Abstract

We demonstrate the generation of filament array with orthogonal polarizations in air by using specifically designed wedge-type birefringent quartz plates. Experimental results show that the number of the generated filaments can be expressed as N = 2n wherenis the number of quartz plates inserted in the laser propagation path. By manipulating the optic axis of the quartz plates with respect to the polarization direction of the input laser pulse, the generated filaments can be separated into two parts with the polarization directions perpendicular with each other. The separation distance between the adjacent filaments is found to be linearly dependent on the focal length of external focusing lens. Our results provide a simple and efficient way to generate regular and reproductive femtosecond filament array in air.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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    [Crossref] [PubMed]
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    [Crossref]
  3. A. Couairon and A. Mysyrowicz, “Femtosecond filamentation in transparent media,” Phys. Rep. 441(2-4), 47–189 (2007).
    [Crossref]
  4. L. Bergé, S. Skupin, F. Lederer, G. Méjean, J. Yu, J. Kasparian, E. Salmon, J. P. Wolf, M. Rodriguez, L. Wöste, R. Bourayou, and R. Sauerbrey, “Multiple filamentation of terawatt laser pulses in air,” Phys. Rev. Lett. 92(22), 225002 (2004).
    [Crossref] [PubMed]
  5. S. Rostami Fairchild, W. Walasik, D. Kepler, M. Baudelet, N. M. Litchinitser, and M. Richardson, “Free-space nonlinear beam combining for high intensity projection,” Sci. Rep. 7(1), 10147 (2017).
    [Crossref] [PubMed]
  6. S. A. Hosseini, Q. Luo, B. Ferland, W. Liu, S. L. Chin, O. G. Kosareva, N. A. Panov, N. Akozbek, and V. P. Kandidov, “Competition of multiple filaments during the propagation of intense femtosecond laser pulses,” Phys. Rev. A 70(3), 033802 (2004).
    [Crossref]
  7. 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]
  8. 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]
  9. 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. A 80(5), 051802 (2009).
    [Crossref]
  10. Y. Ren, M. Alshershby, Z. Hao, Z. Zhao, and J. Lin, “Microwave guiding along double femtosecond filaments in air,” Phys. Rev. E 88(1), 013104 (2013).
    [Crossref] [PubMed]
  11. J. Zhao, L. Guo, W. Chu, B. Zeng, H. Gao, Y. Cheng, and W. Liu, “Simple method to enhance terahertz radiation from femtosecond laser filament array with a step phase plate,” Opt. Lett. 40(16), 3838–3841 (2015).
    [Crossref] [PubMed]
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    [Crossref] [PubMed]
  13. W. Walasik and N. M. Litchinitser, “Dynamics of large femtosecond filament arrays: possibilities, limitations, and trade-offs,” ACS Photonics 3(4), 640–646 (2016).
    [Crossref]
  14. T. Grow and A. Gaeta, “Dependence of multiple filamentation on beam ellipticity,” Opt. Express 13(12), 4594–4599 (2005).
    [Crossref] [PubMed]
  15. 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]
  16. H. Schroeder, J. Liu, and S. Chin, “From random to controlled small-scale filamentation in water,” Opt. Express 12(20), 4768–4774 (2004).
    [Crossref] [PubMed]
  17. D. E. Shipilo, N. A. Panov, E. S. Sunchugasheva, D. V. Mokrousova, A. V. Shutov, V. D. Zvorykin, N. N. Ustinovskii, L. V. Seleznev, A. B. Savel’ev, O. G. Kosareva, S. L. Chin, and A. A. Ionin, “Fifteen meter long uninterrupted filaments from sub-terawatt ultraviolet pulse in air,” Opt. Express 25(21), 25386–25391 (2017).
    [Crossref] [PubMed]
  18. 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. B 90(3-4), 391–394 (2008).
    [Crossref]
  19. P. Rohwetter, M. Queißer, K. Stelmaszczyk, M. Fechner, and L. Wöste, “Laser multiple filamentation control in air using a smooth phase mask,” Phys. Rev. A 77(1), 013812 (2008).
    [Crossref]
  20. H. Gao, W. Chu, G. Yu, B. Zeng, J. Zhao, Z. Wang, W. Liu, Y. Cheng, and Z. Xu, “Femtosecond laser filament array generated with step phase plate in air,” Opt. Express 21(4), 4612–4622 (2013).
    [Crossref] [PubMed]
  21. N. Jhajj, E. W. Rosenthal, R. Birnbaum, J. K. Wahlstrand, and H. M. Milchberg, “Demonstration of long-lived high-power optical waveguides in air,” Phys. Rev. X 4(1), 011027 (2014).
    [Crossref]
  22. A. Camino, Z. Hao, X. Liu, and J. Lin, “Control of laser filamentation in fused silica by a periodic microlens array,” Opt. Express 21(7), 7908–7915 (2013).
    [Crossref] [PubMed]
  23. T. Xi, Z. Zhao, and Z. Hao, “Femtosecond laser filamentation with a microlens array in air,” J. Opt. Soc. Am. B 32(1), 163–166 (2015).
    [Crossref]
  24. S. J. Gao and S. X. Ouyang, “Influence of γ-ray irradiation on absorption in silica glasses,” Guangpuxue Yu Guangpu Fenxi 23, 1060–1064 (2003).
  25. H. L. Xu and S. L. Chin, “Femtosecond laser filamentation for atmospheric sensing,” Sensors (Basel) 11(1), 32–53 (2010).
    [Crossref] [PubMed]
  26. W. Liu and S. Chin, “Direct measurement of the critical power of femtosecond Ti:Sapphire laser pulse in air,” Opt. Express 13(15), 5750–5755 (2005).
    [Crossref] [PubMed]
  27. J. H. Marburger, “Self-focusing: theory,” Prog. Quantum Electron. 4, 35–110 (1975).
    [Crossref]
  28. F. Théberge, W. Liu, P. T. Simard, A. Becker, and S. L. Chin, “Plasma density inside a femtosecond laser filament in air: Strong dependence on external focusing,” Phys. Rev. E 74(3), 036406 (2006).
    [Crossref] [PubMed]

