Abstract

We report on the observation of Type I third-harmonic generation induced by a train of femtosecond laser pulses in nematic liquid crystals. We find that as the average power of the train is increased, the frequency conversion process is enhanced as a consequence of the tight confinement of the pulses into a nonlocal spatial soliton.

© 2010 Optical Society of America

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References

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  1. Y. S. Kivshar and G. P. Agrawal, Optical Solitons: From Fibers to Photonic Crystals (Academic, 2003).
  2. M. Peccianti and G. Assanto, Phys. Rev. E 65, 035603(R) (2002).
    [CrossRef]
  3. M. Peccianti, C. Conti, G. Assanto, A. de Luca, and C. Umeton, Nature 432, 733 (2004).
    [CrossRef] [PubMed]
  4. G. Assanto, A. Fratalocchi, and M. Peccianti, Opt. Express 15, 5248 (2007).
    [CrossRef] [PubMed]
  5. P. G. De Gennes and J. Prost, The Physics of Liquid Crystals (Oxford U. Press, 1993).
  6. A. W. Snyder and D. J. Mitchell, Science 276, 1538 (1997).
    [CrossRef]
  7. C. Conti, M. Peccianti, and G. Assanto, Phys. Rev. Lett. 91, 073901 (2003).
    [CrossRef] [PubMed]
  8. C. Conti, M. Peccianti, and G. Assanto, Phys. Rev. Lett. 92, 113902 (2004).
    [CrossRef] [PubMed]
  9. A. Alberucci, M. Peccianti, and G. Assanto, Opt. Lett. 30, 1381 (2005).
    [CrossRef] [PubMed]
  10. M. Peccianti, A. Dyadyusha, M. Kaczmarek, and G. Assanto, Nat. Phys. 2, 737 (2006).
    [CrossRef]
  11. I. B. Burgess, M. Peccianti, G. Assanto, and R. Morandotti, Phys. Rev. Lett. 102, 203903 (2009).
    [CrossRef] [PubMed]
  12. J. Beeckman, X. Hutsebaut, C. Cambournac, and M. Haelterman, IEEE J. Quantum Electron. 41, 735 (2005).
    [CrossRef]
  13. M. Peccianti, I. B. Burgess, G. Assanto, and R. Morandotti, Opt. Express 18, 5934 (2010).
    [CrossRef] [PubMed]
  14. H. C. Gurgov and O. Cohen, Opt. Express 17, 7052 (2009).
    [CrossRef] [PubMed]
  15. S. Lan, M. Shih, G. Mizell, J. Giordmaine, Z. Chen, C. Anastassiou, J. Martin, and M. Segev, Opt. Lett. 24, 1145(1999).
    [CrossRef]
  16. J. W. Shelton and Y. R. Shen, Phys. Rev. A 5, 1867 (1972).
    [CrossRef]
  17. D. Yelin, Y. Silberberg, Y. Barad, and J. S. Patel, Phys. Rev. Lett. 82, 3046 (1999).
    [CrossRef]
  18. J. Kosugi and K. Kajikawa, Appl. Phys. Lett. 84, 5013 (2004).
    [CrossRef]
  19. M. Born and E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light, 7th ed. (Pergamon, 2002).
    [PubMed]
  20. L. S. Goldberg and J. M. Scnnur, Appl. Phys. Lett. 14, 306 (1969).
    [CrossRef]
  21. I. C. Khoo, Liquid Crystals: Physical Properties and Nonlinear Optical Phenomena (Wiley, 1995).
  22. M. Warenghem, J. F. Blach, and J. F. Henninot, J. Opt. Soc. Am. B 25, 1882 (2008).
    [CrossRef]

2010 (1)

2009 (2)

H. C. Gurgov and O. Cohen, Opt. Express 17, 7052 (2009).
[CrossRef] [PubMed]

I. B. Burgess, M. Peccianti, G. Assanto, and R. Morandotti, Phys. Rev. Lett. 102, 203903 (2009).
[CrossRef] [PubMed]

2008 (1)

