Abstract

By using a finite-difference time-domain method, we analyze self-focusing effects in a nonlinear Kerr film and demonstrate that the near-field intensity distribution at the film surface can reach a stable state at only a few hundred femtoseconds after the incidence of the beam. Our simulations also show that the formation of multiple filamentations in the near-field is quite sensitive to the thickness of the nonlinear film and the power of the laser beam, strongly indicating the existence of nonlinear Fabry-Perot interference effects of the linearly polarized incident light.

© 2004 Optical Society of America

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  1. R. Y. Chiao, E. Garmire, and C. H. Townes, “Self-trapping of optical beams,” Phys. Rev. Lett. 13, 479 (1964).
    [Crossref]
  2. V. I. Talanov, “Self-focusing of waves in nonlinear media,” JETP Lett. 2, 138 (1965).
  3. J. A. Fleck and P. L. Kelley, “Temporal aspect of the self-focusing of optical beams,” Appl. Phys. Lett. 15, 313 (1969).
    [Crossref]
  4. M. D. Feit and J. A. Fleck, “Beam nonparaxiality, filament formation, and beam breakup in the self-focusing of optical beams,” J. Opt. Soc. Am. B 5, 633 (1988).
    [Crossref]
  5. K. D. Moll, A. L. Gaeta, and G. Fibich, “Self-similar optical wave collapse: observation of the townes profile,” Phys. Rev. Lett. 90, 203902-1 (2003).
    [Crossref]
  6. G. Fibich and A. L. Gaeta, “Critical power for self-focusing in bulk media and in hollow waveguides,” Opt. Lett. 25, 335 (2000).
    [Crossref]
  7. G. Fibich and B. Ilan, “Multiple filamentation of circularly polarized beams,” Phys. Rev. Lett. 89, 013901-1 (2002).
    [Crossref]
  8. G. Fibich and B. Ilan, “Vectorial and random effects in self-focusing and in multiple filamentation,” PHYSICA D 157, 112 (2001).
    [Crossref]
  9. G. Fibich, W. Ren, and X.-P. Wang, “Numerical simulations of self-focusing of ultrafast laser pulses.” Phys. Rev. E 67, 056603 (2003).
    [Crossref]
  10. R. M. Joseph and A. Taflove, “Spatial soliton deflection mechanism indicated by FDTD Maxwell’s equations modeling,” IEEE Photon. Tech. Lett. 6, 1251 (1994).
    [Crossref]
  11. R. W. Ziolkowski and J. B. Judkins, “Full-wave vector Maxwell equation modeling of the self-focusing of ultrashort optical pulses in a nonlinear Kerr medium exhibiting a finite response time,” J. Opt. Soc. Am. B 10, 186 (1993).
    [Crossref]
  12. K. B. Song, J. Lee, J. H. Kim, K. Cho, and S. K. Kim, “Direct observation of self-focusing with subdiffraction limited resolution using near-field scanning optical microscope,” Phy. Rev. Lett. 85, 3842 (2000)
    [Crossref]
  13. Y. Choi, J. H. Park, M. R. Kim, W. Jhe, and B. K. Rhee, “Direct observation of self-focusing near the diffraction limit in polycrystalline silicon film,” Appl. Phys. Lett. 78, 856 (2001)
    [Crossref]
  14. J. Tominaga, T. Nakano, and N. Atoda, “An approach for recording and readout beyond the diffraction limit with an Sb thin film,” Appl. Phys. Lett. 73, 2078 (1998).
    [Crossref]
  15. K. S. Yee, “Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media,” IEEE Trans. Antennas Propagat. 14, 302 (1966).
    [Crossref]

2003 (2)

K. D. Moll, A. L. Gaeta, and G. Fibich, “Self-similar optical wave collapse: observation of the townes profile,” Phys. Rev. Lett. 90, 203902-1 (2003).
[Crossref]

G. Fibich, W. Ren, and X.-P. Wang, “Numerical simulations of self-focusing of ultrafast laser pulses.” Phys. Rev. E 67, 056603 (2003).
[Crossref]

2002 (1)

G. Fibich and B. Ilan, “Multiple filamentation of circularly polarized beams,” Phys. Rev. Lett. 89, 013901-1 (2002).
[Crossref]

2001 (2)

G. Fibich and B. Ilan, “Vectorial and random effects in self-focusing and in multiple filamentation,” PHYSICA D 157, 112 (2001).
[Crossref]