2017 (2)

2016 (1)

W. Walasik and N. M. Litchinitser, “Dynamics of large femtosecond filament arrays: possibilities, limitations, and trade-offs,” ACS Photonics 3(4), 640–646 (2016).
[Crossref]

2015 (2)

2014 (2)

N. Jhajj, E. W. Rosenthal, R. Birnbaum, J. K. Wahlstrand, and H. M. Milchberg, “Demonstration of long-lived high-power optical waveguides in air,” Phys. Rev. X 4(1), 011027 (2014).
[Crossref]

A. Camino, Z. Hao, X. Liu, and J. Lin, “High spectral power femtosecond supercontinuum source by use of microlens array,” Opt. Lett. 39(4), 747–750 (2014).
[Crossref] [PubMed]

2013 (3)

2010 (1)

H. L. Xu and S. L. Chin, “Femtosecond laser filamentation for atmospheric sensing,” Sensors (Basel) 11(1), 32–53 (2010).
[Crossref] [PubMed]

2009 (1)

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. A 80(5), 051802 (2009).
[Crossref]

2008 (2)

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. B 90(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. A 77(1), 013812 (2008).
[Crossref]

2007 (1)

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

2006 (2)

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]

F. Théberge, W. Liu, P. T. Simard, A. Becker, and S. L. Chin, “Plasma density inside a femtosecond laser filament in air: Strong dependence on external focusing,” Phys. Rev. E 74(3), 036406 (2006).
[Crossref] [PubMed]

2005 (4)

W. Liu and S. Chin, “Direct measurement of the critical power of femtosecond Ti:Sapphire laser pulse in air,” Opt. Express 13(15), 5750–5755 (2005).
[Crossref] [PubMed]

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]

T. Grow and A. Gaeta, “Dependence of multiple filamentation on beam ellipticity,” Opt. Express 13(12), 4594–4599 (2005).
[Crossref] [PubMed]

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]

2004 (3)

H. Schroeder, J. Liu, and S. Chin, “From random to controlled small-scale filamentation in water,” Opt. Express 12(20), 4768–4774 (2004).
[Crossref] [PubMed]

L. Bergé, S. Skupin, F. Lederer, G. Méjean, J. Yu, J. Kasparian, E. Salmon, J. P. Wolf, M. Rodriguez, L. Wöste, R. Bourayou, and R. Sauerbrey, “Multiple filamentation of terawatt laser pulses in air,” Phys. Rev. Lett. 92(22), 225002 (2004).
[Crossref] [PubMed]

S. A. Hosseini, Q. Luo, B. Ferland, W. Liu, S. L. Chin, O. G. Kosareva, N. A. Panov, N. Akozbek, and V. P. Kandidov, “Competition of multiple filaments during the propagation of intense femtosecond laser pulses,” Phys. Rev. A 70(3), 033802 (2004).
[Crossref]

2003 (1)

S. J. Gao and S. X. Ouyang, “Influence of γ-ray irradiation on absorption in silica glasses,” Guangpuxue Yu Guangpu Fenxi 23, 1060–1064 (2003).