2007 (1)

2006 (1)

M. Peccianti, A. Dyadyusha, M. Kaczmarek, and G. Assanto, Nat. Phys. 2, 737 (2006).
[CrossRef]

2005 (2)

J. Beeckman, X. Hutsebaut, C. Cambournac, and M. Haelterman, IEEE J. Quantum Electron. 41, 735 (2005).
[CrossRef]

A. Alberucci, M. Peccianti, and G. Assanto, Opt. Lett. 30, 1381 (2005).
[CrossRef] [PubMed]

2004 (3)

J. Kosugi and K. Kajikawa, Appl. Phys. Lett. 84, 5013 (2004).
[CrossRef]

C. Conti, M. Peccianti, and G. Assanto, Phys. Rev. Lett. 92, 113902 (2004).
[CrossRef] [PubMed]

M. Peccianti, C. Conti, G. Assanto, A. de Luca, and C. Umeton, Nature 432, 733 (2004).
[CrossRef] [PubMed]

2003 (2)

Y. S. Kivshar and G. P. Agrawal, Optical Solitons: From Fibers to Photonic Crystals (Academic, 2003).

C. Conti, M. Peccianti, and G. Assanto, Phys. Rev. Lett. 91, 073901 (2003).
[CrossRef] [PubMed]

2002 (2)

M. Peccianti and G. Assanto, Phys. Rev. E 65, 035603(R) (2002).
[CrossRef]

M. Born and E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light, 7th ed. (Pergamon, 2002).
[PubMed]

1999 (2)

1997 (1)

A. W. Snyder and D. J. Mitchell, Science 276, 1538 (1997).
[CrossRef]

1995 (1)

I. C. Khoo, Liquid Crystals: Physical Properties and Nonlinear Optical Phenomena (Wiley, 1995).

1993 (1)

P. G. De Gennes and J. Prost, The Physics of Liquid Crystals (Oxford U. Press, 1993).

1972 (1)

J. W. Shelton and Y. R. Shen, Phys. Rev. A 5, 1867 (1972).
[CrossRef]

1969 (1)

L. S. Goldberg and J. M. Scnnur, Appl. Phys. Lett. 14, 306 (1969).
[CrossRef]

Agrawal, G. P.

Y. S. Kivshar and G. P. Agrawal, Optical Solitons: From Fibers to Photonic Crystals (Academic, 2003).

Alberucci, A.

Anastassiou, C.

Assanto, G.

M. Peccianti, I. B. Burgess, G. Assanto, and R. Morandotti, Opt. Express 18, 5934 (2010).
[CrossRef] [PubMed]

I. B. Burgess, M. Peccianti, G. Assanto, and R. Morandotti, Phys. Rev. Lett. 102, 203903 (2009).
[CrossRef] [PubMed]

G. Assanto, A. Fratalocchi, and M. Peccianti, Opt. Express 15, 5248 (2007).
[CrossRef] [PubMed]

M. Peccianti, A. Dyadyusha, M. Kaczmarek, and G. Assanto, Nat. Phys. 2, 737 (2006).
[CrossRef]

A. Alberucci, M. Peccianti, and G. Assanto, Opt. Lett. 30, 1381 (2005).
[CrossRef] [PubMed]

M. Peccianti, C. Conti, G. Assanto, A. de Luca, and C. Umeton, Nature 432, 733 (2004).
[CrossRef] [PubMed]

C. Conti, M. Peccianti, and G. Assanto, Phys. Rev. Lett. 92, 113902 (2004).
[CrossRef] [PubMed]

C. Conti, M. Peccianti, and G. Assanto, Phys. Rev. Lett. 91, 073901 (2003).
[CrossRef] [PubMed]

M. Peccianti and G. Assanto, Phys. Rev. E 65, 035603(R) (2002).
[CrossRef]

Barad, Y.

