Abstract

We propose a simple technique based on electric field induced second harmonic (EFISH) generation of femtosecond pulses to measure the third order susceptibility χ (3)(2ω,0,ω,ω) in glasses. First we present the principle of the method, then we validate our experimental set-up and develop unexpected aspects of EFISH technique. Finally, we give a numerical value of the third order susceptibility in various glasses and discuss these results.

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References

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  1. G. R. Meredith, B. Buchalter, C. Hanzlik, "Third order susceptibility determination by third harmonic generation," J. Chem. Phys. 78, 1533 (1983)
    [CrossRef]
  2. Kalpoulos, G. A. Kenney Wallace, P. M. Kroger, E. Quitevis, S. C. Wallace, Picosecond Phenomena III, (Springer Verlag, Berlin, West Germany, 1982) pp. 221-7.
    [CrossRef]
  3. M. O. Martin, L. Canioni, L. Sarger, "Measurements of complex third-order optical susceptibility in a collinear pump-probe experiment," Opt. Lett. 23 1874-76 (1998).
    [CrossRef]
  4. M. Sheik-Bahae, A. A. Said, T.H. Wei, D.J. Hagan, E. W. Van Stryland, "Sensitive measurement of optical non-linearities using a single beam," IEEE J. Q. E. QE-26, 760 (1990).
    [CrossRef]
  5. P. Langot, S. Montant, E. Freysz, "Measurement of non-instantaneous contribution to x (3) in different liquids using femtosecond chirped pulses," Opt. Commmun. 176, 459-472 (2000).
    [CrossRef]
  6. B.F. Levine, C. G. Bethea, "Second and third order hyperpolarizabilities of organic molecules," J. Chem. Phys. 63, 2666 (1975).
    [CrossRef]
  7. R.A. Myers, N. Mukherjee, S.R.J. Brueck, "Large second-order nonlinearity in poled fused silica," Opt. Lett. 16, 1732 (1991).
    [CrossRef] [PubMed]
  8. P. N. Butcher, D. Cotter, The Elements of Nonlinear Optics, (Cambridge University Press, 1990).
    [CrossRef]
  9. P. D. Maker, R. W. Terhune, M. Nisenoff, C.M. Savage, "Effects of dispersion and focusing on the production of optical harmonics," Phys. Rev. Lett. 8, 21 (1962).
    [CrossRef]
  10. S. A. Akhmanov, V. A. Vysloukh, A. S. Chirkin, Optics of Femtosecond Laser Pulses, (American Institute of Physics, 1992), Chap. 3.
  11. S. Montant, "Etude des non-lin�arit�s d'ordre deux et trois de verres," thesis Univ. Bordeaux 1 (1999).
  12. H. Guillet de Chatellus, S. Montant, E. Freysz, "Evidence and dynamics of optical poling in lead silicates," Proceedings of Bragg Gratings, Photosensitivity, and Poling in Glass Waveguides (Optical Society of America, Washington, D.C., 2001).

Other

G. R. Meredith, B. Buchalter, C. Hanzlik, "Third order susceptibility determination by third harmonic generation," J. Chem. Phys. 78, 1533 (1983)
[CrossRef]

Kalpoulos, G. A. Kenney Wallace, P. M. Kroger, E. Quitevis, S. C. Wallace, Picosecond Phenomena III, (Springer Verlag, Berlin, West Germany, 1982) pp. 221-7.
[CrossRef]

M. O. Martin, L. Canioni, L. Sarger, "Measurements of complex third-order optical susceptibility in a collinear pump-probe experiment," Opt. Lett. 23 1874-76 (1998).
[CrossRef]

M. Sheik-Bahae, A. A. Said, T.H. Wei, D.J. Hagan, E. W. Van Stryland, "Sensitive measurement of optical non-linearities using a single beam," IEEE J. Q. E. QE-26, 760 (1990).
[CrossRef]

P. Langot, S. Montant, E. Freysz, "Measurement of non-instantaneous contribution to x (3) in different liquids using femtosecond chirped pulses," Opt. Commmun. 176, 459-472 (2000).
[CrossRef]