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]

1995 (1)

1975 (1)

J. H. Marburger, “Self-focusing: theory,” Prog. Quantum Electron. 4, 35–110 (1975).
[Crossref]

Akozbek, N.

S. A. Hosseini, Q. Luo, B. Ferland, W. Liu, S. L. Chin, O. G. Kosareva, N. A. Panov, N. Akozbek, and V. P. Kandidov, “Competition of multiple filaments during the propagation of intense femtosecond laser pulses,” Phys. Rev. A 70(3), 033802 (2004).
[Crossref]

Aközbek, N.

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]

Alshershby, M.

Y. Ren, M. Alshershby, Z. Hao, Z. Zhao, and J. Lin, “Microwave guiding along double femtosecond filaments in air,” Phys. Rev. E 88(1), 013104 (2013).
[Crossref] [PubMed]

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. A 80(5), 051802 (2009).
[Crossref]

Baudelet, M.

S. Rostami Fairchild, W. Walasik, D. Kepler, M. Baudelet, N. M. Litchinitser, and M. Richardson, “Free-space nonlinear beam combining for high intensity projection,” Sci. Rep. 7(1), 10147 (2017).
[Crossref] [PubMed]

Becker, A.

F. Théberge, W. Liu, P. T. Simard, A. Becker, and S. L. Chin, “Plasma density inside a femtosecond laser filament in air: Strong dependence on external focusing,” Phys. Rev. E 74(3), 036406 (2006).
[Crossref] [PubMed]

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]

Bergé, L.

L. Bergé, S. Skupin, F. Lederer, G. Méjean, J. Yu, J. Kasparian, E. Salmon, J. P. Wolf, M. Rodriguez, L. Wöste, R. Bourayou, and R. Sauerbrey, “Multiple filamentation of terawatt laser pulses in air,” Phys. Rev. Lett. 92(22), 225002 (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]

Birnbaum, R.

N. Jhajj, E. W. Rosenthal, R. Birnbaum, J. K. Wahlstrand, and H. M. Milchberg, “Demonstration of long-lived high-power optical waveguides in air,” Phys. Rev. X 4(1), 011027 (2014).
[Crossref]

Bourayou, R.

L. Bergé, S. Skupin, F. Lederer, G. Méjean, J. Yu, J. Kasparian, E. Salmon, J. P. Wolf, M. Rodriguez, L. Wöste, R. Bourayou, and R. Sauerbrey, “Multiple filamentation of terawatt laser pulses in air,” Phys. Rev. Lett. 92(22), 225002 (2004).
[Crossref] [PubMed]

Braun, A.

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. A 80(5), 051802 (2009).
[Crossref]

Camino, A.

Cheng, Y.

Chin, S.

Chin, S. L.

D. E. Shipilo, N. A. Panov, E. S. Sunchugasheva, D. V. Mokrousova, A. V. Shutov, V. D. Zvorykin, N. N. Ustinovskii, L. V. Seleznev, A. B. Savel’ev, O. G. Kosareva, S. L. Chin, and A. A. Ionin, “Fifteen meter long uninterrupted filaments from sub-terawatt ultraviolet pulse in air,” Opt. Express 25(21), 25386–25391 (2017).
[Crossref] [PubMed]

H. L. Xu and S. L. Chin, “Femtosecond laser filamentation for atmospheric sensing,” Sensors (Basel) 11(1), 32–53 (2010).
[Crossref] [PubMed]

F. Théberge, W. Liu, P. T. Simard, A. Becker, and S. L. Chin, “Plasma density inside a femtosecond laser filament in air: Strong dependence on external focusing,” Phys. Rev. E 74(3), 036406 (2006).
[Crossref] [PubMed]

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]

S. A. Hosseini, Q. Luo, B. Ferland, W. Liu, S. L. Chin, O. G. Kosareva, N. A. Panov, N. Akozbek, and V. P. Kandidov, “Competition of multiple filaments during the propagation of intense femtosecond laser pulses,” Phys. Rev. A 70(3), 033802 (2004).
[Crossref]

Chu, W.

