Abstract

We have reproduced the process of two-dimensional array generation by using two crossing laser beams in a YAG crystal plate based on numerical simulation considering cross-phase modulation (XPM) and self-focusing. Furthermore, we come to the conclusion that both XPM and the cylindrical symmetry breaking in the initial beam profile contributes to the generation of two-dimensional array. In addition, we have studied the threshold input laser beam power for the two crossing beams splitting in a YAG crystal plate. Our study could be valuable in various applications, such as 2-D all-optical switching devices or multicolor pump-probe experiments.

© 2015 Optical Society of America

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References

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  1. H. Crespo, J. T. Mendonça, and A. Dos Santos, “Cascaded highly nondegenerate four-wave-mixing phenomenon in transparent isotropic condensed media,” Opt. Lett. 25(11), 829–831 (2000).
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    [Crossref] [PubMed]
  4. M. Zhi and A. V. Sokolov, “Broadband coherent light generation in a Raman-active crystal driven by two-color femtosecond laser pulses,” Opt. Lett. 32(15), 2251–2253 (2007).
    [Crossref] [PubMed]
  5. E. Matsubara, T. Sekikawa, and M. Yamashita, “Generation of ultrashort optical pulses using multiple coherent anti-Stokes Raman scattering in a crystal at room temperature,” Appl. Phys. Lett. 92(7), 071104 (2008).
    [Crossref]
  6. H. Matsuki, K. Inoue, and E. Hanamura, “Multiple coherent anti-Stokes Raman scattering due to phonon grating in KNbO3 induced by crossed beams of two-color femtosecond pulses,” Phys. Rev. B 75(2), 024102 (2007).
    [Crossref]
  7. K. Inoue, J. Kato, E. Hanamura, H. Matsuki, and E. Matsubara, “Broadband coherent radiation based on peculiar multiple Raman scattering by laser-induced phonon grating in TiO2,” Phys. Rev. B 76(4), 041101 (2007).
    [Crossref]
  8. E. Matsubara, K. Inoue, and E. Hanamura, “Violation of Raman selection rules induced by two femtosecond laser pulses in KTaO3,” Phys. Rev. B 72(13), 134101 (2005).
    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
  12. J. Liu, T. Kobayashi, and Z. Wang, “Generation of broadband two-dimensional multicolored arrays in a sapphire plate,” Opt. Express 17(11), 9226–9234 (2009).
    [Crossref] [PubMed]
  13. J. P. He, J. Liu, and T. Kobayashi, “Tunable multicolored femtosecond pulse generation using cascaded four-wave mixing in bulk materials,” Appl. Sci. 4(3), 444–467 (2014).
    [Crossref]
  14. A. Dubietis, G. Tamošauskas, G. Fibich, and B. Ilan, “Multiple filamentation induced by input-beam ellipticity,” Opt. Lett. 29(10), 1126–1128 (2004).
    [Crossref] [PubMed]
  15. W. Liu and S. L. Chin, “Abnormal wavelength dependence of the self-cleaning phenomenon during femtosecond-laser-pulse filamentation,” Phys. Rev. A 76(1), 013826 (2007).
    [Crossref]
  16. F. Silva, D. R. Austin, A. Thai, M. Baudisch, M. Hemmer, D. Faccio, A. Couairon, and J. Biegert, “Multi-octave supercontinuum generation from mid-infrared filamentation in a bulk crystal,” Nat. Commun. 3, 807 (2012).
    [Crossref] [PubMed]
  17. L. Sudrie, A. Couairon, M. Franco, B. Lamouroux, B. Prade, S. Tzortzakis, and A. Mysyrowicz, “Femtosecond laser-induced damage and filamentary propagation in fused silica,” Phys. Rev. Lett. 89(18), 186601 (2002).
    [Crossref] [PubMed]
  18. A. Dubietis, G. Tamošauskas, G. Fibich, and B. Ilan, “Multiple filamentation induced by input-beam ellipticity,” Opt. Lett. 29(10), 1126–1128 (2004).
    [Crossref] [PubMed]
  19. 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. A 79(3), 033843 (2009).
    [Crossref]

2014 (1)

J. P. He, J. Liu, and T. Kobayashi, “Tunable multicolored femtosecond pulse generation using cascaded four-wave mixing in bulk materials,” Appl. Sci. 4(3), 444–467 (2014).
[Crossref]

2012 (1)

F. Silva, D. R. Austin, A. Thai, M. Baudisch, M. Hemmer, D. Faccio, A. Couairon, and J. Biegert, “Multi-octave supercontinuum generation from mid-infrared filamentation in a bulk crystal,” Nat. Commun. 3, 807 (2012).
[Crossref] [PubMed]