D. Yelin, Y. Silberberg, Y. Barad, and J. S. Patel, Phys. Rev. Lett. 82, 3046 (1999).
[CrossRef]

Beeckman, J.

J. Beeckman, X. Hutsebaut, C. Cambournac, and M. Haelterman, IEEE J. Quantum Electron. 41, 735 (2005).
[CrossRef]

Blach, J. F.

Born, M.

M. Born and E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light, 7th ed. (Pergamon, 2002).
[PubMed]

Burgess, I. B.

M. Peccianti, I. B. Burgess, G. Assanto, and R. Morandotti, Opt. Express 18, 5934 (2010).
[CrossRef] [PubMed]

I. B. Burgess, M. Peccianti, G. Assanto, and R. Morandotti, Phys. Rev. Lett. 102, 203903 (2009).
[CrossRef] [PubMed]

Cambournac, C.

J. Beeckman, X. Hutsebaut, C. Cambournac, and M. Haelterman, IEEE J. Quantum Electron. 41, 735 (2005).
[CrossRef]

Chen, Z.

Cohen, O.

Conti, C.

M. Peccianti, C. Conti, G. Assanto, A. de Luca, and C. Umeton, Nature 432, 733 (2004).
[CrossRef] [PubMed]

C. Conti, M. Peccianti, and G. Assanto, Phys. Rev. Lett. 92, 113902 (2004).
[CrossRef] [PubMed]

C. Conti, M. Peccianti, and G. Assanto, Phys. Rev. Lett. 91, 073901 (2003).
[CrossRef] [PubMed]

De Gennes, P. G.

P. G. De Gennes and J. Prost, The Physics of Liquid Crystals (Oxford U. Press, 1993).

de Luca, A.

M. Peccianti, C. Conti, G. Assanto, A. de Luca, and C. Umeton, Nature 432, 733 (2004).
[CrossRef] [PubMed]

Dyadyusha, A.

M. Peccianti, A. Dyadyusha, M. Kaczmarek, and G. Assanto, Nat. Phys. 2, 737 (2006).
[CrossRef]

Fratalocchi, A.

Giordmaine, J.

Goldberg, L. S.

L. S. Goldberg and J. M. Scnnur, Appl. Phys. Lett. 14, 306 (1969).
[CrossRef]

Gurgov, H. C.

Haelterman, M.

J. Beeckman, X. Hutsebaut, C. Cambournac, and M. Haelterman, IEEE J. Quantum Electron. 41, 735 (2005).
[CrossRef]

Henninot, J. F.

Hutsebaut, X.

J. Beeckman, X. Hutsebaut, C. Cambournac, and M. Haelterman, IEEE J. Quantum Electron. 41, 735 (2005).
[CrossRef]

Kaczmarek, M.

M. Peccianti, A. Dyadyusha, M. Kaczmarek, and G. Assanto, Nat. Phys. 2, 737 (2006).
[CrossRef]

Kajikawa, K.

J. Kosugi and K. Kajikawa, Appl. Phys. Lett. 84, 5013 (2004).
[CrossRef]

Khoo, I. C.

I. C. Khoo, Liquid Crystals: Physical Properties and Nonlinear Optical Phenomena (Wiley, 1995).

Kivshar, Y. S.

Y. S. Kivshar and G. P. Agrawal, Optical Solitons: From Fibers to Photonic Crystals (Academic, 2003).

Kosugi, J.

J. Kosugi and K. Kajikawa, Appl. Phys. Lett. 84, 5013 (2004).
[CrossRef]

Lan, S.

Martin, J.

Mitchell, D. J.

A. W. Snyder and D. J. Mitchell, Science 276, 1538 (1997).
[CrossRef]

Mizell, G.

Morandotti, R.

M. Peccianti, I. B. Burgess, G. Assanto, and R. Morandotti, Opt. Express 18, 5934 (2010).
[CrossRef] [PubMed]

I. B. Burgess, M. Peccianti, G. Assanto, and R. Morandotti, Phys. Rev. Lett. 102, 203903 (2009).
[CrossRef] [PubMed]

Patel, J. S.