Couairon, A.

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

Ding, L. E.

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. A 80(5), 051802 (2009).
[Crossref]

Du, D.

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. A 77(1), 013812 (2008).
[Crossref]

Ferland, B.

S. A. Hosseini, Q. Luo, B. Ferland, W. Liu, S. L. Chin, O. G. Kosareva, N. A. Panov, N. Akozbek, and V. P. Kandidov, “Competition of multiple filaments during the propagation of intense femtosecond laser pulses,” Phys. Rev. A 70(3), 033802 (2004).
[Crossref]

Franco, M.

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]

Gaeta, A.

Gao, H.

Gao, S. J.

S. J. Gao and S. X. Ouyang, “Influence of γ-ray irradiation on absorption in silica glasses,” Guangpuxue Yu Guangpu Fenxi 23, 1060–1064 (2003).

Gautier, J.

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. B 90(3-4), 391–394 (2008).
[Crossref]

Grow, T.

Guo, L.

Hao, Z.

Hauri, C. P.

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. B 90(3-4), 391–394 (2008).
[Crossref]

Hosseini, S. 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]

S. A. Hosseini, Q. Luo, B. Ferland, W. Liu, S. L. Chin, O. G. Kosareva, N. A. Panov, N. Akozbek, and V. P. Kandidov, “Competition of multiple filaments during the propagation of intense femtosecond laser pulses,” Phys. Rev. A 70(3), 033802 (2004).
[Crossref]

Ionin, A. A.

Jhajj, N.

N. Jhajj, E. W. Rosenthal, R. Birnbaum, J. K. Wahlstrand, and H. M. Milchberg, “Demonstration of long-lived high-power optical waveguides in air,” Phys. Rev. X 4(1), 011027 (2014).
[Crossref]

Kandidov, V. P.

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]

S. A. Hosseini, Q. Luo, B. Ferland, W. Liu, S. L. Chin, O. G. Kosareva, N. A. Panov, N. Akozbek, and V. P. Kandidov, “Competition of multiple filaments during the propagation of intense femtosecond laser pulses,” Phys. Rev. A 70(3), 033802 (2004).
[Crossref]

Kasparian, J.

L. Bergé, S. Skupin, F. Lederer, G. Méjean, J. Yu, J. Kasparian, E. Salmon, J. P. Wolf, M. Rodriguez, L. Wöste, R. Bourayou, and R. Sauerbrey, “Multiple filamentation of terawatt laser pulses in air,” Phys. Rev. Lett. 92(22), 225002 (2004).
[Crossref] [PubMed]

Kepler, D.

S. Rostami Fairchild, W. Walasik, D. Kepler, M. Baudelet, N. M. Litchinitser, and M. Richardson, “Free-space nonlinear beam combining for high intensity projection,” Sci. Rep. 7(1), 10147 (2017).
[Crossref] [PubMed]

Korn, G.

Kosareva, O. G.

D. E. Shipilo, N. A. Panov, E. S. Sunchugasheva, D. V. Mokrousova, A. V. Shutov, V. D. Zvorykin, N. N. Ustinovskii, L. V. Seleznev, A. B. Savel’ev, O. G. Kosareva, S. L. Chin, and A. A. Ionin, “Fifteen meter long uninterrupted filaments from sub-terawatt ultraviolet pulse in air,” Opt. Express 25(21), 25386–25391 (2017).
[Crossref] [PubMed]

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]

S. A. Hosseini, Q. Luo, B. Ferland, W. Liu, S. L. Chin, O. G. Kosareva, N. A. Panov, N. Akozbek, and V. P. Kandidov, “Competition of multiple filaments during the propagation of intense femtosecond laser pulses,” Phys. Rev. A 70(3), 033802 (2004).
[Crossref]

Lederer, F.