Y. Choi, J. H. Park, M. R. Kim, W. Jhe, and B. K. Rhee, “Direct observation of self-focusing near the diffraction limit in polycrystalline silicon film,” Appl. Phys. Lett. 78, 856 (2001)
[Crossref]

2000 (2)

K. B. Song, J. Lee, J. H. Kim, K. Cho, and S. K. Kim, “Direct observation of self-focusing with subdiffraction limited resolution using near-field scanning optical microscope,” Phy. Rev. Lett. 85, 3842 (2000)
[Crossref]

G. Fibich and A. L. Gaeta, “Critical power for self-focusing in bulk media and in hollow waveguides,” Opt. Lett. 25, 335 (2000).
[Crossref]

1998 (1)

J. Tominaga, T. Nakano, and N. Atoda, “An approach for recording and readout beyond the diffraction limit with an Sb thin film,” Appl. Phys. Lett. 73, 2078 (1998).
[Crossref]

1994 (1)

R. M. Joseph and A. Taflove, “Spatial soliton deflection mechanism indicated by FDTD Maxwell’s equations modeling,” IEEE Photon. Tech. Lett. 6, 1251 (1994).
[Crossref]

1993 (1)

1988 (1)

1969 (1)

J. A. Fleck and P. L. Kelley, “Temporal aspect of the self-focusing of optical beams,” Appl. Phys. Lett. 15, 313 (1969).
[Crossref]

1966 (1)

K. S. Yee, “Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media,” IEEE Trans. Antennas Propagat. 14, 302 (1966).
[Crossref]

1965 (1)

V. I. Talanov, “Self-focusing of waves in nonlinear media,” JETP Lett. 2, 138 (1965).

1964 (1)

R. Y. Chiao, E. Garmire, and C. H. Townes, “Self-trapping of optical beams,” Phys. Rev. Lett. 13, 479 (1964).
[Crossref]

Atoda, N.

J. Tominaga, T. Nakano, and N. Atoda, “An approach for recording and readout beyond the diffraction limit with an Sb thin film,” Appl. Phys. Lett. 73, 2078 (1998).
[Crossref]

Chiao, R. Y.

R. Y. Chiao, E. Garmire, and C. H. Townes, “Self-trapping of optical beams,” Phys. Rev. Lett. 13, 479 (1964).
[Crossref]

Cho, K.

K. B. Song, J. Lee, J. H. Kim, K. Cho, and S. K. Kim, “Direct observation of self-focusing with subdiffraction limited resolution using near-field scanning optical microscope,” Phy. Rev. Lett. 85, 3842 (2000)
[Crossref]

Choi, Y.

Y. Choi, J. H. Park, M. R. Kim, W. Jhe, and B. K. Rhee, “Direct observation of self-focusing near the diffraction limit in polycrystalline silicon film,” Appl. Phys. Lett. 78, 856 (2001)
[Crossref]

Feit, M. D.

Fibich, G.

K. D. Moll, A. L. Gaeta, and G. Fibich, “Self-similar optical wave collapse: observation of the townes profile,” Phys. Rev. Lett. 90, 203902-1 (2003).
[Crossref]

G. Fibich, W. Ren, and X.-P. Wang, “Numerical simulations of self-focusing of ultrafast laser pulses.” Phys. Rev. E 67, 056603 (2003).
[Crossref]

G. Fibich and B. Ilan, “Multiple filamentation of circularly polarized beams,” Phys. Rev. Lett. 89, 013901-1 (2002).
[Crossref]

G. Fibich and B. Ilan, “Vectorial and random effects in self-focusing and in multiple filamentation,” PHYSICA D 157, 112 (2001).
[Crossref]

G. Fibich and A. L. Gaeta, “Critical power for self-focusing in bulk media and in hollow waveguides,” Opt. Lett. 25, 335 (2000).
[Crossref]

Fleck, J. A.

M. D. Feit and J. A. Fleck, “Beam nonparaxiality, filament formation, and beam breakup in the self-focusing of optical beams,” J. Opt. Soc. Am. B 5, 633 (1988).
[Crossref]

J. A. Fleck and P. L. Kelley, “Temporal aspect of the self-focusing of optical beams,” Appl. Phys. Lett. 15, 313 (1969).
[Crossref]

Gaeta, A. L.

K. D. Moll, A. L. Gaeta, and G. Fibich, “Self-similar optical wave collapse: observation of the townes profile,” Phys. Rev. Lett. 90, 203902-1 (2003).
[Crossref]

G. Fibich and A. L. Gaeta, “Critical power for self-focusing in bulk media and in hollow waveguides,” Opt. Lett. 25, 335 (2000).
[Crossref]

Garmire, E.