D. Yelin, Y. Silberberg, Y. Barad, and J. S. Patel, Phys. Rev. Lett. 82, 3046 (1999).
[CrossRef]

Peccianti, M.

M. Peccianti, I. B. Burgess, G. Assanto, and R. Morandotti, Opt. Express 18, 5934 (2010).
[CrossRef] [PubMed]

I. B. Burgess, M. Peccianti, G. Assanto, and R. Morandotti, Phys. Rev. Lett. 102, 203903 (2009).
[CrossRef] [PubMed]

G. Assanto, A. Fratalocchi, and M. Peccianti, Opt. Express 15, 5248 (2007).
[CrossRef] [PubMed]

M. Peccianti, A. Dyadyusha, M. Kaczmarek, and G. Assanto, Nat. Phys. 2, 737 (2006).
[CrossRef]

A. Alberucci, M. Peccianti, and G. Assanto, Opt. Lett. 30, 1381 (2005).
[CrossRef] [PubMed]

C. Conti, M. Peccianti, and G. Assanto, Phys. Rev. Lett. 92, 113902 (2004).
[CrossRef] [PubMed]

M. Peccianti, C. Conti, G. Assanto, A. de Luca, and C. Umeton, Nature 432, 733 (2004).
[CrossRef] [PubMed]

C. Conti, M. Peccianti, and G. Assanto, Phys. Rev. Lett. 91, 073901 (2003).
[CrossRef] [PubMed]

M. Peccianti and G. Assanto, Phys. Rev. E 65, 035603(R) (2002).
[CrossRef]

Prost, J.

P. G. De Gennes and J. Prost, The Physics of Liquid Crystals (Oxford U. Press, 1993).

Scnnur, J. M.

L. S. Goldberg and J. M. Scnnur, Appl. Phys. Lett. 14, 306 (1969).
[CrossRef]

Segev, M.

Shelton, J. W.

J. W. Shelton and Y. R. Shen, Phys. Rev. A 5, 1867 (1972).
[CrossRef]

Shen, Y. R.

J. W. Shelton and Y. R. Shen, Phys. Rev. A 5, 1867 (1972).
[CrossRef]

Shih, M.

Silberberg, Y.

D. Yelin, Y. Silberberg, Y. Barad, and J. S. Patel, Phys. Rev. Lett. 82, 3046 (1999).
[CrossRef]

Snyder, A. W.

A. W. Snyder and D. J. Mitchell, Science 276, 1538 (1997).
[CrossRef]

Umeton, C.

M. Peccianti, C. Conti, G. Assanto, A. de Luca, and C. Umeton, Nature 432, 733 (2004).
[CrossRef] [PubMed]

Warenghem, M.

Wolf, E.

M. Born and E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light, 7th ed. (Pergamon, 2002).
[PubMed]

Yelin, D.

D. Yelin, Y. Silberberg, Y. Barad, and J. S. Patel, Phys. Rev. Lett. 82, 3046 (1999).
[CrossRef]

Appl. Phys. Lett. (2)

J. Kosugi and K. Kajikawa, Appl. Phys. Lett. 84, 5013 (2004).
[CrossRef]

L. S. Goldberg and J. M. Scnnur, Appl. Phys. Lett. 14, 306 (1969).
[CrossRef]

IEEE J. Quantum Electron. (1)

J. Beeckman, X. Hutsebaut, C. Cambournac, and M. Haelterman, IEEE J. Quantum Electron. 41, 735 (2005).
[CrossRef]

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

Nat. Phys. (1)

M. Peccianti, A. Dyadyusha, M. Kaczmarek, and G. Assanto, Nat. Phys. 2, 737 (2006).
[CrossRef]

Nature (1)

M. Peccianti, C. Conti, G. Assanto, A. de Luca, and C. Umeton, Nature 432, 733 (2004).
[CrossRef] [PubMed]

Opt. Express (3)