L. Bergé, S. Skupin, F. Lederer, G. Méjean, J. Yu, J. Kasparian, E. Salmon, J. P. Wolf, M. Rodriguez, L. Wöste, R. Bourayou, and R. Sauerbrey, “Multiple filamentation of terawatt laser pulses in air,” Phys. Rev. Lett. 92(22), 225002 (2004).
[Crossref] [PubMed]

Li, R.

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]

Lin, J.

Litchinitser, N. M.

S. Rostami Fairchild, W. Walasik, D. Kepler, M. Baudelet, N. M. Litchinitser, and M. Richardson, “Free-space nonlinear beam combining for high intensity projection,” Sci. Rep. 7(1), 10147 (2017).
[Crossref] [PubMed]

W. Walasik and N. M. Litchinitser, “Dynamics of large femtosecond filament arrays: possibilities, limitations, and trade-offs,” ACS Photonics 3(4), 640–646 (2016).
[Crossref]

Liu, J.

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. Chin, “From random to controlled small-scale filamentation in water,” Opt. Express 12(20), 4768–4774 (2004).
[Crossref] [PubMed]

Liu, W.

J. Zhao, L. Guo, W. Chu, B. Zeng, H. Gao, Y. Cheng, and W. Liu, “Simple method to enhance terahertz radiation from femtosecond laser filament array with a step phase plate,” Opt. Lett. 40(16), 3838–3841 (2015).
[Crossref] [PubMed]

H. Gao, W. Chu, G. Yu, B. Zeng, J. Zhao, Z. Wang, W. Liu, Y. Cheng, and Z. Xu, “Femtosecond laser filament array generated with step phase plate in air,” Opt. Express 21(4), 4612–4622 (2013).
[Crossref] [PubMed]

F. Théberge, W. Liu, P. T. Simard, A. Becker, and S. L. Chin, “Plasma density inside a femtosecond laser filament in air: Strong dependence on external focusing,” Phys. Rev. E 74(3), 036406 (2006).
[Crossref] [PubMed]

W. Liu and S. Chin, “Direct measurement of the critical power of femtosecond Ti:Sapphire laser pulse in air,” Opt. Express 13(15), 5750–5755 (2005).
[Crossref] [PubMed]

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]

S. A. Hosseini, Q. Luo, B. Ferland, W. Liu, S. L. Chin, O. G. Kosareva, N. A. Panov, N. Akozbek, and V. P. Kandidov, “Competition of multiple filaments during the propagation of intense femtosecond laser pulses,” Phys. Rev. A 70(3), 033802 (2004).
[Crossref]

Liu, X.

Lu, P. F.

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. A 80(5), 051802 (2009).
[Crossref]

Lu, X.

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]

Luo, Q.

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]

S. A. Hosseini, Q. Luo, B. Ferland, W. Liu, S. L. Chin, O. G. Kosareva, N. A. Panov, N. Akozbek, and V. P. Kandidov, “Competition of multiple filaments during the propagation of intense femtosecond laser pulses,” Phys. Rev. A 70(3), 033802 (2004).
[Crossref]

Marburger, J. H.

J. H. Marburger, “Self-focusing: theory,” Prog. Quantum Electron. 4, 35–110 (1975).
[Crossref]

Méjean, G.

L. Bergé, S. Skupin, F. Lederer, G. Méjean, J. Yu, J. Kasparian, E. Salmon, J. P. Wolf, M. Rodriguez, L. Wöste, R. Bourayou, and R. Sauerbrey, “Multiple filamentation of terawatt laser pulses in air,” Phys. Rev. Lett. 92(22), 225002 (2004).
[Crossref] [PubMed]

Milchberg, H. M.

N. Jhajj, E. W. Rosenthal, R. Birnbaum, J. K. Wahlstrand, and H. M. Milchberg, “Demonstration of long-lived high-power optical waveguides in air,” Phys. Rev. X 4(1), 011027 (2014).
[Crossref]

Mokrousova, D. V.

Mourou, G.

Mysyrowicz, A.

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

Ouyang, S. X.

S. J. Gao and S. X. Ouyang, “Influence of γ-ray irradiation on absorption in silica glasses,” Guangpuxue Yu Guangpu Fenxi 23, 1060–1064 (2003).

Panov, N. A.