2009 (4)

2008 (3)

2007 (4)

W. Liu and S. L. Chin, “Abnormal wavelength dependence of the self-cleaning phenomenon during femtosecond-laser-pulse filamentation,” Phys. Rev. A 76(1), 013826 (2007).
[Crossref]

H. Matsuki, K. Inoue, and E. Hanamura, “Multiple coherent anti-Stokes Raman scattering due to phonon grating in KNbO3 induced by crossed beams of two-color femtosecond pulses,” Phys. Rev. B 75(2), 024102 (2007).
[Crossref]

K. Inoue, J. Kato, E. Hanamura, H. Matsuki, and E. Matsubara, “Broadband coherent radiation based on peculiar multiple Raman scattering by laser-induced phonon grating in TiO2,” Phys. Rev. B 76(4), 041101 (2007).
[Crossref]

M. Zhi and A. V. Sokolov, “Broadband coherent light generation in a Raman-active crystal driven by two-color femtosecond laser pulses,” Opt. Lett. 32(15), 2251–2253 (2007).
[Crossref] [PubMed]

2006 (1)

H. Zeng, J. Wu, H. Xu, and K. Wu, “Generation and weak beam control of two-dimensional multicolored arrays in a quadratic nonlinear medium,” Phys. Rev. Lett. 96(8), 083902 (2006).
[Crossref] [PubMed]

2005 (1)

E. Matsubara, K. Inoue, and E. Hanamura, “Violation of Raman selection rules induced by two femtosecond laser pulses in KTaO3,” Phys. Rev. B 72(13), 134101 (2005).
[Crossref]

2004 (2)

2002 (1)

L. Sudrie, A. Couairon, M. Franco, B. Lamouroux, B. Prade, S. Tzortzakis, and A. Mysyrowicz, “Femtosecond laser-induced damage and filamentary propagation in fused silica,” Phys. Rev. Lett. 89(18), 186601 (2002).
[Crossref] [PubMed]

2000 (1)

Austin, D. R.

F. Silva, D. R. Austin, A. Thai, M. Baudisch, M. Hemmer, D. Faccio, A. Couairon, and J. Biegert, “Multi-octave supercontinuum generation from mid-infrared filamentation in a bulk crystal,” Nat. Commun. 3, 807 (2012).
[Crossref] [PubMed]

Baudisch, M.

F. Silva, D. R. Austin, A. Thai, M. Baudisch, M. Hemmer, D. Faccio, A. Couairon, and J. Biegert, “Multi-octave supercontinuum generation from mid-infrared filamentation in a bulk crystal,” Nat. Commun. 3, 807 (2012).
[Crossref] [PubMed]

Biegert, J.

F. Silva, D. R. Austin, A. Thai, M. Baudisch, M. Hemmer, D. Faccio, A. Couairon, and J. Biegert, “Multi-octave supercontinuum generation from mid-infrared filamentation in a bulk crystal,” Nat. Commun. 3, 807 (2012).
[Crossref] [PubMed]

Chin, S. L.

W. Liu and S. L. Chin, “Abnormal wavelength dependence of the self-cleaning phenomenon during femtosecond-laser-pulse filamentation,” Phys. Rev. A 76(1), 013826 (2007).
[Crossref]

Couairon, A.

F. Silva, D. R. Austin, A. Thai, M. Baudisch, M. Hemmer, D. Faccio, A. Couairon, and J. Biegert, “Multi-octave supercontinuum generation from mid-infrared filamentation in a bulk crystal,” Nat. Commun. 3, 807 (2012).
[Crossref] [PubMed]

L. Sudrie, A. Couairon, M. Franco, B. Lamouroux, B. Prade, S. Tzortzakis, and A. Mysyrowicz, “Femtosecond laser-induced damage and filamentary propagation in fused silica,” Phys. Rev. Lett. 89(18), 186601 (2002).
[Crossref] [PubMed]

Crespo, H.

Dos Santos, A.

Dubietis, A.

Faccio, D.

F. Silva, D. R. Austin, A. Thai, M. Baudisch, M. Hemmer, D. Faccio, A. Couairon, and J. Biegert, “Multi-octave supercontinuum generation from mid-infrared filamentation in a bulk crystal,” Nat. Commun. 3, 807 (2012).
[Crossref] [PubMed]

Fibich, G.

Franco, M.

