu, T.-T. Xi, Q.-H. Gong, and J. Zhang, “Filamentation of interacting femtosecond laser pulses in air,” Appl. Phys. B93(2-3), 463–468 (2008).
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Y. Fu, H. Gao, W. Chu, J. Ni, H. Xiong, H. Xu, J. Yao, B. Zeng, W. Liu, Y. Cheng, Z. Xu, and S. L. Chin, “Control of filament branching in air by astigmatically focused femtosecond laser pulses,” Appl. Phys. B103(2), 435–439 (2011).
[CrossRef]

Y. X. Fu, H. Xiong, H. Xu, J. P. Yao, B. Zeng, W. Chu, Y. Cheng, Z. Z. Xu, W. W. Liu, and S. L. Chin, “Generation of extended filaments of femtosecond pulses in air by use of a single-step phase plate,” Opt. Lett.34(23), 3752–3754 (2009).
[CrossRef] [PubMed]

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Y. Fu, H. Gao, W. Chu, J. Ni, H. Xiong, H. Xu, J. Yao, B. Zeng, W. Liu, Y. Cheng, Z. Xu, and S. L. Chin, “Control of filament branching in air by astigmatically focused femtosecond laser pulses,” Appl. Phys. B103(2), 435–439 (2011).
[CrossRef]

Y. X. Fu, H. Xiong, H. Xu, J. P. Yao, B. Zeng, W. Chu, Y. Cheng, Z. Z. Xu, W. W. Liu, and S. L. Chin, “Generation of extended filaments of femtosecond pulses in air by use of a single-step phase plate,” Opt. Lett.34(23), 3752–3754 (2009).
[CrossRef] [PubMed]

Xu, S.

H. Gao, X. Sun, B. Zeng, S. Xu, W. Chu, W. Liu, Y. Cheng, Z. Xu, and G. Mu, “Cylindrical symmetry breaking leads to multiple filamentation generation when focusing femtosecond lasers with axicons in methanol,” J. Opt.14(6), 065203 (2012).
[CrossRef]

Xu, S. Q.

Xu, Z.

H. Gao, X. Sun, B. Zeng, S. Xu, W. Chu, W. Liu, Y. Cheng, Z. Xu, and G. Mu, “Cylindrical symmetry breaking leads to multiple filamentation generation when focusing femtosecond lasers with axicons in methanol,” J. Opt.14(6), 065203 (2012).
[CrossRef]

Y. Fu, H. Gao, W. Chu, J. Ni, H. Xiong, H. Xu, J. Yao, B. Zeng, W. Liu, Y. Cheng, Z. Xu, and S. L. Chin, “Control of filament branching in air by astigmatically focused femtosecond laser pulses,” Appl. Phys. B103(2), 435–439 (2011).
[CrossRef]

J. Liu, H. Schroeder, S. L. Chin, R. Li, and Z. Xu, “Ultrafast control of multiple filamentation by ultrafast laser pulses,” Appl. Phys. Lett.87(16), 161105 (2005).
[CrossRef]

Xu, Z. Z.

Yang, H.

Yang, J.

S. L. Chin, A. Talebpour, J. Yang, S. Petit, V. P. Kandidov, O. G. Kosareva, and M. P. Tamarov, “Filamentation of femtosecond laser pulses in turbulent air,” Appl. Phys. B74(1), 67–76 (2002).
[CrossRef]

A. Talebpour, J. Yang, and S. L. Chin, “Semi-empirical model for the rate of tunnel ionization of N2 and O2 molecule in an intense Ti: sapphire laser pulse,” Opt. Commun.163(1-3), 29–32 (1999).
[CrossRef]

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Yao, J.

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Figures (8)

Fig. 1
Fig. 1

Experimental setup.

Fig. 2
Fig. 2

Schematic diagram of the phase plates: (a) SCPP; (b) QCPP; (c) EOPP.

Fig. 3
Fig. 3

(a)-(d) Side images of multiple filaments using QCPP with focal length of f = 50 cm: (a) z = 46.5 cm, (b) z = 49.5 cm, (c) z = 50.5 cm, and (d) z = 51 cm. (e)-(f) The cross-section beam profiles captured by burn paper at corresponding distances of panels (a)-(d).

Fig. 4
Fig. 4

(a)-(c) Side images of multiple filaments: (a) using SCPP, f = 50 cm, z = 46.5 cm; (b) using SCPP, f = 100 cm, z = 95 cm; (c) using EOPP, f = 50 cm, z = 49.5 cm. (d)-(f) corresponding cross-section beam profiles inside the filaments.

Fig. 5
Fig. 5

The minimum separation distances of two diagonal filaments for three phase plates as a function of the focal length. (a) Experimental results; (b) Simulation results.

Fig. 6
Fig. 6

(a)-(d) Simulated laser intensity distribution as a function of propagation distance during linear propagation: (a) using SCPP, f = 50 cm; (b) using QCPP, f = 50 cm; (c) using QCPP, f = 100 cm; (d) using EOPP, f = 100 cm. (e)-(f) the corresponding cross-section beam profiles at the focus. The intensity is normalized.

Fig. 7
Fig. 7

(a)-(d) Simulated laser intensity distribution during the nonlinear propagation: (a) using SCPP, f = 50 cm; (b) using QCPP, f = 50 cm; (c) using QCPP, f = 100 cm; (d) using EOPP, f = 100 cm. (e)-(f) Corresponding cross-section beam profiles inside the filaments. For (e) z = 48 cm; For (f) z = 50 cm; For (g) z = 96 cm; For (h) z = 85 cm.

Fig. 8
Fig. 8

(a) and (b) The longitudinal intensity distribution with the eight-octant phase plate using the axicon during the nonlinear propagation and linear propagation, respectively. (c) and (d) the cross-section beam profiles during the nonlinear and linear propagation at the distance of z = 25 cm. For (b) and (d), the intensity is normalized.

Equations (2)

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2ik A z +( 2 x 2 + 2 y 2 )A+2 k 2 ΔnA+ik β m I m1 A=0
A(x,y,z=0)=exp( x 2 + y 2 w 0 2 )exp(i k 0 x 2 + y 2 2f )exp(iθ)

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