D. E. Shipilo, N. A. Panov, E. S. Sunchugasheva, D. V. Mokrousova, A. V. Shutov, V. D. Zvorykin, N. N. Ustinovskii, L. V. Seleznev, A. B. Savel’ev, O. G. Kosareva, S. L. Chin, and A. A. Ionin, “Fifteen meter long uninterrupted filaments from sub-terawatt ultraviolet pulse in air,” Opt. Express 25(21), 25386–25391 (2017).
[Crossref] [PubMed]

S. A. Hosseini, Q. Luo, B. Ferland, W. Liu, S. L. Chin, O. G. Kosareva, N. A. Panov, N. Akozbek, and V. P. Kandidov, “Competition of multiple filaments during the propagation of intense femtosecond laser pulses,” Phys. Rev. A 70(3), 033802 (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. B 90(3-4), 391–394 (2008).
[Crossref]

Prade, B.

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]

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. A 77(1), 013812 (2008).
[Crossref]

Ren, Y.

Y. Ren, M. Alshershby, Z. Hao, Z. Zhao, and J. Lin, “Microwave guiding along double femtosecond filaments in air,” Phys. Rev. E 88(1), 013104 (2013).
[Crossref] [PubMed]

Richardson, M.

S. Rostami Fairchild, W. Walasik, D. Kepler, M. Baudelet, N. M. Litchinitser, and M. Richardson, “Free-space nonlinear beam combining for high intensity projection,” Sci. Rep. 7(1), 10147 (2017).
[Crossref] [PubMed]

Rodriguez, M.

L. Bergé, S. Skupin, F. Lederer, G. Méjean, J. Yu, J. Kasparian, E. Salmon, J. P. Wolf, M. Rodriguez, L. Wöste, R. Bourayou, and R. Sauerbrey, “Multiple filamentation of terawatt laser pulses in air,” Phys. Rev. Lett. 92(22), 225002 (2004).
[Crossref] [PubMed]

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. A 77(1), 013812 (2008).
[Crossref]

Rosenthal, E. W.

N. Jhajj, E. W. Rosenthal, R. Birnbaum, J. K. Wahlstrand, and H. M. Milchberg, “Demonstration of long-lived high-power optical waveguides in air,” Phys. Rev. X 4(1), 011027 (2014).
[Crossref]

Rostami Fairchild, S.

S. Rostami Fairchild, W. Walasik, D. Kepler, M. Baudelet, N. M. Litchinitser, and M. Richardson, “Free-space nonlinear beam combining for high intensity projection,” Sci. Rep. 7(1), 10147 (2017).
[Crossref] [PubMed]

Salmon, E.

L. Bergé, S. Skupin, F. Lederer, G. Méjean, J. Yu, J. Kasparian, E. Salmon, J. P. Wolf, M. Rodriguez, L. Wöste, R. Bourayou, and R. Sauerbrey, “Multiple filamentation of terawatt laser pulses in air,” Phys. Rev. Lett. 92(22), 225002 (2004).
[Crossref] [PubMed]

Sauerbrey, R.

L. Bergé, S. Skupin, F. Lederer, G. Méjean, J. Yu, J. Kasparian, E. Salmon, J. P. Wolf, M. Rodriguez, L. Wöste, R. Bourayou, and R. Sauerbrey, “Multiple filamentation of terawatt laser pulses in air,” Phys. Rev. Lett. 92(22), 225002 (2004).
[Crossref] [PubMed]

Savel’ev, A. B.

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. Chin, “From random to controlled small-scale filamentation in water,” Opt. Express 12(20), 4768–4774 (2004).
[Crossref] [PubMed]

Seleznev, L. V.

Shipilo, D. E.

Shutov, A. V.

Simard, P. T.

F. Théberge, W. Liu, P. T. Simard, A. Becker, and S. L. Chin, “Plasma density inside a femtosecond laser filament in air: Strong dependence on external focusing,” Phys. Rev. E 74(3), 036406 (2006).
[Crossref] [PubMed]

Skupin, S.

L. Bergé, S. Skupin, F. Lederer, G. Méjean, J. Yu, J. Kasparian, E. Salmon, J. P. Wolf, M. Rodriguez, L. Wöste, R. Bourayou, and R. Sauerbrey, “Multiple filamentation of terawatt laser pulses in air,” Phys. Rev. Lett. 92(22), 225002 (2004).
[Crossref] [PubMed]

Squier, J.

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. A 77(1), 013812 (2008).
[Crossref]

Sunchugasheva, E. S.