L. Sudrie, A. Couairon, M. Franco, B. Lamouroux, B. Prade, S. Tzortzakis, and A. Mysyrowicz, “Femtosecond laser-induced damage and filamentary propagation in fused silica,” Phys. Rev. Lett. 89(18), 186601 (2002).
[Crossref] [PubMed]

Hanamura, E.

H. Matsuki, K. Inoue, and E. Hanamura, “Multiple coherent anti-Stokes Raman scattering due to phonon grating in KNbO3 induced by crossed beams of two-color femtosecond pulses,” Phys. Rev. B 75(2), 024102 (2007).
[Crossref]

K. Inoue, J. Kato, E. Hanamura, H. Matsuki, and E. Matsubara, “Broadband coherent radiation based on peculiar multiple Raman scattering by laser-induced phonon grating in TiO2,” Phys. Rev. B 76(4), 041101 (2007).
[Crossref]

E. Matsubara, K. Inoue, and E. Hanamura, “Violation of Raman selection rules induced by two femtosecond laser pulses in KTaO3,” Phys. Rev. B 72(13), 134101 (2005).
[Crossref]

He, J. P.

J. P. He, J. Liu, and T. Kobayashi, “Tunable multicolored femtosecond pulse generation using cascaded four-wave mixing in bulk materials,” Appl. Sci. 4(3), 444–467 (2014).
[Crossref]

Hemmer, M.

F. Silva, D. R. Austin, A. Thai, M. Baudisch, M. Hemmer, D. Faccio, A. Couairon, and J. Biegert, “Multi-octave supercontinuum generation from mid-infrared filamentation in a bulk crystal,” Nat. Commun. 3, 807 (2012).
[Crossref] [PubMed]

Ilan, B.

Inoue, K.

H. Matsuki, K. Inoue, and E. Hanamura, “Multiple coherent anti-Stokes Raman scattering due to phonon grating in KNbO3 induced by crossed beams of two-color femtosecond pulses,” Phys. Rev. B 75(2), 024102 (2007).
[Crossref]

K. Inoue, J. Kato, E. Hanamura, H. Matsuki, and E. Matsubara, “Broadband coherent radiation based on peculiar multiple Raman scattering by laser-induced phonon grating in TiO2,” Phys. Rev. B 76(4), 041101 (2007).
[Crossref]

E. Matsubara, K. Inoue, and E. Hanamura, “Violation of Raman selection rules induced by two femtosecond laser pulses in KTaO3,” Phys. Rev. B 72(13), 134101 (2005).
[Crossref]

Jukna, V.

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. A 79(3), 033843 (2009).
[Crossref]

Kato, J.

K. Inoue, J. Kato, E. Hanamura, H. Matsuki, and E. Matsubara, “Broadband coherent radiation based on peculiar multiple Raman scattering by laser-induced phonon grating in TiO2,” Phys. Rev. B 76(4), 041101 (2007).
[Crossref]

Kobayashi, T.

Lamouroux, B.

L. Sudrie, A. Couairon, M. Franco, B. Lamouroux, B. Prade, S. Tzortzakis, and A. Mysyrowicz, “Femtosecond laser-induced damage and filamentary propagation in fused silica,” Phys. Rev. Lett. 89(18), 186601 (2002).
[Crossref] [PubMed]

Liu, J.

Liu, W.

W. Liu and S. L. Chin, “Abnormal wavelength dependence of the self-cleaning phenomenon during femtosecond-laser-pulse filamentation,” Phys. Rev. A 76(1), 013826 (2007).
[Crossref]

Majus, D.

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. A 79(3), 033843 (2009).
[Crossref]

Matsubara, E.

E. Matsubara, T. Sekikawa, and M. Yamashita, “Generation of ultrashort optical pulses using multiple coherent anti-Stokes Raman scattering in a crystal at room temperature,” Appl. Phys. Lett. 92(7), 071104 (2008).
[Crossref]

K. Inoue, J. Kato, E. Hanamura, H. Matsuki, and E. Matsubara, “Broadband coherent radiation based on peculiar multiple Raman scattering by laser-induced phonon grating in TiO2,” Phys. Rev. B 76(4), 041101 (2007).
[Crossref]

E. Matsubara, K. Inoue, and E. Hanamura, “Violation of Raman selection rules induced by two femtosecond laser pulses in KTaO3,” Phys. Rev. B 72(13), 134101 (2005).
[Crossref]

Matsuki, H.

H. Matsuki, K. Inoue, and E. Hanamura, “Multiple coherent anti-Stokes Raman scattering due to phonon grating in KNbO3 induced by crossed beams of two-color femtosecond pulses,” Phys. Rev. B 75(2), 024102 (2007).
[Crossref]

K. Inoue, J. Kato, E. Hanamura, H. Matsuki, and E. Matsubara, “Broadband coherent radiation based on peculiar multiple Raman scattering by laser-induced phonon grating in TiO2,” Phys. Rev. B 76(4), 041101 (2007).
[Crossref]

Mendonça, J. T.