R. Y. Chiao, E. Garmire, and C. H. Townes, “Self-trapping of optical beams,” Phys. Rev. Lett. 13, 479 (1964).
[Crossref]

Ilan, B.

G. Fibich and B. Ilan, “Multiple filamentation of circularly polarized beams,” Phys. Rev. Lett. 89, 013901-1 (2002).
[Crossref]

G. Fibich and B. Ilan, “Vectorial and random effects in self-focusing and in multiple filamentation,” PHYSICA D 157, 112 (2001).
[Crossref]

Jhe, W.

Y. Choi, J. H. Park, M. R. Kim, W. Jhe, and B. K. Rhee, “Direct observation of self-focusing near the diffraction limit in polycrystalline silicon film,” Appl. Phys. Lett. 78, 856 (2001)
[Crossref]

Joseph, R. M.

R. M. Joseph and A. Taflove, “Spatial soliton deflection mechanism indicated by FDTD Maxwell’s equations modeling,” IEEE Photon. Tech. Lett. 6, 1251 (1994).
[Crossref]

Judkins, J. B.

Kelley, P. L.

J. A. Fleck and P. L. Kelley, “Temporal aspect of the self-focusing of optical beams,” Appl. Phys. Lett. 15, 313 (1969).
[Crossref]

Kim, J. H.

K. B. Song, J. Lee, J. H. Kim, K. Cho, and S. K. Kim, “Direct observation of self-focusing with subdiffraction limited resolution using near-field scanning optical microscope,” Phy. Rev. Lett. 85, 3842 (2000)
[Crossref]

Kim, M. R.

Y. Choi, J. H. Park, M. R. Kim, W. Jhe, and B. K. Rhee, “Direct observation of self-focusing near the diffraction limit in polycrystalline silicon film,” Appl. Phys. Lett. 78, 856 (2001)
[Crossref]

Kim, S. K.

K. B. Song, J. Lee, J. H. Kim, K. Cho, and S. K. Kim, “Direct observation of self-focusing with subdiffraction limited resolution using near-field scanning optical microscope,” Phy. Rev. Lett. 85, 3842 (2000)
[Crossref]

Lee, J.

K. B. Song, J. Lee, J. H. Kim, K. Cho, and S. K. Kim, “Direct observation of self-focusing with subdiffraction limited resolution using near-field scanning optical microscope,” Phy. Rev. Lett. 85, 3842 (2000)
[Crossref]

Moll, K. D.

K. D. Moll, A. L. Gaeta, and G. Fibich, “Self-similar optical wave collapse: observation of the townes profile,” Phys. Rev. Lett. 90, 203902-1 (2003).
[Crossref]

Nakano, T.

J. Tominaga, T. Nakano, and N. Atoda, “An approach for recording and readout beyond the diffraction limit with an Sb thin film,” Appl. Phys. Lett. 73, 2078 (1998).
[Crossref]

Park, J. H.

Y. Choi, J. H. Park, M. R. Kim, W. Jhe, and B. K. Rhee, “Direct observation of self-focusing near the diffraction limit in polycrystalline silicon film,” Appl. Phys. Lett. 78, 856 (2001)
[Crossref]

Ren, W.

G. Fibich, W. Ren, and X.-P. Wang, “Numerical simulations of self-focusing of ultrafast laser pulses.” Phys. Rev. E 67, 056603 (2003).
[Crossref]

Rhee, B. K.

Y. Choi, J. H. Park, M. R. Kim, W. Jhe, and B. K. Rhee, “Direct observation of self-focusing near the diffraction limit in polycrystalline silicon film,” Appl. Phys. Lett. 78, 856 (2001)
[Crossref]

Song, K. B.

K. B. Song, J. Lee, J. H. Kim, K. Cho, and S. K. Kim, “Direct observation of self-focusing with subdiffraction limited resolution using near-field scanning optical microscope,” Phy. Rev. Lett. 85, 3842 (2000)
[Crossref]

Taflove, A.

R. M. Joseph and A. Taflove, “Spatial soliton deflection mechanism indicated by FDTD Maxwell’s equations modeling,” IEEE Photon. Tech. Lett. 6, 1251 (1994).
[Crossref]

Talanov, V. I.

V. I. Talanov, “Self-focusing of waves in nonlinear media,” JETP Lett. 2, 138 (1965).

Tominaga, J.