Théberge, F.

F. Théberge, W. Liu, P. T. Simard, A. Becker, and S. L. Chin, “Plasma density inside a femtosecond laser filament in air: Strong dependence on external focusing,” Phys. Rev. E 74(3), 036406 (2006).
[Crossref] [PubMed]

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]

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. B 90(3-4), 391–394 (2008).
[Crossref]

Tzortzakis, S.

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]

Ustinovskii, N. N.

Wahlstrand, J. K.

N. Jhajj, E. W. Rosenthal, R. Birnbaum, J. K. Wahlstrand, and H. M. Milchberg, “Demonstration of long-lived high-power optical waveguides in air,” Phys. Rev. X 4(1), 011027 (2014).
[Crossref]

Walasik, W.

S. Rostami Fairchild, W. Walasik, D. Kepler, M. Baudelet, N. M. Litchinitser, and M. Richardson, “Free-space nonlinear beam combining for high intensity projection,” Sci. Rep. 7(1), 10147 (2017).
[Crossref] [PubMed]

W. Walasik and N. M. Litchinitser, “Dynamics of large femtosecond filament arrays: possibilities, limitations, and trade-offs,” ACS Photonics 3(4), 640–646 (2016).
[Crossref]

Wang, Z.

Wolf, J. P.

L. Bergé, S. Skupin, F. Lederer, G. Méjean, J. Yu, J. Kasparian, E. Salmon, J. P. Wolf, M. Rodriguez, L. Wöste, R. Bourayou, and R. Sauerbrey, “Multiple filamentation of terawatt laser pulses in air,” Phys. Rev. Lett. 92(22), 225002 (2004).
[Crossref] [PubMed]

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. A 77(1), 013812 (2008).
[Crossref]

L. Bergé, S. Skupin, F. Lederer, G. Méjean, J. Yu, J. Kasparian, E. Salmon, J. P. Wolf, M. Rodriguez, L. Wöste, R. Bourayou, and R. Sauerbrey, “Multiple filamentation of terawatt laser pulses in air,” Phys. Rev. Lett. 92(22), 225002 (2004).
[Crossref] [PubMed]

Wu, J.

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. A 80(5), 051802 (2009).
[Crossref]

Xi, T.

Xi, T. T.

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]

Xu, H. L.

H. L. Xu and S. L. Chin, “Femtosecond laser filamentation for atmospheric sensing,” Sensors (Basel) 11(1), 32–53 (2010).
[Crossref] [PubMed]

Xu, Z.

H. Gao, W. Chu, G. Yu, B. Zeng, J. Zhao, Z. Wang, W. Liu, Y. Cheng, and Z. Xu, “Femtosecond laser filament array generated with step phase plate in air,” Opt. Express 21(4), 4612–4622 (2013).
[Crossref] [PubMed]

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]

Yu, G.

Yu, J.

L. Bergé, S. Skupin, F. Lederer, G. Méjean, J. Yu, J. Kasparian, E. Salmon, J. P. Wolf, M. Rodriguez, L. Wöste, R. Bourayou, and R. Sauerbrey, “Multiple filamentation of terawatt laser pulses in air,” Phys. Rev. Lett. 92(22), 225002 (2004).
[Crossref] [PubMed]

Zeitoun, P.

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. B 90(3-4), 391–394 (2008).
[Crossref]

Zeng, B.

Zeng, H. P.

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. A 80(5), 051802 (2009).
[Crossref]

Zhang, J.

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]

Zhao, J.

Zhao, Z.

T. Xi, Z. Zhao, and Z. Hao, “Femtosecond laser filamentation with a microlens array in air,” J. Opt. Soc. Am. B 32(1), 163–166 (2015).
[Crossref]

Y. Ren, M. Alshershby, Z. Hao, Z. Zhao, and J. Lin, “Microwave guiding along double femtosecond filaments in air,” Phys. Rev. E 88(1), 013104 (2013).
[Crossref] [PubMed]

Zvorykin, V. D.