B.F. Levine, C. G. Bethea, "Second and third order hyperpolarizabilities of organic molecules," J. Chem. Phys. 63, 2666 (1975).
[CrossRef]

R.A. Myers, N. Mukherjee, S.R.J. Brueck, "Large second-order nonlinearity in poled fused silica," Opt. Lett. 16, 1732 (1991).
[CrossRef] [PubMed]

P. N. Butcher, D. Cotter, The Elements of Nonlinear Optics, (Cambridge University Press, 1990).
[CrossRef]

P. D. Maker, R. W. Terhune, M. Nisenoff, C.M. Savage, "Effects of dispersion and focusing on the production of optical harmonics," Phys. Rev. Lett. 8, 21 (1962).
[CrossRef]

S. A. Akhmanov, V. A. Vysloukh, A. S. Chirkin, Optics of Femtosecond Laser Pulses, (American Institute of Physics, 1992), Chap. 3.

S. Montant, "Etude des non-lin�arit�s d'ordre deux et trois de verres," thesis Univ. Bordeaux 1 (1999).

H. Guillet de Chatellus, S. Montant, E. Freysz, "Evidence and dynamics of optical poling in lead silicates," Proceedings of Bragg Gratings, Photosensitivity, and Poling in Glass Waveguides (Optical Society of America, Washington, D.C., 2001).

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Figures (8)

Fig. 1.
Fig. 1.

Sketch of the EFISH experiment in a glass sample

Fig. 2.
Fig. 2.

Evolution of the EFISH signal Ii2ω versus the applied voltage

Fig. 3.
Fig. 3.

Spectral density of the EFISH signal Ii2ω(Ω)

Fig. 4.
Fig. 4.

. Profile of χ (2) (z) for electrodes covering the whole surface sample

Fig. 4.
Fig. 4.

. Profile of |χ~eff(2)(q)|2 and I(Ω) for χ(2)(z) presented in Fig. 4a and a gaussian s(Ω).

Fig. 5.
Fig. 5.

. Profile of χ (2) (z) for electrodes partly covering the surface sample

Fig. 5.
Fig. 5.

. Profile of |χ~eff(2)(q)|2 and I(Ω) for the χ(2)(z) presented in Fig. 5a and a gaussian s(Ω).

Fig. 6.
Fig. 6.

a) Configuration of the electrodes deposited on the wedged glass sample. b) EFISH I(Ω) signal recorded at different positions sketched in the wedged sample.

Tables (1)

Tables Icon

Table 1. Values of χ (3) and of the absorption coefficient at 400 nm for different glasses

Equations (7)

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P i 2 ω ( z ) χ iyjk ( 3 ) ( 2 ω , 0 , ω , ω ) E y 0 E j ω E k ω e i Δ k z
I i 2 ω 0 L Z χ iyjk ( 3 ) E y 0 E j ω E k ω e i Δ k z dz 2 [ χ iyjk ( 3 ) . E y 0 ] 2 L z 2 ( I ω ) 2 sin c 2 ( Δ k L z 2 )
I i 2 ω ( Ω ) 0 L Z χ iyjk ( 3 ) . E y 0 [ E j ω ( Ω Ω ) E k ω ( Ω ) d Ω ] e i Δ k ( Ω ) z dz 2
I i 2 ω ( Ω ) χ iyjk ( 3 ) . E y 0 2 L z 2 sin c 2 ( 1 2 ( Δ k 0 + Δ u 1 Ω ) L z ) s 2 ω ( Ω )
I i 2 ω [ χ iyjk ( 3 ) . E y 0 ] 2 2 ( Δ k 0 ) 2 s 2 ω ( Ω ) d Ω
I 2 ω ( Ω ) 0 L Z χ eff ( 2 ) ( z ) . e i Δ k ( Ω ) z dz 2 s 2 ω ( Ω )
I 2 ω ( Ω ) χ ˜ eff ( 2 ) ( Δ k ( Ω ) ) 2 s 2 ω ( Ω ) = χ ˜ eff ( 2 ) ( Δ k 0 + Δ u 1 Ω ) 2 s 2 ω ( Ω )

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