Opt. Lett. (2)

Phys. Rev. A (1)

J. W. Shelton and Y. R. Shen, Phys. Rev. A 5, 1867 (1972).
[CrossRef]

Phys. Rev. E (1)

M. Peccianti and G. Assanto, Phys. Rev. E 65, 035603(R) (2002).
[CrossRef]

Phys. Rev. Lett. (4)

I. B. Burgess, M. Peccianti, G. Assanto, and R. Morandotti, Phys. Rev. Lett. 102, 203903 (2009).
[CrossRef] [PubMed]

C. Conti, M. Peccianti, and G. Assanto, Phys. Rev. Lett. 91, 073901 (2003).
[CrossRef] [PubMed]

C. Conti, M. Peccianti, and G. Assanto, Phys. Rev. Lett. 92, 113902 (2004).
[CrossRef] [PubMed]

D. Yelin, Y. Silberberg, Y. Barad, and J. S. Patel, Phys. Rev. Lett. 82, 3046 (1999).
[CrossRef]

Science (1)

A. W. Snyder and D. J. Mitchell, Science 276, 1538 (1997).
[CrossRef]

Other (4)

M. Born and E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light, 7th ed. (Pergamon, 2002).
[PubMed]

I. C. Khoo, Liquid Crystals: Physical Properties and Nonlinear Optical Phenomena (Wiley, 1995).

Y. S. Kivshar and G. P. Agrawal, Optical Solitons: From Fibers to Photonic Crystals (Academic, 2003).

P. G. De Gennes and J. Prost, The Physics of Liquid Crystals (Oxford U. Press, 1993).

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Figures (5)

Fig. 1
Fig. 1

Sketch of the experimental setup.

Fig. 2
Fig. 2

(a) Sketch of the propagation geometry, emphasizing the walk-off between ordinary (o) and extraordinary (e) Poynting vectors. (b) Photograph of a red probe colaunched in an e-polarized spatial soliton excited at 1550 nm . The mixed polarization of the probe excites both a confined signal walking off with the soliton and a diffracting o wave. (c) Calculated phase mismatch for Type I ( e e e e ) and Type II ( e o e o ) THG versus angle θ.

Fig. 3
Fig. 3

TH evolution in the y z plane in the case of (a) no cw pump and (b) for a P = 6 mW cw pump at 1550 nm colaunched with the femtosecond pulse train at 1500 nm .

Fig. 4
Fig. 4

TH intensity distribution in pseudo colors at the cell output ( x y ) for cw pump powers of (a) 2, (b) 4, (c) 7, and (d) 9 mW , respectively. At low power (a) only the o-polarized THG is visible. As the soliton is formed (b)–(d), a guided e TH becomes apparent within the spatial soliton (LHS). The color scaling and the peak normalization emphasize the high intensity of the THG within the soliton profile, with the image of the o component fading away as the power is increased from (a) to (d).

Fig. 5
Fig. 5

Intensity distribution of the TH at the cell output for cw pump powers of (a) 2, (b) 4, (c) 5, and (d) 7 mW , respectively. A sideways shift of the o TH is clearly visible.

Equations (5)

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δ = arctan [ ( n | | 2 n 2 ) sin ( θ ) cos ( θ ) n 2 + ( n | | 2 n 2 ) cos ( θ ) 2 ] ,
P TH e = χ 2222 E FF e E FF e E FF e + 3 χ 1122 E FF o E FF o E FF e ,
P TH o = χ 1111 E FF o E FF o E FF o + 3 χ 2211 E FF e E FF e E FF o .
Δ k e e e e = 3 k FF e k TH e = [ n e ( λ FF , θ ) n e ( λ FF / 3 , θ ) ] 6 π / λ FF ,
Δ k e o e o = 2 k FF e + k FF o k TH o = [ 2 n e ( λ FF , θ ) + n o ( λ FF ) 3 n o ( λ FF / 3 ) ] 2 π / λ FF .

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