ACS Photonics (1)

W. Walasik and N. M. Litchinitser, “Dynamics of large femtosecond filament arrays: possibilities, limitations, and trade-offs,” ACS Photonics 3(4), 640–646 (2016).
[Crossref]

Appl. Phys. B (1)

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. B 90(3-4), 391–394 (2008).
[Crossref]

Appl. Phys. Lett. (1)

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]

Can. J. Phys. (1)

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]

Guangpuxue Yu Guangpu Fenxi (1)

S. J. Gao and S. X. Ouyang, “Influence of γ-ray irradiation on absorption in silica glasses,” Guangpuxue Yu Guangpu Fenxi 23, 1060–1064 (2003).

J. Opt. Soc. Am. B (1)

Opt. Express (6)

Opt. Lett. (3)

Phys. Rep. (1)

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

Phys. Rev. A (3)

S. A. Hosseini, Q. Luo, B. Ferland, W. Liu, S. L. Chin, O. G. Kosareva, N. A. Panov, N. Akozbek, and V. P. Kandidov, “Competition of multiple filaments during the propagation of intense femtosecond laser pulses,” Phys. Rev. A 70(3), 033802 (2004).
[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. A 80(5), 051802 (2009).
[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. A 77(1), 013812 (2008).
[Crossref]

Phys. Rev. E (2)

Y. Ren, M. Alshershby, Z. Hao, Z. Zhao, and J. Lin, “Microwave guiding along double femtosecond filaments in air,” Phys. Rev. E 88(1), 013104 (2013).
[Crossref] [PubMed]

F. Théberge, W. Liu, P. T. Simard, A. Becker, and S. L. Chin, “Plasma density inside a femtosecond laser filament in air: Strong dependence on external focusing,” Phys. Rev. E 74(3), 036406 (2006).
[Crossref] [PubMed]

Phys. Rev. Lett. (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]

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]

L. Bergé, S. Skupin, F. Lederer, G. Méjean, J. Yu, J. Kasparian, E. Salmon, J. P. Wolf, M. Rodriguez, L. Wöste, R. Bourayou, and R. Sauerbrey, “Multiple filamentation of terawatt laser pulses in air,” Phys. Rev. Lett. 92(22), 225002 (2004).
[Crossref] [PubMed]

Phys. Rev. X (1)

N. Jhajj, E. W. Rosenthal, R. Birnbaum, J. K. Wahlstrand, and H. M. Milchberg, “Demonstration of long-lived high-power optical waveguides in air,” Phys. Rev. X 4(1), 011027 (2014).
[Crossref]

Prog. Quantum Electron. (1)

J. H. Marburger, “Self-focusing: theory,” Prog. Quantum Electron. 4, 35–110 (1975).
[Crossref]

Sci. Rep. (1)

S. Rostami Fairchild, W. Walasik, D. Kepler, M. Baudelet, N. M. Litchinitser, and M. Richardson, “Free-space nonlinear beam combining for high intensity projection,” Sci. Rep. 7(1), 10147 (2017).
[Crossref] [PubMed]

Sensors (Basel) (1)

H. L. Xu and S. L. Chin, “Femtosecond laser filamentation for atmospheric sensing,” Sensors (Basel) 11(1), 32–53 (2010).
[Crossref] [PubMed]

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Figures (4)

Fig. 1
Fig. 1 (a) Schematic of the experimental setup. HWP: half-wave plate, P1, P2: WTQP (quartz plate with a small wedge angle on the output surface) and GTP: Glan-Taylor polarizer. (b) Scheme for generating the filament array by using WTQPs. OA: optic axis; θ: the wedge angle between the front and back surfaces; Insets: Scheme for the alignment of laser polarization and optic axes of WTQPs. (c)-(e) the images of the filament(s) recorded under the same conditions from the side of the filament(s) without WTQP, and with one WTQP and two WTQP s, respectively. The arrows denote the laser propagation direction.
Fig. 2
Fig. 2 (a)-(c) Photos taken from the side of the filaments in a higher resolution, and (d)-(f) spatial distribution of filament(s) recorded by a burn paper in the absence of WTQP, and in the presence of one WTQP and two WTQPs, respectively.
Fig. 3
Fig. 3 Images of the holes drilled on the burn paper in the case of two WTQPs. (a) o light (left column), (b) e light (left column) and o light (right column), and (c) e light.
Fig. 4
Fig. 4 Separation distance between the filament cores in the filament array formed by using one WTQP as a function of length of the external focal lens. The three images at the top show the filament-drilled holes by using the external lens with the focal lengths of 40, 75, and 100 cm, respectively.

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