Mysyrowicz, A.

L. Sudrie, A. Couairon, M. Franco, B. Lamouroux, B. Prade, S. Tzortzakis, and A. Mysyrowicz, “Femtosecond laser-induced damage and filamentary propagation in fused silica,” Phys. Rev. Lett. 89(18), 186601 (2002).
[Crossref] [PubMed]

Prade, B.

L. Sudrie, A. Couairon, M. Franco, B. Lamouroux, B. Prade, S. Tzortzakis, and A. Mysyrowicz, “Femtosecond laser-induced damage and filamentary propagation in fused silica,” Phys. Rev. Lett. 89(18), 186601 (2002).
[Crossref] [PubMed]

Sekikawa, T.

E. Matsubara, T. Sekikawa, and M. Yamashita, “Generation of ultrashort optical pulses using multiple coherent anti-Stokes Raman scattering in a crystal at room temperature,” Appl. Phys. Lett. 92(7), 071104 (2008).
[Crossref]

Silva, F.

F. Silva, D. R. Austin, A. Thai, M. Baudisch, M. Hemmer, D. Faccio, A. Couairon, and J. Biegert, “Multi-octave supercontinuum generation from mid-infrared filamentation in a bulk crystal,” Nat. Commun. 3, 807 (2012).
[Crossref] [PubMed]

Sokolov, A. V.

Sudrie, L.

L. Sudrie, A. Couairon, M. Franco, B. Lamouroux, B. Prade, S. Tzortzakis, and A. Mysyrowicz, “Femtosecond laser-induced damage and filamentary propagation in fused silica,” Phys. Rev. Lett. 89(18), 186601 (2002).
[Crossref] [PubMed]

Tamošauskas, G.

Thai, A.

F. Silva, D. R. Austin, A. Thai, M. Baudisch, M. Hemmer, D. Faccio, A. Couairon, and J. Biegert, “Multi-octave supercontinuum generation from mid-infrared filamentation in a bulk crystal,” Nat. Commun. 3, 807 (2012).
[Crossref] [PubMed]

Tzortzakis, S.

L. Sudrie, A. Couairon, M. Franco, B. Lamouroux, B. Prade, S. Tzortzakis, and A. Mysyrowicz, “Femtosecond laser-induced damage and filamentary propagation in fused silica,” Phys. Rev. Lett. 89(18), 186601 (2002).
[Crossref] [PubMed]

Valiulis, G.

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. A 79(3), 033843 (2009).
[Crossref]

Wang, Z.

Wu, J.

H. Zeng, J. Wu, H. Xu, and K. Wu, “Generation and weak beam control of two-dimensional multicolored arrays in a quadratic nonlinear medium,” Phys. Rev. Lett. 96(8), 083902 (2006).
[Crossref] [PubMed]

Wu, K.

H. Zeng, J. Wu, H. Xu, and K. Wu, “Generation and weak beam control of two-dimensional multicolored arrays in a quadratic nonlinear medium,” Phys. Rev. Lett. 96(8), 083902 (2006).
[Crossref] [PubMed]

Xu, H.

H. Zeng, J. Wu, H. Xu, and K. Wu, “Generation and weak beam control of two-dimensional multicolored arrays in a quadratic nonlinear medium,” Phys. Rev. Lett. 96(8), 083902 (2006).
[Crossref] [PubMed]

Yamashita, M.

E. Matsubara, T. Sekikawa, and M. Yamashita, “Generation of ultrashort optical pulses using multiple coherent anti-Stokes Raman scattering in a crystal at room temperature,” Appl. Phys. Lett. 92(7), 071104 (2008).
[Crossref]

Zeng, H.

H. Zeng, J. Wu, H. Xu, and K. Wu, “Generation and weak beam control of two-dimensional multicolored arrays in a quadratic nonlinear medium,” Phys. Rev. Lett. 96(8), 083902 (2006).
[Crossref] [PubMed]

Zhang, J.

Zhi, M.