J. Tominaga, T. Nakano, and N. Atoda, “An approach for recording and readout beyond the diffraction limit with an Sb thin film,” Appl. Phys. Lett. 73, 2078 (1998).
[Crossref]

Townes, C. H.

R. Y. Chiao, E. Garmire, and C. H. Townes, “Self-trapping of optical beams,” Phys. Rev. Lett. 13, 479 (1964).
[Crossref]

Wang, X.-P.

G. Fibich, W. Ren, and X.-P. Wang, “Numerical simulations of self-focusing of ultrafast laser pulses.” Phys. Rev. E 67, 056603 (2003).
[Crossref]

Yee, K. S.

K. S. Yee, “Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media,” IEEE Trans. Antennas Propagat. 14, 302 (1966).
[Crossref]

Ziolkowski, R. W.

Appl. Phys. Lett. (3)

J. A. Fleck and P. L. Kelley, “Temporal aspect of the self-focusing of optical beams,” Appl. Phys. Lett. 15, 313 (1969).
[Crossref]

Y. Choi, J. H. Park, M. R. Kim, W. Jhe, and B. K. Rhee, “Direct observation of self-focusing near the diffraction limit in polycrystalline silicon film,” Appl. Phys. Lett. 78, 856 (2001)
[Crossref]

J. Tominaga, T. Nakano, and N. Atoda, “An approach for recording and readout beyond the diffraction limit with an Sb thin film,” Appl. Phys. Lett. 73, 2078 (1998).
[Crossref]

IEEE Photon. Tech. Lett. (1)

R. M. Joseph and A. Taflove, “Spatial soliton deflection mechanism indicated by FDTD Maxwell’s equations modeling,” IEEE Photon. Tech. Lett. 6, 1251 (1994).
[Crossref]

IEEE Trans. Antennas Propagat. (1)

K. S. Yee, “Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media,” IEEE Trans. Antennas Propagat. 14, 302 (1966).
[Crossref]

J. Opt. Soc. Am. B (2)

JETP Lett. (1)

V. I. Talanov, “Self-focusing of waves in nonlinear media,” JETP Lett. 2, 138 (1965).

Opt. Lett. (1)

Phy. Rev. Lett. (1)

K. B. Song, J. Lee, J. H. Kim, K. Cho, and S. K. Kim, “Direct observation of self-focusing with subdiffraction limited resolution using near-field scanning optical microscope,” Phy. Rev. Lett. 85, 3842 (2000)
[Crossref]

Phys. Rev. E (1)

G. Fibich, W. Ren, and X.-P. Wang, “Numerical simulations of self-focusing of ultrafast laser pulses.” Phys. Rev. E 67, 056603 (2003).
[Crossref]

Phys. Rev. Lett. (3)

G. Fibich and B. Ilan, “Multiple filamentation of circularly polarized beams,” Phys. Rev. Lett. 89, 013901-1 (2002).
[Crossref]

R. Y. Chiao, E. Garmire, and C. H. Townes, “Self-trapping of optical beams,” Phys. Rev. Lett. 13, 479 (1964).
[Crossref]

K. D. Moll, A. L. Gaeta, and G. Fibich, “Self-similar optical wave collapse: observation of the townes profile,” Phys. Rev. Lett. 90, 203902-1 (2003).
[Crossref]

PHYSICA D (1)

G. Fibich and B. Ilan, “Vectorial and random effects in self-focusing and in multiple filamentation,” PHYSICA D 157, 112 (2001).
[Crossref]

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Figures (4)

Fig. 1.
Fig. 1.

Temporal dynamics of intensity distribution at 336nm-thick film surface obtained by 3D FDTD method.

Fig. 2.
Fig. 2.

Intensity distribution in a nonlinear Kerr bulk medium after propagating 336nm from the surface.

Fig. 3.
Fig. 3.

Near-field intensity distribution of film with various thickness obtained by 3D FDTD method.

Fig. 4.
Fig. 4.

Near-field intensity distribution of a nonlinear Kerr film for various beam powers obtained by 3D FDTD method.

Equations (3)

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P NL ( x , t ) = ε 0 χ ( 3 ) ( t τ ) E ( x , τ ) 2 E ( x , t ) d τ
P NL ( x , t ) ε 0 χ 0 ( 3 ) E ( t ) 2 E ( t )
E ( t ) = D ( t ) ε 0 ( 1 + χ ( 1 ) + χ 0 ( 3 ) E ( t ) 2 )

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