Appl. Phys. Lett. (1)

E. Matsubara, T. Sekikawa, and M. Yamashita, “Generation of ultrashort optical pulses using multiple coherent anti-Stokes Raman scattering in a crystal at room temperature,” Appl. Phys. Lett. 92(7), 071104 (2008).
[Crossref]

Appl. Sci. (1)

J. P. He, J. Liu, and T. Kobayashi, “Tunable multicolored femtosecond pulse generation using cascaded four-wave mixing in bulk materials,” Appl. Sci. 4(3), 444–467 (2014).
[Crossref]

Nat. Commun. (1)

F. Silva, D. R. Austin, A. Thai, M. Baudisch, M. Hemmer, D. Faccio, A. Couairon, and J. Biegert, “Multi-octave supercontinuum generation from mid-infrared filamentation in a bulk crystal,” Nat. Commun. 3, 807 (2012).
[Crossref] [PubMed]

Opt. Express (3)

Opt. Lett. (6)

Phys. Rev. A (2)

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. A 79(3), 033843 (2009).
[Crossref]

W. Liu and S. L. Chin, “Abnormal wavelength dependence of the self-cleaning phenomenon during femtosecond-laser-pulse filamentation,” Phys. Rev. A 76(1), 013826 (2007).
[Crossref]

Phys. Rev. B (3)

H. Matsuki, K. Inoue, and E. Hanamura, “Multiple coherent anti-Stokes Raman scattering due to phonon grating in KNbO3 induced by crossed beams of two-color femtosecond pulses,” Phys. Rev. B 75(2), 024102 (2007).
[Crossref]

K. Inoue, J. Kato, E. Hanamura, H. Matsuki, and E. Matsubara, “Broadband coherent radiation based on peculiar multiple Raman scattering by laser-induced phonon grating in TiO2,” Phys. Rev. B 76(4), 041101 (2007).
[Crossref]

E. Matsubara, K. Inoue, and E. Hanamura, “Violation of Raman selection rules induced by two femtosecond laser pulses in KTaO3,” Phys. Rev. B 72(13), 134101 (2005).
[Crossref]

Phys. Rev. Lett. (2)

H. Zeng, J. Wu, H. Xu, and K. Wu, “Generation and weak beam control of two-dimensional multicolored arrays in a quadratic nonlinear medium,” Phys. Rev. Lett. 96(8), 083902 (2006).
[Crossref] [PubMed]

L. Sudrie, A. Couairon, M. Franco, B. Lamouroux, B. Prade, S. Tzortzakis, and A. Mysyrowicz, “Femtosecond laser-induced damage and filamentary propagation in fused silica,” Phys. Rev. Lett. 89(18), 186601 (2002).
[Crossref] [PubMed]

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Figures (3)

Fig. 1
Fig. 1 Schematics of the simulation process. (a) Two laser beams were synchronously focused into a 1mm-thick sapphire plate with a crossing angle of 1.87°. (b) The cross section of the two beams on the surface of the sapphire plate. (c) longitudinal distribution of the two crossing laser beams in the y = 0 plane.
Fig. 2
Fig. 2 Simulation result with two crossing elliptical laser beams. (a) and (b) pattern of input beam1 and beam beam2, (c) longitudinal laser intensity distribution in the y = 0 plane and transverse intensity distribution at (d) z = 0.5 mm, (e) z = 0.6 mm, (f) z = 0.7 mm, (g) z = 0.8 mm, (h) z = 0.9 mm, (i) z = 1 mm.
Fig. 3
Fig. 3 Simulatied longitudinal laser intensity distribution in the y = 0 plane and cross section with two crossing elliptical laser beams when the input laser power of beam2 is set as (a) and (d) P = 5 Pcr, (b) and (e) P = 10 Pcr, (c) and (f) P = 15 Pcr.

Equations (9)

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E 1 = A 1 e i ω 1 t + k 1 z and E 2 = A 2 e i ω 2 t + k 2 z
E = E 1 + E 2
P = ε 0 χ ( 3 ) E 3
2 i k 1 A z + Δ A = u 0 ω 1 P N L ( ω 1 )
P N L ( ω 1 ) = ε 0 χ ( 3 ) ( ω 1 , ω 1 , ω 1 , ω 1 ) [ 3 A 1 2 A 1 * ] + ε 0 χ ( 3 ) ( ω 1 , ω 2 , ω 2 , ω 1 ) [ 6 A 1 A 2 * A 1 ]
2 i k 1 A 1 z + Δ A 1 + 2 k 1 2 n 1 Δ n A 1 = 0
Δ n = n 2 I 1 + 2 n 2 I 2 α ( I 1 + I 2 ) m
2 i k 2 A 2 z + Δ A 2 + 2 k 2 2 n 2 [ n 2 I 2 + 2 n 2 I 1 α ( I 1 + I 2 ) 6 ] A 2 = 0
P c r = 3.77 λ 2 / ( 8 π n 2 n )

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